Dynamics doi: 10.3390/dynamics6040051

Authors: Jelena Milojković Miljana Milić Slobodan Bojanić Octavio Nieto Vančo Litovski

A conceptually new circuit macromodeling of a DC-to-DC converter will be introduced. The motivation comes from the need for the simulation of converters in an electrical environment exhibiting very slow response. By introducing the circuit macromodel of the DC-to-DC converter, the switching is overcome and much larger simulation time steps—and, consequently, much shorter elapsed computer times—become possible. A procedure for the extraction of macromodel parameters is proposed in conjunction with its topology. The effectiveness of the model was tested on a system consisting of a cascade connection of a DC-to-DC converter and a battery charger.

Dynamics doi: 10.3390/dynamics6040050

Authors: Lakhveer Kaur Mohamed E. M. Alngar Houria Triki Anjan Biswas

Optical solitary waves in a cascaded quadratic medium are investigated using the Lie symmetry analysis and a generalized G′/G-expansion approach. The governing nonlinear evolution equation incorporates group-velocity dispersion, self-phase modulation, and two nonlinear derivative terms representing self-steepening contributions. Its real-valued formulation admits a four-dimensional non-Abelian symmetry algebra comprising phase rotation, translations, and a combined scaling and phase transformation. A traveling-wave reduction establishes compatibility conditions linking the wave velocity and self-steepening coefficients and yields a second-order nonlinear ordinary differential equation. The generalized expansion produces two parameter branches of exact hyperbolic wave solutions, including combo-bright-singular, dark, and singular structures subject to explicit parameter and denominator conditions. The analytical solution families are further examined through direct residual verification, linear spectral analysis, and modulation instability analysis, providing independent assessments of their validity and the stability of the nonzero background supporting the dark-soliton solution. For a representative admissible parameter set, the selected dark-soliton profile exhibits a localized intensity notch on a finite background and translates uniformly with the propagation coordinate. Three-dimensional surfaces, two-dimensional profiles, and contour plots of the intensity, modulus, and real and imaginary components distinguish envelope translation from carrier-phase evolution. The results provide a systematic characterization of the admissible solution branches, their regularity conditions, and their stability properties, while offering analytical reference profiles for subsequent numerical propagation and perturbation studies.

Dynamics doi: 10.3390/dynamics6040049

Authors: Abolfazl Baloochiyan Andrei Kuvshinikov Laurel Smurawa Marufa Akter Upoma Min Y. Pack

The word hydrogel encompasses a variety of commercially relevant water-swollen, highly porous materials often utilized in pharmaceutical and food industries. In a variety of applications, hydrogels are mixed with other materials to form a composite, yet how such heterogeneous hydrogels respond to dynamic forces is not well understood. This study has sought to experimentally probe how millimetric fiber-reinforced hydrogel balls dynamically respond to impacts. High-speed imaging and dynamography were used in tandem to validate the dynamic response of sodium alginate hydrogels undergoing impact. The results demonstrate that the peak force follows Hertzian scaling with impact velocity for the parameter space tested (e.g., 0% cellulose and 10% cellulose), yet there is a divergence in the coefficient of restitution behavior between hydrogels with and without cellulose fiber reinforcement.

Dynamics doi: 10.3390/dynamics6040048

Authors: Jiaqi Wang Yahui Niu Ahmadjan Muhammadhaji

Restricted by the inherent limitations of integer-order rumor propagation models, the application of fractional-order derivatives in rumor-spreading dynamics has attracted increasing research attention. In this paper, a delayed fractional-order ISR rumor propagation model with saturated control terms is established. The stability of system equilibrium points and the Hopf bifurcation induced by time delay are analyzed. Numerical simulations reveal that the critical bifurcation delay increases monotonically with the fractional order, which indicates that the stability region of the system expands as the fractional order increases. Moreover, the introduction of government saturated intervention can effectively suppress rumor diffusion. The obtained conclusions can provide theoretical support for public opinion prevention and control.

Dynamics doi: 10.3390/dynamics6040047

Authors: Gonzalo Ares de Parga Fabián A. Pavón-Casas Juan F. García-Camacho José I. Jiménez-Aquino

The memory time τK is identified with the collision time τc by calculating the memory time using an Ornstein–Uhlenbeck model. The effective momentum-transfer cross-section is used to derive the relaxation time τr for various relativistic models with and without quantum effects and the radiation reaction. Models based on Møller scattering are also considered. The distinction between collision and relaxation times is established, as is the role they play in a non-Markovian relativistic generalized Langevin equation based on the Landau–Lifshitz equation. The memory time τK does not generally coincide with the relaxation time, but we show that in unphysical cases, they coincide. Relaxation times are calculated progressively by considering the differential cross-sections from various models ranging across the relativistic proposals of Rutherford; Huschilt and Baylis; Aguiar, Barroso, and Barone; and a modified Mott model. We also improve a Landau–Lifshitz model, but the effects due to the radiation reaction are negligible. Finally, the Møller model yields the best result, as it accounts for quantum effects in electron–electron collisions. Given the nondegenerate energy levels and fields considered here, a non-Markovian generalized Langevin equation based on the Landau–Lifshitz equation is derived.

Dynamics doi: 10.3390/dynamics6040046

Authors: Dahan Xu Corina Sandu John B. Ferris

Tires are of particular significance in vehicle studies, as they are the connection between the vehicle and the terrain. The tire model proposed in this study treats the tire as an elastic circular cylindrical shell on a nonlinear elastic foundation, with the goal of addressing the need for quick and accurate estimation of tire performance. The mechanics and structure of a tire are reflected in the model, creating strong connections among the physical properties of the tire and the model parameters. The forces and deformation equations are derived analytically with the energy method and solved with numerical approximations. The equations address nonlinear stiffness contributed by different parts of a tire, providing high accuracy in terms of spindle force prediction and pressure distribution without involving intense computational effort. The model is calibrated with experimental data to identify its parameters and is then used to simulate tire performance under other conditions. The simulated results are consistent with the experimental results, with R2 values greater than 0.98.

Dynamics doi: 10.3390/dynamics6040045

Authors: May M. Helal Nidhal F. Ali Rasha M. Yaseen Ahmed A. Mohsen

We study a delayed reaction–diffusion susceptible–infectious–recovered (SIR) epidemic model with a Holling type-II incidence function. The model incorporates spatial diffusion and a discrete delay in the infectious input to the transmission term. We first formulate the model and discuss the existence and uniqueness of nonnegative solutions under suitable nonnegative initial histories. We then investigate the disease-free and endemic equilibria and derive the epidemic threshold by linearizing the infected equation at the disease-free equilibrium. For this normalised model the threshold quantity is given by R0 the normalisation is such that the disease free susceptible level is equal to one. We prove the disease-free stability result for the strict subthreshold case R0<1 and separate the critical case R0=1 from this regime. The existence of a positive endemic equilibrium for R0>1 is characterised. The stability of this equilibrium in the presence of a time delay requires that the characteristic equation and the global stability argument be consistent with the delay-dependent dynamics. The effects of diffusion, saturated incidence and delay are studied by numerical simulations. Transient oscillations are distinguished from sustained oscillations. The results presented here elucidate the assumptions and limitations of the proposed spatial epidemic model.

Dynamics doi: 10.3390/dynamics6040044

Authors: Mohammadreza Amoozgar Jiajun Huang

In this paper, the aeroelastic stability of hingeless rotor blades in the descent flight by including the effects of vortex ring state (VRS) has been qualitatively investigated. The blade is modelled as a cantilevered beam using an exact formulation, while the aerodynamic loads are modelled using the quasi-steady Greenberg’s aerodynamic theory combined with a prescribed induced velocity due to the vortex ring state. An identified VRS-induced velocity, from a curve fit to flight-test data, is coupled to the aerodynamic model to complete the formulation for the descent flight. The aeroelastic model is first validated in hover against the published results for a four-bladed hingeless rotor. Quantitatively, the maximum deviation between the present predictions and the reference results is approximately 6%, confirming the accuracy of the proposed modelling approach. The model is then used to qualitatively investigate the effect of the vortex ring state on the aeroelastic stability of the rotor during descent flight. The results show that the instability region of the blade shrinks during descent compared to hover, an effect that is more pronounced at lower precone angles. Increasing the torsional and lead-lag frequency ratios, as well as the descent velocity, are both shown to further influence the extent of the instability region. However, when the identified VRS-induced velocity model is used in place of a constant-inflow assumption, the predicted instability region expands and a greater descent velocity is required before the rotor becomes fully stable, highlighting the importance of accounting for VRS aerodynamics when assessing the qualitative aeroelastic stability trends of rotor blades in descent flight.

Dynamics doi: 10.3390/dynamics6040043

Authors: Pavan Kumar Vaddi Wenbo Jia Hong Wang

Hydro-generator cooling arrays are sparsely instrumented, limiting estimation of heat-exchanger (HX) parameters from plant data for thermal modeling. This study develops and validates a 48-state quasi-linear parameter-varying (qLPV) gray-box model for twelve fin-and-tube air-to-water HXs in a hydro generator cooling system. Four equivalent three-HX groups use four serial cells each, and manufacturer-specified geometry and empirical correlations provide operating-dependent conductance values rather than fitted parameters. Of 19 coefficients, eleven are fixed, and eight effective group coefficients are estimated. Rated predictions reproduce manufacturer outlet temperatures within 0.6 °C, providing catalog-consistency verification. Coefficient calibration uses a 4.03 h window from a 48,241-sample (13.4 h) plant record. With the estimated coefficients frozen, combined filtered root-mean-square error (RMSE) values on the full record are 0.183 and 0.179 °C on the north and south sides of the cooler array. Multistart Nelder–Mead and direct four-dimensional simplicial homology global optimization (SHGO) yield numerically equivalent coefficient estimates. The resulting model is computationally economical and provides a physics-based plant-specific baseline for record replay, recalibration and prospective monitoring.

Dynamics doi: 10.3390/dynamics6040042

Authors: Bulat B. Batuev Sergey V. Sukhov

Accurate reconstruction of nonlinear time-dependent dynamics is a fundamental challenge for recurrent spiking neural networks and neuromorphic signal-processing systems. In this work, we compare two prediction-error architectures for nonlinear state reconstruction: a model with an external comparator and a model employing a dedicated spiking population to encode prediction error. Both architectures are implemented within the Neural Engineering Framework and trained using the local Prescribed Error Sensitivity learning rule. The proposed approach is evaluated on a two-dimensional periodic oscillator and the nonlinear Lorenz system. The reconstruction fidelity is assessed using the reconstruction error together with amplitude-envelope correlation, instantaneous-frequency correlation, phase-locking value, mean phase difference, and computational efficiency. The results demonstrate that both architectures accurately reconstruct nonlinear dynamics, while the spiking error representation provides a larger stable operating region and a more explicit spike-based representation of the bottom-up prediction-error pathway.

Dynamics doi: 10.3390/dynamics6040041

Authors: José Luis Ponte Bejarano Juan Carlos Ponte Bejarano Edmundo Rubén Vergara Moreno Eddy Cristiam Miranda Ramos Erico Salomón Durand Pereda Josualdo Carlos Villar Quiroz

This study investigates conditions under which information dimension provides an upper bound for Hausdorff dimension using Shannon entropy and box occupancy. We establish a sufficient entropic condition and introduce the asymptotic entropic quotient, which measures the proportion of maximal entropy retained across scales. Its complement quantifies entropy loss, while its reciprocal defines an entropic correction factor. Cantor-type examples show that the quotient distinguishes distributions sharing the same geometric support. For finite samples, we justify a constrained least-squares estimator and develop a multi-criteria procedure for selecting the principal scaling window. The framework is applied to the Hénon, Lorenz, Ikeda, Rössler, and Chua double-scroll attractors, with sensitivity analyses for sample size and window selection. Estimated entropy losses range from 3.69% to 8.35%, and the entropic quotients remain stable across the tested conditions. The correction improves agreement with the reported Hausdorff dimension for Lorenz. For Hénon, it does not improve that agreement, although both estimates remain compatible with reported fractal dimensions. Results for Ikeda, Rössler, and Chua are consistent in scale with reported dimensions. Overall, the quotient provides distributional information beyond box occupancy and supports a finite-scale interpretation of entropy loss and its associated dimensional correction.

Dynamics doi: 10.3390/dynamics6030040

Authors: Alexandros Karvounis Alexandros Arailopoulos

Reducing unsprung mass in high-performance braking systems is critical for vehicle dynamics, but applying topology optimization (TO) to conventional solid discs under combined thermo-mechanical loading often causes “thermal entrapment” and structural failure. This study addresses this limitation by proposing a floating disc architecture and a two-stage computational framework. First, TO via the SIMP algorithm was applied to the Aluminum 7075-T6 inner carrier strictly under mechanical loads, decoupling artificial thermal stresses and yielding a fixed, optimized geometry. Results show the TO achieved a drastic 53% mass reduction (from 0.218 kg to 0.102 kg) specifically for the inner carrier component. Second, a high-fidelity Surrogate Model (Digital Twin) of this new geometry was developed to bypass the immense computational cost of multi-parameter, non-linear thermo-mechanical Finite Element Analysis (FEA). Utilizing Latin Hypercube Sampling (LHS) across 15 design scenarios and the Genetic Aggregation algorithm, the surrogate model was trained to predict real-time responses. Subsequently, the Digital Twin predicted stress and temperature fields with near-perfect accuracy (R2≈0.9998), rapidly identifying the limit braking scenario. Fatigue analysis confirmed the final component safely withstands 106 extreme braking cycles (safety factor 1.65).

Dynamics doi: 10.3390/dynamics6030039

Authors: Dahan Xu Corina Sandu John B. Ferris

Tires are the interface between a vehicle and the ground, through which forces and moments are generated. They are therefore critical components of a vehicle, creating a need to estimate their performance under various conditions. The tire model proposed in this study models the tire as an elastic beam on an elastic foundation, similar to a flexible ring model but with more nonlinear terms justified and included. It offers quick and accurate estimates for spindle force and longitudinal pressure distribution with little computational effort. The model is analytically derived with the energy method, building strong connections among the model parameters and physical properties of the tire. It is then solved with numerical approximations. The simulation results show good alignment with the experimental data.

Dynamics doi: 10.3390/dynamics6030038

Authors: Masego Mafora Abdullahi Rashid Adem Ben Muatjetjeja Ahmed H. Arnous Anjan Biswas

Higher-dimensional fourth-order nonlinear evolution equations model the competition among anisotropic dispersion, derivative coupling, and nonlinear wave steepening, but exact reductions can become unreliable when the governing equation, invariants, or parameter branches are not checked consistently. This study analyzes a (2+1)-dimensional fourth-order nonlinear evolution equation because a verified analytical description of its conservation structure, invariant waves, and spectral sideband behavior is useful both for qualitative wave interpretation and for benchmarking numerical calculations. The equation admits an exact local conservation-law family and a verified Lie point-symmetry subalgebra. Its invariant and traveling-wave reductions produce a non-degenerate Jacobi-elliptic gradient family, a bounded hyperbolic front, and one- and two-exponential waves subject to explicit dispersion and nonresonance conditions. Linearization about an affine exact background gives a closed quadratic sideband-dispersion relation, an explicit discriminant, and the corresponding growth rate. The analysis shows that genuine wave branches must be separated from parameter choices that collapse the reduced equation to an identity. The main contribution is therefore a consistency-first framework that combines symmetry reduction, conservation laws, exact-wave construction, admissibility conditions, and direct residual verification, thereby going beyond earlier treatments centered mainly on isolated lump or interaction formulas.

Dynamics doi: 10.3390/dynamics6030037

Authors: Nidia Aracely Cisneros-Cárdenas Victor M. Maytorena Saul F. Moreno Resty L. Durán Jesus F. Hinojosa

Solar thermal calorimeters serve as foundational reference instruments for quantifying absorbed thermal power, evaluating optical-to-thermal conversion efficiency, and validating computational models in concentrated solar thermal (CST) research. This review synthesizes recent numerical, thermo-hydraulic, and experimental advancements, evaluating the evolution from basic single-tube configurations to high-confinement cavity calorimeters (achieving apparent absorptances >0.99) and flat-plate architecture enhanced with impinging jets and internal fin arrays. The selection of working fluids is examined; water accounts for approximately 87% of reported implementations due to low property uncertainty, whereas synthetic oils and gaseous coolants expand operating temperature ranges at the expense of thermochemical degradation and parasitic pumping penalties. Furthermore, critical thermo-hydraulic challenges induced by extreme non-uniform heat fluxes are identified, including structural thermal bowing, parallel-channel flow maldistribution, recirculation traps, and buoyancy-driven instabilities occurring at Richardson numbers Ri≫10. Metrological constraints related to solar reflection interference in non-contact thermometry and calibration drift in photometric target arrays are also critically addressed. Finally, key strategic research directions are outlined, emphasizing high-temperature advanced materials, active flow equalization, real-time multi-physics digital twins, and standardized dynamic testing metrology.

Dynamics doi: 10.3390/dynamics6030036

Authors: Emilio Santos

I contend that physics should provide a coherent account of reality, in addition to being an efficient algorithm for the prediction of empirical results. This article offers pictures of reality derived from theories of modern physics. In particular, it is shown that Bose quantum fields may be interpreted as pure wave fields via the Weyl–Wigner representation, the most relevant result being the existence of a stochastic vacuum field corresponding to the quantum vacuum fluctuations of the standard, canonical, formulation of field theory. That field provides explanations for the particle (photons) behavior of the electromagnetic field. Also, a realistic interpretation is offered for interference experiments with actual particles, like atoms. The interpretation of classical general relativity is standard but emphasis is given to the principle of equivalence. Problems like spacetime singularities (black holes) and the empirical violation of Bell inequalities are touched on but slightly. Asides from these problems, the main incompleteness of the article is the absence of a realistic interpretation of Fermi fields.

Dynamics doi: 10.3390/dynamics6030035

Authors: Phan Anh Duong Jin-Woo Bae

The decarbonization of maritime transport demands propulsion and onboard energy systems that simultaneously achieve ultra-low emissions, high power density, and robust operational reliability. Nuclear propulsion, particularly when coupled with small modular reactors (SMRs), offers a compelling pathway due to its near-zero operational emissions and exceptional energy density; however, the efficient utilization of high-grade nuclear thermal energy under shipboard constraints remains a critical challenge. To address this issue, this study presents a comprehensive thermodynamic and exergy-based assessment of a novel cascaded waste heat recovery (WHR) architecture designed for a 100 MW class nuclear-powered vessel, integrating a supercritical carbon dioxide (sCO2) cycle with downstream steam Rankine (SRC) and Kalina cycles. Detailed process modeling is performed using Aspen HYSYS to quantify energy and exergy performance at the component and system levels. The proposed cascade exploits the complementary thermodynamic characteristics of each cycle, enabling staged recovery of high-, medium-, and low-grade heat from the nuclear secondary loop. Results indicate that while the sCO2 cycle dominates gross power generation due to its high power density and favorable high-temperature performance, its net efficiency is constrained by substantial compression work and associated auxiliary losses. In contrast, the SRC and Kalina cycles exhibit significantly higher energy efficiencies, demonstrating superior suitability for medium- and low-temperature waste heat utilization. Through thermodynamic synergy, the integrated sCO2–SRC–Kalina configuration achieves an overall energy efficiency of 20.73%, representing a substantial improvement over a standalone sCO2-based WHR system. Exergy destruction analysis reveals that system irreversibilities are primarily concentrated in heat exchangers, particularly the primary heat exchanger interfacing the nuclear heat source with the sCO2 loop, whereas turbomachinery contributions are comparatively minor. These findings highlight heat exchanger design optimization and improved temperature matching as the most effective pathways for further performance enhancement. Overall, this study demonstrates that multi-cycle cascade integration provides a viable and high-efficiency solution for nuclear marine energy recovery, with strong implications for advanced hydrogen energy systems and other high-performance power generation applications requiring compactness, scalability, and thermodynamic robustness.

Dynamics doi: 10.3390/dynamics6030034

Authors: Dimitri Volchenkov

A distribution feeder is built meshed and operated radially, so at any instant it occupies one of a combinatorial family of topologically radial configurations. We show that this family, weighted in the natural maximum-entropy way, is a determinantal point process whose kernel is the transfer-current matrix of the network, and we read that kernel in the operator’s language: the probability that a line section is energised equals its own self transfer-current factor, Foster’s sum rule is the trace identity, and the covariance of two switching states is minus the square of their normalised transfer current. Independent faults leave the feeder exactly within this family for any number of faults, whereas no restoration mechanism ignorant of the section resistances can return it there; among those that can, one is canonical, being the unique mechanism that reverses the fault, and its weight is the section’s transfer-current factor in the post-fault network with everything still energised shorted. We show, and report, that these weights are a structural diagnostic and not a repair priority. The maintained feeder is solved in closed form, and an exact transport equation prices what a reinforcement programme costs the feeder’s ability to reconfigure. The central spanning-tree and sector identities are verified against exhaustive enumeration; the dynamical and sensitivity statements are checked by exact master-equation computations and finite differences.

Dynamics doi: 10.3390/dynamics6030033

Authors: Iman Rousta Forough Mohammadi Ravari Haraldur Olafsson Jaromir Krzyszczak

Vegetation dynamics are highly sensitive to climate variability and constitute a key indicator of ecosystem condition, particularly in arid and semi-arid environments where field observations are often limited. This study investigated the spatiotemporal dynamics of vegetation and their relationships with climatic factors in the Quaraqum Watershed during 2001–2022 using multi-source remote sensing datasets. Vegetation dynamics were characterized using the Normalized Difference Vegetation Index (NDVI) derived from MODIS imagery, Land Surface Temperature (LST) was obtained from MODIS products, and precipitation data were obtained from the CHIRPS dataset. Spatial and temporal patterns and trends were examined using Geographic Information System (GIS) techniques, while the relationships between NDVI and climatic variables were quantified using Pearson correlation and multiple linear regression analyses. The results revealed a pronounced west-to-east decrease in precipitation accompanied by increasing temperature across the watershed. Annual precipitation reached maximum values of 389.20 mm in 2019 and 370.79 mm in 2009, whereas the lowest values, 172.50 mm and 171.50 mm, were recorded in 2008 and 2021, respectively. Spring was the wettest season, whereas summer was the driest. Vegetation cover was highest in spring and exhibited an increasing long-term trend, while autumn and winter showed the lowest vegetation cover and declining trends. Correlation analysis revealed a strong positive relationship between NDVI and precipitation and a weaker negative relationship between NDVI and LST. These results suggest that precipitation availability was more strongly associated with vegetation variability than thermal conditions. Multiple regression analysis further indicated that precipitation was the primary climatic variable explaining annual NDVI variability, while the inclusion of LST did not substantially increase the explained variance of the model. Overall, these findings highlight the dominant role of moisture availability in shaping vegetation dynamics in the Quaraqum Watershed, with thermal conditions representing an additional environmental factor affecting vegetation responses.

Dynamics doi: 10.3390/dynamics6030032

Authors: Cécile Barbachoux Joseph Kouneiher

We introduce a deterministic class of constraint-coupled reaction–diffusion systems in which an internally generated field modulates transport and reaction processes while being regenerated by the same dynamics that it regulates. This feedback structure provides a minimal mathematical framework for studying dynamically consequential endogenous regulation in spatially extended non-equilibrium systems; the presence of a causal loop alone is not identified with organizational autonomy. The model is formulated as a quasilinear parabolic system on a bounded domain. Positivity, boundedness, viability, equilibrium stability, and spatial localization are treated as distinct mathematical properties. Under structural assumptions on the diffusion and reaction terms, we establish local classical well-posedness, preservation of non-negativity, and global existence under boundedness or forward-invariant-region conditions. Viability is formulated as forward invariance of subsets of an infinite-dimensional phase space rather than as a local pointwise balance. A minimal three-field realization, consisting of a resource field, an organizing field, and a constraint field, is then analyzed. We derive conditions for the existence of positive homogeneous equilibria, obtain sufficient criteria for homogeneous and full modal stability, and characterize stationary and oscillatory spatial instability thresholds through a mode-dependent dispersion relation. We complement the analysis with conservative two-dimensional finite-volume simulations. Below the predicted spatial-instability threshold, perturbations decay, whereas above threshold a persistent heterogeneous state forms with a dominant scale consistent with the dispersion relation. Constraint level sets, occupied fraction, connected components, and concentration indices quantify the resulting dynamically generated localization. Feedback-ablation controls show that, for the representative parameter set, removing either transport or reaction feedback eliminates the finite-wavenumber instability, while alternative bounded monotone constitutive laws preserve spatial patterning. The framework therefore distinguishes externally imposed regulation, passive outputs, and dynamically consequential endogenous feedback, and provides a basis for investigating bounded self-maintenance and localization without equating loop topology with autonomy.

Dynamics doi: 10.3390/dynamics6030031

Authors: Adebola Samuel Adeoye Ezekiel Olaoluwa Omole Thomas Olubunmi Awodola Olayiwola Babarinsa David Opeoluwa Oyewola Aseel Smerat

Functionally graded (FG) beams have been used more and more in highly designed structures under dynamic loading due to their graded mechanical properties and excellent performance. Their transient response on complex elastic foundations is, however, not easily predicted due to the material heterogeneity, shear deformation, rotary inertia, and coupled effect of the foundation parameters. The purpose of this study is thus to propose an accurate and efficient computational model for the dynamic analysis of FG Timoshenko beams supported by biparametric Vlasov foundations under harmonic excitation. The formulation takes into account the space-varying material properties, Timoshenko shear deformation, rotary inertia, and coupled Winkler–shear interaction of the Vlasov foundation. The governing equations are numerically solved in space with the high-order spectral element method (SEM) and in time with the Hilber–Hughes–Taylor (HHT) scheme. The resulting framework is used to study the transient displacement and vibration response with respect to the excitation frequency, material gradation index, and stiffness and damping properties of the foundation. The numerical results prove that the results converge quickly in space and time and also indicate that the dynamic response is significantly affected by the interaction between the gradation of material and the parameters of the foundation. The displacement amplitude, resonance behavior, and vibration characteristics are significantly altered by any variations in the gradation index and foundation characteristics. The results obtained with the proposed formulation are in good agreement with those available from the benchmark solutions, thus validating the correctness and reliability of the formulation. The SEM–HHT methodology offers a reliable, precise, and low-computational-cost solution for transient analysis of FG Timoshenko beams on biparametric Vlasov foundations under harmonic excitation. The proposed framework offers a powerful predictive tool for vibration analysis, response control, and design of advanced FG beam systems that can be applied in aerospace, marine, smart infrastructure, and other high-performance engineering structures.

Dynamics doi: 10.3390/dynamics6030030

Authors: Flavia Pennini Angelo Plastino

We investigate the information-geometric structure of a self-consistent second-virial approximation with the van der Waals form of the second virial coefficient, using the Fisher information as a generating potential. By constructing the associated Hessian metric and scalar curvature, we obtain a geometric description of thermodynamic fluctuations that complements the standard equation-of-state approach. We show that interaction effects enter the Fisher information selectively through their temperature dependence, with attractive interactions playing the dominant role while excluded-volume contributions remain subleading. The Hessian determinant of the Fisher information changes sign along well-defined crossover loci in the reduced parameter space, separating regions of saddle-like and locally convex curvature of the fluctuation landscape, and diverges as D˜−12 at the closure boundary. The scalar curvature diverges at the closure boundary as a simple pole, with a leading term that is universal and independent of the interaction parameters. We derive its exact closed-form expression, which shows that the curvature is negative for weak-to-moderate effective coupling but turns positive in the strong-coupling regime, where the underlying Fisher–Rao metric loses positive-definiteness. The curvature diverges on approach to this metric boundary, which lies strictly inside the mechanically stable region, short of the closure boundary itself. These results demonstrate that Fisher geometry provides a selective probe of interaction-induced fluctuations, capturing how thermal states reorganize under temperature variations rather than encoding phase transitions directly. This approach offers a complementary perspective on interacting systems and suggests new avenues for extending information-geometric methods to more strongly correlated and quantum regimes.

Dynamics doi: 10.3390/dynamics6030029

Authors: Hannah Kravitz Christina Durón Moysey Brio

Many epidemiological models assume either closed populations or continuous demographic turnover. We consider an intermediate setting in which exchange occurs through discrete pulses. In this paper, we introduce a population-conserving compartmental epidemiological model with pulse population exchange at a set of prescribed times. At each pulse, a fraction of the population in each compartment is replaced by a combination of susceptible and immunized individuals. In contrast to typical pulse birth or pulse vaccination models where only a single compartment undergoes a pulse population change, the pulses in this model have competing effects: removing infectious individuals reduces the force of infection, while introducing new susceptibles increases it. In addition, when some part of the incoming population is immunized, the net effect of pulses becomes state-dependent. After presenting the model, we prove both conservation of total population and non-negativity in each compartment. We then show that while the non-pulsed system has only the disease-free equilibrium, the demographic changes introduced by the pulses can produce two new types of solution: a pulse-periodic endemic equilibrium and a second wave of infection. We derive an exact expression for a post-pulse endemic equilibrium in terms of the integrals of the solutions between equispaced pulses using the Poincaré map. Next, we identify the exact threshold at which the pulse-induced reduction in the susceptible population changes sign. Above the threshold, the pulses in all compartments contribute to a net reduction in the force of infection. Below this threshold, competing effects take hold—incoming susceptible individuals replenish the susceptible compartment, while departing exposed and infectious individuals no longer contribute to secondary infections. Finally, using parameters motivated by recent outbreaks of disease on cruise ships, we characterize this threshold mechanism and investigate the effect of pulse start time on the solution trajectories.

Dynamics doi: 10.3390/dynamics6030028

Authors: Geylani M. Panakhov Eldar M. Abbasov Dennis A. Siginer Sayavur I. Bakhtiyarov Vusal H. Guseynov

The results of the experiments on the transport process of fluid flow through a pipeline under temperature gradient conditions between the internal and external environments, and on continuous gas generation at the contact boundary of the transported media, are presented in this paper. The test results showed that under non-isothermal flow conditions, a slippage effect will impact flow velocity and pressure, as well as the temperature distributions in variable cross-section pipes. Laboratory experiments were conducted in order to study the effects of the gas nucleus at the pipe walls on the hydrodynamic characteristics of the fluid flow. It is shown that the throughput capacity of the pipe is affected by the temperature difference between the oil and the pipe walls. The test results also demonstrated that at certain temperature gradients on the border layer, the pipe’s capacity reaches its maximum value. Quantitatively, the hydroconductivity of Q/ΔP increased from about 1.45 × 10−5 m3/(s·MPa) under relatively isothermal conditions to a maximum value of approximately 2.04 × 10−5 m3/(s·MPa) with a temperature difference in the oil–pipe-wall zone of about 3–5 K, which corresponds to an increase of about 41%. With a further increase in the temperature difference, the hydroconductivity decreased to about 1.64 × 10−5 m3/(s·MPa) at 10 K and then stabilized in the range of (1.60–1.64) × 10−5 m3/(s·MPa). This non-monotonic behavior is explained by the temperature-induced release of gas and the formation of a gas-saturated wall zone, which initially reduces the effective resistance of the wall and creates an apparent sliding effect. At high temperature differences, gas accumulation, thermal insulation of the wall area and two-phase flow disturbances limit this effect, which leads to the decrease and subsequent stabilization of the pipe capacity.

Dynamics doi: 10.3390/dynamics6030027

Authors: Ricardo A. Calix Ajaykumar Rejith Tae-Hoon Kim

The world consists of many dynamical and chaotic systems whose underlying functions can be highly nonlinear. Traditional engineering and scientific methods emphasize simplifying problems, sometimes to the point that valuable information may be lost. Instead, understanding of these systems may require analysis of the underlying dynamics. In the past, the technique of discovering and analyzing strange attractors has yielded some success. However, much work is still needed. Machine learning (ML)-based models such as deep neural networks which are based on nonlinear functions may provide a great set of techniques to help in the discovery of structure in dynamical systems. In this paper, we propose an ML-based approach to search for structure in dynamical systems using Neural Input Optimization (NIO). We discuss our methodology and present promising results. Quantitative results help to validate our proposed NIO methodology for structure discovery.

Dynamics doi: 10.3390/dynamics6030026

Authors: Marco A. García-Márquez Irán Ramos-Prieto Francisco Soto-Eguibar Héctor M. Moya-Cessa

We investigate the dynamics of a driven quantum field coupled to a finite-temperature reservoir. The corresponding master equation is solved using superoperator techniques, yielding an analytical expression for the density operator. To obtain a compact and physically transparent description of the dynamics, we adopt a phase-space representation based on the Husimi Q-function. For an initially coherent state, we derive a closed-form Gaussian expression for the Husimi Q-function whose stationary limit corresponds to a displaced thermal state. This approach also enables an analytical study of quantum-interference dynamics for an initial superposition of coherent states. Furthermore, we derive the corresponding Fokker–Planck equation for the Husimi Q-function and obtain closed-form expressions for relevant statistical quantities, including the mean photon number, the photon-number standard deviation, and the Mandel parameter. We also investigate the Wehrl and linear entropies, which quantify the loss of phase-space information and purity induced by the thermal environment. The framework provides a complete analytical characterization of the phase-space dynamics, photon statistics, and entropic properties of driven–dissipative quantum fields while avoiding the explicit manipulation of the density operator.

Dynamics doi: 10.3390/dynamics6030025

Authors: Laira Pinto Borges Júnia Natália Mendes Batista Amarílis Severino e Souza Rodrigo Béttega

The accuracy of CFD-DEM simulations of particulate systems strongly depends on the proper characterization of particle–particle and particle–wall interaction parameters. In this study, the coefficients of restitution, static friction, and rolling friction for ABS–ABS and ABS–acrylic interactions were experimentally determined for acrylonitrile butadiene styrene (ABS) spheres using free-fall, inclined-plane, and launch-ramp tests, respectively. The obtained parameters were subsequently applied in CFD-DEM simulations of a three-dimensional conical spouted bed operating with different solid loads. In parallel, experimental fluid dynamic tests were conducted to obtain characteristic pressure drop curves and determine the minimum spouting velocity. The experimental results exhibited the typical behavior of spouted beds, including hysteresis between the curves obtained by increasing and decreasing the inlet air velocity and higher minimum spouting velocities at greater solid loads. The CFD-DEM simulations successfully reproduced the main hydrodynamic features of the system, yielding deviations of 0.9%, 6.9%, and 20.5% for the minimum spouting velocities corresponding to solid loads of 400 g, 300 g, and 200 g, respectively. A comparison with the interaction parameters reported in the literature showed that the coefficients obtained through direct measurement provided better agreement between the experimental and simulated results. These findings highlight the importance of accurately characterizing interaction parameters to achieve reliable CFD-DEM simulations of spouted bed systems.

Dynamics doi: 10.3390/dynamics6030024

Authors: Yargo P. Souza Felipe S. Loureiro Delfim Soares Walnório G. Ferreira Webe J. Mansur

A new family of fourth-order accurate time integration schemes is developed by introducing two complex time sub-steps into the classical Newmark family of second-order algorithms. These sub-steps consist of a pair of complex conjugate numbers, enabling the triangularization of a complex-valued effective stiffness matrix. The proposed formulation can be easily implemented in existing codes with only minor modifications to the standard Newmark algorithm. The solution is composed of both real (physical) and imaginary components. The real component provides fourth-order accuracy even in the presence of external loads and physical damping, while the imaginary component offers additional insight into the distribution of numerical errors, an original feature not previously reported for implicit formulations. Compared to the classical Newmark method with a time-step size four times smaller, the proposed scheme exhibits significantly lower numerical dissipation and dispersion errors. Furthermore, the sub-step procedure extends the critical time step of conditionally stable members of the Newmark family by a factor of 3. The numerical analysis performed in the proposed time integration method, along with the results obtained for dynamic structural problems, including a complex three-dimensional (3D) application, clearly demonstrate that the method outperforms both Fung’s fourth-order complex scheme and the classical Newmark approach in terms of accuracy.

Dynamics doi: 10.3390/dynamics6020023

Authors: North Yates Fernando Ponta Joshua Reese Alayna Farrell

A fundamental aspect in the design of modern utility-scale wind turbines is predicting the vibrational response of their blades when excited by gust pulses of various amplitudes and frequencies in atmospheric flow. Improved designs based on accurate blade-response predictions can prevent extreme oscillations, reduce fatigue stress, and extend turbine’s operational life. In previously published works, the authors introduced and applied a novel technique that provided an energy-based Reduced-Order Characterization (ROC) for the oscillatory response of wind turbine rotors, when excited by wind gust pulses with different combinations of timespan and amplitude under various operational conditions. Those studies established the universal nature of the ROC by expressing the turbine aeroelastic response as a vibrational Stability Map, plotted in terms of non-dimensional quantities, which could be applied to turbines of any size that share a similar blade construction. In the present paper, the authors will expand the ROC technique beyond the scope of their previously published studies, to analyze the Multi-Modal Response observed in regions located at the external boundaries of the stable zones of the Stability Map. This will provide valuable information about rotor stability behavior in extreme turbine operational conditions which were previously unexplored.

Dynamics doi: 10.3390/dynamics6020022

Authors: Sarp Adali

Variational principles and variationally consistent boundary conditions are presented for double-layer graphene nanoribbons undergoing time-dependent and free vibrations. The van der Waals forces acting in the core region are modelled as shear and tensile–compressive effects. The nonlocal constitutive formulation of the problem is based on the sandwich beam model in order to represent the graphene nanoribbon layers as faces and van der Waals forces acting in the core region. The constitutive equations which govern the vibrations of the nanoribbons are in the form of four coupled partial differential equations involving the in-plane and out-of-plane deflections. The first part of the study involves the derivation of the variational principle for the system undergoing time-dependent vibrations. Hamilton’s principle is formulated based on the kinetic and potential energies of the system. The next section involves the freely vibrating nanoribbon system and the formulation of the variational principle for this case is given. Based on this formulation, the expressions for the Rayleigh quotients are obtained for the longitudinal natural frequency and the transverse natural frequency. The last section involves the derivation of the variationally consistent boundary conditions and the expressions for the shear force and moment at the boundaries.

Dynamics doi: 10.3390/dynamics6020021

Authors: João Pedro Spadão Rui Marcos Grombone Vasconcellos Murilo Sartorato Wilian Miranda dos Santos

Lift-plus-cruise electric vertical takeoff and landing (eVTOL) aircraft exhibit complex stability characteristics during transition flight, when rotor-borne and wing-borne regimes coexist. This work investigates the dynamic stability of a lift-plus-cruise eVTOL using a nonlinear six-degree-of-freedom model incorporating aerodynamic forces, tractor propulsion, and vertical lifter dynamics. Linearization about representative trimmed conditions enables longitudinal and lateral–directional modal analysis. The results identify a critical near-stall region where lift-curve slope reduction markedly decreases short-period damping. Residual lifter authority partially compensates for this degradation, improving stability in the transition regime. To ensure smooth control transfer, an airspeed-dependent blending strategy between hover and fixed-wing controllers is implemented. Comparative analyses show that a sigmoid blending law improves the minimum short-period damping ratio relative to a linear strategy while preserving similar overall damping variation. Closed-loop simulations of a complete mission profile demonstrate the effectiveness of the proposed approach and reveal an asymmetric dynamic response between hover-to-forward and forward-to-hover transitions. These findings provide a physically grounded explanation for stability degradation during transition and establish practical guidelines for control authority blending in lift-plus-cruise eVTOL aircraft.

Dynamics doi: 10.3390/dynamics6020020

Authors: Anna Markhotok

The effect of atom size on the shock-wave structure in a binary monatomic gas mixture with Rydberg atoms has been investigated. The problem was solved numerically using the system of hydrodynamic equations in argon gas for the atom-size ratios between 2 and 100, T = 1500 K, and the density between 1017 and 1020 m−3. It was found that the presence of larger-sized atoms in the mixture results in shock front splitting that is on the order of the mean free path for this component. The results could be of interest in supersonic plasma dynamics and in astrophysics, studying shock waves in the environments where high-n Rydberg states are present.

Dynamics doi: 10.3390/dynamics6020019

Authors: Zhao Ni Xinfeng Zhang Jie Bai Bing Rao Jiawen Dai Bangji Zhang Zheshuo Zhang

In high-rise firefighting scenarios, unmanned aerial vehicles (UAVs) equipped with water-spraying systems are subjected to high-intensity and rapidly time-varying reaction forces induced by high-speed water jets. These forces introduce mismatched uncertainties with unknown bounds and make stable flight control particularly challenging. To address this problem, this paper proposes an adaptive robust constraint-following control (ARCFC) strategy for vector–rotor UAVs (VRUAVs). The controller is developed directly for the strongly nonlinear dynamics of the VRUAV without resorting to model linearization. Within a constraint-following-based nonlinear regulation framework, water-jet effects are explicitly modeled as rapidly time-varying uncertainties with unknown bounds, and an adaptive law is introduced to estimate conservative uncertainty bounds online for robust compensation. Lyapunov-based analysis is conducted to establish the uniform boundedness and uniform ultimate boundedness of the closed-loop system, and simulation results are presented to verify the effectiveness of the proposed approach. Compared with representative conventional control methods, the proposed ARCFC strategy provides improved disturbance-rejection capability and enhanced flight stability under demanding firefighting conditions.

Dynamics doi: 10.3390/dynamics6020018

Authors: Sebastiano Ettore Spoto

A recent two-layer theory for long-runout turbidity currents explains sustained bypass by allowing a dense lower layer to exchange mass with a more dilute upper layer while avoiding rapid over-thickening. Here, a morphodynamic extension is developed that couples suspended load and bed exchange while treating the two-layer hydrodynamics as a prescribed background. A suspended-sediment balance with bed exchange and Exner’s equation are written on that background, the depositional state variable B=Es/(rC) is introduced, and an exact nonlinear evolution equation for B is derived within the prescribed-background setting. In the weak-exchange limit this equation reduces to an algebraic onset criterion, thereby identifying the regime in which the simpler threshold is valid. Applied to an Amazon-like local-normal-flow reconstruction, the model shows that finite exchange shifts depositional onset upstream relative to the weak-exchange estimate. Background-fidelity checks, grid-refinement tests and closure/inlet sensitivities are reported to delimit the quantitative use of the reduced application. The framework is therefore best interpreted as a coupled reduced theory for suspended load and bed exchange on a prescribed two-layer bypass background rather than a fully hydro-morphodynamic closure.

Dynamics doi: 10.3390/dynamics6020017

Authors: Wasaif H. R. Alruwaele Jitesh S. B. Gajjar

First of all thank you for your comments [...]

Dynamics doi: 10.3390/dynamics6020016

Authors: Carlos A. Valentim Sergio A. David

Computational modeling and machine learning have impacted several different areas of science and accelerated advancements in multiple venues. Yet traditional machine learning models have many well-known drawbacks: besides demanding a significant amount of data, they may fail to generalize beyond training data, are often treated as “black boxes”, and may predict physically inconsistent results. In response to these limitations, Physics-Informed Machine Learning (PIML) has emerged as a new area that integrates domain knowledge, such as energy or mass conservation, directly into data-driven algorithms. This review paper examines the foundations and main strategies of PIML, organizing the approaches into three categories: automated discovery and system identification, continuous-time modeling, and operator learning. In addition, Physics-Informed Neural Networks are analyzed in a dedicated section that covers architecture fundamentals, forward and inverse problem formulations, loss function design and implementation challenges. The paper also presents a survey of interdisciplinary applications of PIML in materials science, biomedical engineering, and fractional calculus. In this context, the review also analyzes open challenges and outlines future directions in the field.

Dynamics doi: 10.3390/dynamics6020015

Authors: Asterios Pantokratoras

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Dynamics doi: 10.3390/dynamics6020014

Authors: Noha M. Hafez

The physical characteristics of a heated non-Newtonian Eyring–Powell fluid in a conduit with sinusoidally moving ciliated walls are highlighted in this analytical study. The impact of mass transmission is considered in this model. The dimensional form of the governing equations is simplified using the long-wavelength estimation and suitable transformations to produce a set of dimensionless partial differential equations with pertinent boundary conditions. To solve it, the perturbation technique is utilized applying polynomial solutions. The solutions of temperature, concentrations, and velocity profiles are obtained, and then are further analyzed through graphical results. An accurate mathematical solution for the pressure gradient is achieved by integrating the velocity profile over the elliptic cross-section. The non-Newtonian Eyring–Powell fluid flows quicker through this vertical ciliated elliptic duct than the Newtonian fluid. Moreover, the cilia elliptic movement eccentricity and the wave number for metachronal wave have a dual effect on the velocity profile. Increasing the dimensionless flow rate and occlusion leads to an increase in closed contour size, as seen in the streamline description.

Dynamics doi: 10.3390/dynamics6020013

Authors: Edward Bormashenko

A graph-theoretical approach to the analysis of motion and rest in many-body systems is developed. Point bodies are represented as vertices of a complete bi-colored graph, termed the motion–rest graph (MRG). Two vertices are connected by a rust-colored edge when the corresponding bodies are at rest relative to each other; that is, when their mutual distance remains constant in time, bodies moving relative to each other are connected by a cyan edge. It is shown that the logical structure of the relation “to be at rest relative to each other” determines the combinatorial structure of the graph. For one-dimensional motion in classical mechanics and special relativity, this relation is reflexive, symmetric, and transitive, and therefore defines an equivalence relation. As a result, rust edges form disjoint complete cliques corresponding to rest-clusters, and the MRG becomes a semi-transitive complete bi-colored graph that is completely determined by the partition of the bodies into equivalence classes. It is proven that any such graph on five vertices necessarily contains a monochromatic triangle. For two- and three-dimensional motion, the transitivity of relative rest generally fails because constant mutual distance does not imply an equality of velocities in the presence of rotational degrees of freedom. In this case, the MRG is non-transitive, and the Ramsey threshold becomes the classical value R(3, 3) = 6. The approach is extended to mixed sets containing moving bodies and reference points, including the center of mass of the system. Generalizations to general relativity and quantum mechanics are also discussed. In general relativity, transitivity of relative rest is generically lost because global rigid congruences do not generally exist. In quantum mechanics, exact transitivity survives only at the level of idealized delocalized eigenstates, whereas for physically realizable localized states, the notion of mutual rest becomes only approximate. The results demonstrate that the interplay between kinematics, logical properties of relational motion, and Ramsey-type combinatorial constraints gives rise to unavoidable ordered substructures in many-body systems.

Dynamics doi: 10.3390/dynamics6020012

Authors: Ihor Hrytsay Petro Pukach Myroslava Vovk

The results of the development and practical application of a comprehensive system for studying gear cutting processes are presented. The processes are traditional hobbing, modern power skiving, and radial-circular methods. Carrying out these processes is based on the gear teeth continuous generating method using complex kinematics. This complicates the analysis, description and modeling of the processes. The developed system provides for a logical sequence of step-by-step modeling and simulation of interrelated processes and phenomena accompanying gear processing. Reproducing volumetric chips and calculating their parameters provides the basis for determining deformation and contact processes, cutting forces, elastic deformations, machining accuracy and energy costs per operation. After establishing the operation to overcome friction and heat flows, the degree of heating and the temperature of the working surfaces are calculated to predict tool wear and its service life. Based on the parametric non-uniformity of the considered processes, the intensity of oscillations and vibrations of gear cutting machines is predicted, and their impact on the quality of gear surfaces and the accuracy of gears is determined. These approaches enable the study of such processes at the level of individual teeth and blades during cutting. They also allow gear cutting technology and cutting tools to be optimized according to the most important criteria and performance assessments.

Dynamics doi: 10.3390/dynamics6010011

Authors: Pedro A. S. Braga Luis A. Aguirre

The Rössler system is a paradigmatic chaotic oscillator widely used to investigate synchronization phenomena. Existing studies on monovariate coupling almost exclusively rely on the x or y variables, while coupling through z is commonly regarded as ineffective. In this work, we report that complete synchronization through the z variable is indeed possible, provided that specific parameter values are chosen. We further consider a parameter regime in which the Rössler system exhibits multistability and show that synchronization via z-coupling occurs only when the dynamics evolve on a particular attractor. Although synchronization can be achieved, the admissible range of coupling strengths is very narrow as determined by the master stability function. For small networks, full connectivity is required, whereas larger networks can tolerate the removal of a limited number of links without losing synchronization. An analytical expression predicting the fraction of connections that must be preserved as a function of network size is derived and validated, revealing that a very high average degree is necessary. This effectively excludes common topologies such as small-world and scale-free networks. Numerical examples with up to 100 oscillators are presented, and potential challenges that may yield new insights are discussed.

Dynamics doi: 10.3390/dynamics6010010

Authors: Christian R. Huyck

Simulated spiking neural networks have been explored for over a hundred years. Many of these networks are driven by biological considerations and an attempt to simulate brains, but others are used with little biological consideration. This paper gives some history of the development of spiking neural models, their use for modelling biological and cognitive phenomena, and for machine learning. It introduces the current state of the art in computational biological neuron and synapse modelling and plasticity. It introduces and reviews balanced spiking networks and their engineering applications. Spiking networks are also used for machine learning, with the hope that their implementation on neuromorphic hardware will bring energy and time savings. Similarly, neuromorphic hardware can enable massive parallelism, supporting larger spiking networks. The use of spiking nets for machine learning, both with biologically plausible models and without, is discussed, showing that effective models already exist. The paper concludes with some notes about implementing spiking nets and a discussion including open questions and future work.

Dynamics doi: 10.3390/dynamics6010009

Authors: Alaa Shumran Abdul-Basset A. Al-Hussein Viet-Thanh Pham

The growing need to safeguard sensitive data in various fields, including in relation to education, banking over the phone, private voice conferences, and the military, has grown as dependence on technology in daily life has increased. Encryption schemes based on chaotic systems are among the most commonly utilized approaches in the security field due to their high levels of safety and reliability. This study proposes a secure audio encryption framework based on the Chameleon chaotic algorithm implemented on a Xilinx ZedBoard Zynq-7000 FPGA. The system was designed using a fixed-point arithmetic format with 32-bit precision (eight integers; 24 fractional bits) with the Xilinx System Generator in MATLAB Simulink R2021b and verified using Vivado. The Chameleon Chaotic System, characterized by its transition from self-excited to hidden attractors through parameter variation, adds complexity to the system dynamics and strengthens the encryption algorithm. The Adaptive Feedback Control technique was applied to synchronize the signals. These methods enhance the security of audio data by ensuring robust and fast synchronization during transmission. The performance of the proposed system was assessed using correlation analysis, the mean squared error, histogram analysis, and audio spectrogram analysis. The system demonstrated strong encryption capabilities with low correlation values (−0.0033). In decryption, they achieved high fidelity with a correlation exceeding 0.999 in noise-free conditions and above 0.9933 under 20 dB AWGN. Adaptive Feedback Control showed superior decryption precision with lower MSEU and higher PSNR, confirming its effectiveness under noisy environments.

Dynamics doi: 10.3390/dynamics6010008

Authors: Ahmed Sadeq Hunaish Fatma Noori Ayoob Fadhil Rahma Tahir Viet-Thanh Pham

This paper investigates the dynamics of a permanent magnet synchronous motor (PMSM) and controls its chaotic speed behavior using the synergetic control technique (SCT). The model includes electrical dynamics in the dq frame and mechanical speed dynamics, with a scalar parameter γ capturing cross-coupling effects. The equilibrium structure and local stability properties of the PMSM are analyzed. For zero input voltages and zero load torque, the system exhibits a pitchfork-type bifurcation in the electrical–mechanical equilibrium as γ crosses a critical value. Explicit expressions are derived for all equilibria, and their stability is characterized using eigenvalue analysis and the Routh–Hurwitz criterion, and a secondary loss of stability via a Hopf-type mechanism is identified. The case of nonzero input voltages with zero load torque is also discussed. Numerical simulations confirm the analytical results and highlight the parameter regions that admit stable operation. Bifurcation diagrams show the different PMSM behaviors as the parameter γ varies. For a certain interval of γ, the PMSM speed undergoes chaotic oscillations. The SCT is introduced to control the chaos. Macro variables are chosen to design the SCT. The derived SCT is implemented to eliminate the chaotic speed. The controller provides good performance in suppressing the chaos. The controller is tested under sudden reference speed change where the controller gets the new reference speed accurately. It is also evaluated under sudden and sinusoidal load torque variations.

Dynamics doi: 10.3390/dynamics6010007

Authors: Umida Baltaeva Bobur Khasanov Hamrobek Hayitbayev Jamol I. Baltaev Yolqin Alikulov

We study the Cauchy problem for a loaded fractional integro-differential equation with a time-dependent diffusion coefficient. By reducing the problem to an equivalent Volterra integral equation of the second kind, we derive explicit analytical representations of solutions under appropriate regularity assumptions. The construction of the associated resolvent kernel allows us to establish existence and uniqueness results and to investigate the role of the fractional order and the loading term in the solution structure. Two illustrative examples are presented to demonstrate the applicability of the proposed approach.

Dynamics doi: 10.3390/dynamics6010006

Authors: Konstantin Rybakov

This article proposes a method for forming invariant stochastic differential systems, namely dynamic systems with trajectories belonging to a given smooth manifold. The Itô or Stratonovich stochastic differential equations with the Wiener component describe dynamic systems, and the manifold is implicitly defined by a differentiable function. A convenient implementation of the algorithm for forming invariant stochastic differential systems within symbolic computation environments characterizes the proposed method. It is based on determining a basis associated with a tangent hyperplane to the manifold. This article discusses the problem of basis degeneration and examines variants that allow for the simple construction of a basis that does not degenerate. Examples of invariant stochastic differential systems are given, and numerical simulations are performed for them.

Dynamics doi: 10.3390/dynamics6010005

Authors: Bo Zhong Yang Lv

The dynamic behaviour of a column excited at the base, e.g., under an earthquake load, has been extensively studied. However, the column may also experience impact at the tip like a heavy-duty truck braking on a bridge. The caused base shear of the pier is very important. In this work, the dynamic behaviour, particularly the impact load from the tip to the base, was studied on two different composites: double basalt- and double flax fibre-reinforced polymer tube (DBFRP and DFFRP)-confined coconut fibre-reinforced concrete (CFRC). For each composite, two columns with a height of 1 m, an inner diameter of the outer tube of 100 mm, and an inner tube of 30 mm were fabricated. The column was fully fixed at the base and struck at the top with an impulse hammer. The base shear was calculated through an equivalent mass method using the acceleration at the tip. The results show that both DBFRP-CFRC and DFFRP-CFRC can dissipate a portion of the impact force, resulting in a reduction in force at the base of the specimens. The base shear of DFFRP-CFRC columns is larger and dissipates energy faster than that of DBFRP-CFRC columns.

Dynamics doi: 10.3390/dynamics6010004

Authors: Dimitri Volchenkov Nuwanthika Karunathilaka Vichithra Amunugama Walawwe Fahad Mostafa

Empirical debates about a “crisis of trust” highlight long-lived pockets of high trust and deep distrust in institutions, as well as abrupt, shock-induced shifts between the two. We propose a probabilistic model in which such phenomena emerge endogenously from social learning on hierarchical networks. Starting from a discrete model on a directed acyclic graph, where each agent makes a binary adoption decision about a single assertion, we derive an effective influence kernel that maps individual priors to stationary adoption probabilities. A continuum limit along hierarchical depth yields a degenerate, non-conservative logistic–diffusion equation for the adoption probability u(x,t), in which diffusion is modulated by (1−u) and increases the integral of u rather than preserving it. To account for micro-level uncertainty, we perturb these dynamics by multiplicative Stratonovich noise with amplitude proportional to u(1−u), strongest in internally polarised layers and vanishing at consensus. At the level of a single depth layer, Stratonovich–Itô conversion and Fokker–Planck analysis show that the noise induces an effective double-well potential with two robust stochastic phases, u≈0 and u≈1, corresponding to persistent distrust and trust. Coupled along depth, this local bistability and degenerate diffusion generate extended domains of trust and distrust separated by fronts, as well as rare, Kramers-type transitions between them. We also formulate the associated stochastic partial differential equation in Martin–Siggia–Rose–Janssen–De Dominicis form, providing a field-theoretic basis for future large-deviation and data-informed analyses of trust landscapes in hierarchical societies.

Dynamics doi: 10.3390/dynamics6010003

Authors: Mauro Pontani Giulio De Angelis Edoardo Maria Leonardi

Multi-revolution Lambert solvers are intended to find the elliptic transfer orbits that are traveled multiple times and connect two specified positions in prescribed time, under the assumption of considering natural (Keplerian) orbital motion in the presence of a single attracting body. This study proposes and tests a new, effective multi-revolution Lambert solver that employs the initial true anomaly, which identifies the initial position along the transfer ellipse, as the unknown variable. The related search interval is identified through closed-form expressions for upper and lower bounds. A simple numerical algorithm is developed and employed over the entire search interval to detect all Lambert solutions. The new multi-revolution solver proposed in this work is simple to understand and easy to implement and is successfully tested in several challenging scenarios (corresponding to some pathological cases reported in the recent scientific literature), as well as for the study of Earth–Mars interplanetary transfers. Comparison with alternative, up-to-date techniques points out that the new approach at hand is able to detect all the feasible transfer ellipses, in all cases, with very satisfactory accuracy in terms of final position error, even in challenging scenarios that include a huge number of revolutions or near-antipodal terminal positions.

Dynamics doi: 10.3390/dynamics6010002

Authors: Athanasios V. Serafeim Nikolaos Th. Fourniotis Demetris Stergiopoulos Andreas Langousis

The uneven distribution of flow in water distribution networks (WDNs) can cause inefficient flows and pressure imbalances as well as degraded water quality in areas where demand is higher than the networks’ design limit. In this study, two faulty connections within a WDN in Greece that exhibited unusual geometric shapes favoring preferential flow paths were investigated. The three-dimensional computational fluid dynamics simulations were performed in ANSYS Fluent solver (v. 23.1) to study the internal behavior of this network for steady-state flows. The standard k-ε model was employed to calculate turbulence and energy losses in this network. In Connection A, which is a cross-shaped junction with two inlets and two outlets, and in Connection B, which is a complex 4 → 1 → 4 manifold connection, more than 80% of total inflow was found to be directed to a single outlet. The pressure contour plots revealed that this is due to the large total head losses associated with pronounced changes in flow direction. The role of explicit junction losses in network modeling and network improvements to improve hydraulic behavior has thereby gained prominence through this study. The applicability and capability of computational fluid dynamics in characterizing complex flow problems in urban WDNs have thereby proven to be significant.

Dynamics doi: 10.3390/dynamics6010001

Authors: Diego S. de la Vega Lizbeth Vargas-Cabrera Olga G. Félix-Beltrán Jesus M. Munoz-Pacheco

Circuit implementation is a widely accepted method for validating theoretical insights observed in chaotic systems. It also serves as a basis for numerous chaos-based engineering applications, including data encryption, random number generation, secure communication, neuromorphic computing, and so forth. To get feasible, compact, and cost-effective circuit implementations of chaotic systems, the underlying mathematical model may be simplified while preserving all rich nonlinear behaviors. In this framework, this manuscript presents a simplified Hopfield Neural Network (HNN) capable of generating a broad spectrum of complex behaviors using a minimal number of electronic elements. Based on Shil’nikov’s theorem for heteroclinic orbits, the number of non-zero synaptic connections in the matrix weights is reduced, while simultaneously using only one nonlinear activation function. As a result of these simplifications, we obtain the most compact electronic implementation of a tri-neuron HNN with the lowest component count but retaining complex dynamics. Comprehensive theoretical and numerical analyses by equilibrium points, density-colored continuation diagrams, basin of attraction, and Lyapunov exponents, confirm the presence of periodic oscillations, spiking, bursting, and chaos. Such chaotic dynamics range from single-scroll chaotic attractors to double-scroll chaotic attractors, as well as coexisting attractors to transient chaos. A brief security application of an S-Box utilizing the presented HNN is also given. Finally, a physical implementation of the HNN is given to confirm the proposed approach. Experimental observations are in good agreement with numerical results, demonstrating the usefulness of the proposed approach.

Dynamics doi: 10.3390/dynamics5040054

Authors: Carlos Alejandro Velázquez-Morales Luis Hernández-Martínez Esteban Tlelo-Cuautle Luis Gerardo de la Fraga

The proposed work introduces a sizing algorithm to achieve a desired linear transconductance in the optimization of operational transconductance amplifiers (OTAs) by applying the gm/ID method to find the initial width (W) and length (L) sizes of the transistors. These size values are used to run the non-dominated sorting genetic algorithm (NSGA-II) to perform a multi-objective optimization of three OTA topologies. The gm/ID method begins with transistor characterization using MATLAB R2024a generated look-up tables (LUTs), which map normalized transconductance of the transistor channel dimensions, and key performance metrics of a complementary metal–oxide–semiconductor (CMOS) technology. The LUTs guide the initial population generation within NSGA-II during the optimization of OTAs to achieve not only a desired transconductance but also accuracy alongside linearity, high DC gain, low power consumption, and stability. The feasible W/L size solutions provided by NSGA-II are used to enhance the CMOS design of a memristor emulator, where the OTA with the desired transconductance is adapted to tune the behavior of the memristor, demonstrating improved pinched hysteresis loop characteristics. In addition, process, voltage and temperature (PVT) variations are performed by using TSMC 180 nm CMOS technology. The memristor-based on optimized OTAs is used to design a Leaky Integrate-and-Fire (LIF) neuron, which produces identical spike counts (seven spikes) under the same input conditions, though the time period varied with a CMOS inverter scaling. It is shown that increasing transistor widths by 100 in the inverter stage, the spike quantity is altered while changing the spiking period. This highlights the role of device sizing in modulating LIF neuron dynamics, and in addition, these findings provide valuable insights for energy-efficient neuromorphic hardware design.

Dynamics doi: 10.3390/dynamics5040053

Authors: Guillermo Chacón-Acosta Adrian Perez-Rodriguez

Diffusion on curved surfaces deviates from the flat case due to geometrical corrections in the evolution of its moments, such as the geodesic mean square displacement. Moreover, anomalous diffusion is widely used to model transport in disordered, confined, or crowded environments and can be described by a temporal subordination scheme, leading to a time-fractional diffusion equation. In this work, we analyze the dynamics of time subordinated anomalous diffusion on curved surfaces. By using a generalized Taylor expansion with fractional derivatives in the Caputo sense, we express the moments as a temporal power series and show that the anomalous exponent couples with curvature terms, leading to a competition between geometric and anomalous effects. This coupling indicates a mechanism through which curvature modulates anomalous transport.

Dynamics doi: 10.3390/dynamics5040052

Authors: Sunder Lal Meena Radhey Shyam Jangid

This research investigates the seismic behavior of continuous-span base-isolated bridges integrated with fluid inerter damper (FID) through a linear analytical framework under recorded earthquake excitations. The resisting mechanism of the FID is modelled as a combination of inertial and viscous forces, which are functions of the relative acceleration and velocity between connected nodes. Linear time-history simulations and a series of parametric analyses are conducted to examine how variations in inertance, damping ratio, and installation location affect key seismic response parameters, including deck acceleration, bearing displacement, and substructure base shear. Comparative analyses with conventional viscous dampers and isolation alone establish the relative effectiveness of FID. Analysis indicates that FID effectively reduces deck accelerations through apparent mass amplification, suppresses bearing displacements via viscous damping, and redistributes seismic forces depending on placement strategies. An optimum inertance range is identified that minimizes accelerations without amplifying base shear, with abutment-level placement proving most effective for pier shear control, while intermediate placement provides balanced reductions. Overall, FID consistently outperforms viscous dampers and conventional isolation, underscoring their potential as an advanced inerter-based solution for both new bridge design and retrofit applications.

Dynamics doi: 10.3390/dynamics5040050

Authors: Illiani Carro-Pérez Juan Gonzalo Barajas-Ramírez

In this study, we explore the emergence of generalized synchronization (GS) in arrays of Hindmarsh–Rose (HR) neurons that are coupled through memristive synapses. We design coupling functions utilizing active memristors to facilitate GS in a bidirectionally coupled two-neuron memristive neural network (MNN). Our analysis employs a nearest neighbor (NN) approach. Our findings indicate that there is a threshold coupling strength for the active memristive synapses required to achieve GS. Additionally, we investigate how memristor parameters affect the temporal characteristics of synchronized neuronal firing patterns. Specifically, we discover that the interburst interval (IBI) is directly proportional to the coupling strength of the memristive synapses, while the interspike interval (ISI) is inversely proportional to this strength.

Dynamics doi: 10.3390/dynamics5040051

Authors: Marco A. Tapia-Valerdi Irán Ramos-Prieto Francisco Soto-Eguibar Héctor M. Moya-Cessa

We provide an analytical framework for describing the propagation of light in waveguide arrays, considering both infinite and semi-infinite cases. The interaction up to second neighbors is taken into account, which provides a more realistic setup. We show that these solutions follow a distinctive structural pattern. This pattern reflects a transition from conventional Bessel functions to the lesser-known one-parameter generalized Bessel functions, offering new insights into the propagation dynamics in these systems.

Dynamics doi: 10.3390/dynamics5040049

Authors: Matthaios Katsanikas Stephen Wiggins

In this paper, we study the different types of trajectories that correspond to a particular orbital behavior of caldera-type Hamiltonian systems. This particular orbital behavior is dynamical matching. Dynamical matching is an important chemical phenomenon that is encountered in many caldera-type organic chemical reactions. In this paper we will distinguish the different types of trajectories that correspond to this phenomenon using periodic orbit dividing surfaces.

Dynamics doi: 10.3390/dynamics5040048

Authors: Gui-Lin She Lei-Lei Gan

This study investigates the combined resonance phenomenon in magneto-electro-elastic (MEE) cylindrical shells under longitudinal and lateral excitations with thermal factors, addressing the complex interaction between mechanical, electrical, and magnetic fields in smart structures. The research aims to establish a theoretical framework for predicting resonance behaviors in energy harvesting and sensing applications. Using Maxwell’s equations and Hamilton’s principle, the governing equations for combined resonance are derived. The method of varying amplitude (MVA) is employed to acquire the combined resonance response across varying parameters. Furthermore, the Runge–Kutta method is applied to investigate the bifurcation and chaotic motion characteristics under different longitudinal and lateral excitation conditions. Key findings reveal the coupling effects of multi-physical fields on resonance frequencies, demonstrating quantitative agreement with prior studies. The results provide fundamental insights into the dynamic characteristics of MEE materials, offering theoretical support for optimizing their performance in adaptive engineering systems.

Dynamics doi: 10.3390/dynamics5040047

Authors: Chamalka Dharmasiri Upeksha Perera

We develop a four-dimensional nonlinear model of a reflexive financial system by extending the Xin–Zhang system with a self-reinforcing sentiment channel. The model comprises four interacting variables—interest rate, investment demand, price index, and market confidence—and incorporates reflexivity to capture feedback between economic fundamentals and investor sentiment. A Lyapunov function shows that the system is well-posed and dissipative, ensuring bounded trajectories. We then analyse the dynamics using standard nonlinear-dynamics tools. Reflexive confidence sustains chaotic motion, inhibits convergence to equilibria, and produces irregular, aperiodic bifurcation patterns; sentiment-driven feedback destabilises a dissipative macroeconomic model and sustains volatility, as evidenced by a positive largest Lyapunov exponent and Kolmogorov–Sinai entropy greater than zero. Using U.S. monthly consumer sentiment and the S&P 500, we observe co-movement, a medium-horizon lead of sentiment, and a nonlinear persistence map wt+1=f(wt)—stylised facts consistent with the model’s self-reinforcing confidence channel.

Dynamics doi: 10.3390/dynamics5040046

Authors: Edward Bormashenko Ramita Sarkar Mark Frenkel Shraga Shoval

We propose a Ramsey approach to the dimensional analysis of physical systems, which complements the seminal Buckingham theorem. Dimensionless constants describing a given physical system are represented as vertices of a graph, referred to as a dimensions graph. Two vertices are connected by an aqua-colored edge if they share at least one common dimensional physical quantity and by a brown edge if they do not. In this way, a bi-colored complete Ramsey graph is obtained. The relations introduced between the vertices of the dimensions graph are non-transitive. According to the Ramsey theorem, a monochromatic triangle must necessarily appear in a dimensions graph constructed from six vertices, regardless of the order of the vertices. Mantel–Turán analysis is applied to study these graphs. The proposed Ramsey approach is extended to graphs constructed from fundamental physical constants. A physical interpretation of the Ramsey analysis of dimensions graphs is suggested. A generalization of the proposed Ramsey scheme to multi-colored Ramsey graphs is also discussed, along with an extension to infinite sets of dimensionless constants. The introduced dimensions graphs are invariant under rotations of reference frames, but they are sensitive to Galilean and Lorentz transformations. The coloring of the dimensions graph is independent of the chosen system of units. The number of vertices in a dimensions graph is relativistically invariant and independent of the system of units.

Dynamics doi: 10.3390/dynamics5040045

Authors: Andrii Slipchuk Petro Pukach Myroslava Vovk

The problem of nonlinear elastic transverse oscillations of a beam moving along its axis and subjected to an axial compressive or tensile force is considered. A theoretical study is carried out using the asymptotic method of nonlinear mechanics KBM (Krylov–Bogolyubov–Mitropolsky). Using this methods, differential equations were obtained in a standard form, determining the law of variation in amplitude and frequency as functions of kinematic, force, and physico-mechanical parameters in both resonant and non-resonant regimes. The fourth-order Runge–Kutta method was applied for the oscillatory system numerical analysis. The computation of complex mathematical expressions and graphical representation of the results were implemented in the mathematical software Maple 15. The results obtained can be applied for engineering calculations of structures containing moving beams subjected to compressive or tensile forces.

Dynamics doi: 10.3390/dynamics5040044

Authors: Umida Baltaeva Bobur Khasanov Omongul Egamberganova Hamrobek Hayitbayev

We investigate the Cauchy problem for a heat equation incorporating variable diffusion coefficients and fractional memory effects modeled by a separable convolution kernel. By employing the fundamental solution of the associated parabolic equation, the problem is reformulated as a Volterra-type integral equation. Under appropriate regularity assumptions, we establish existence and uniqueness of classical solutions. Furthermore, we address an inverse problem aimed at simultaneously recovering the memory kernel and the solution. Using a differentiability-based approach, we derive a stable and well-posed formulation that enables the identification of memory effects in fractional heat models.

Dynamics doi: 10.3390/dynamics5040043

Authors: Luis Manuel Lopez-Jimenez Esteban Tlelo-Cuautle Luis Fortino Cisneros-Sinencio Alejandro Diaz-Sanchez

This paper presents two classic analog oscillators: a relaxation oscillator and a Wien bridge one, where a memristor replaces a resistor. The circuits are simulated in TopSPICE 7.12 using a memristor emulation circuit and commercially available components to evaluate the memristor’s impact. In the case of the relaxation oscillator, which includes the memristor, a notable increase in oscillation frequency was observed compared to the classical circuit, with a nearly 10-fold increase from 790 Hz to 7.78 kHz while maintaining a constant amplitude. This confirms the influence of the memristor’s dynamic resistance on the circuit time constant. On the other hand, the Wien-bridge oscillator exhibits variations in specific parameters, such as peak voltage, amplitude, and frequency. In this case, the oscillation frequency decreased from 405 Hz to 146 Hz with the addition of the memristor, a characteristic introduced by the proposed memristive element’s nonlinear interactions. Experimental results confirm the feasibility of incorporating memristors into classical oscillator circuits, enabling frequency changes while maintaining stable oscillations, allowing reconfigurable and adaptable analog designs that leverage the properties of memristive devices.

Dynamics doi: 10.3390/dynamics5040042

Authors: Oleksiy Kuznyetsov

The dynamics of port-Hamiltonian systems is based on energy balance principles (the first law of thermodynamics) embedded in the structure of the model. However, when dealing with thermodynamic subsystems, the second law (entropy production) should also be explicitly taken into account. Several frameworks were developed as extensions to the thermodynamic domain of port-Hamiltonian systems. In our work, we study three of them, namely irreversible port-Hamiltonian systems, entropy-based generalized Hamiltonian systems, and entropy-production-metric-based port-Hamiltonian systems, which represent alternative approaches of selecting the state variables, the storage function, simplicity of physical interpretation, etc. On the example of a simplified lumped-parameter model of a heat exchanger, we study the frameworks in terms of their implementability for an IDA-PBC-like control and the simplicity of using these frameworks for practitioners already familiar with the port-Hamiltonian systems. The comparative study demonstrated the possibility of using each of these approaches to derive IDA-PBC-like thermodynamically consistent control and provided insight into the applicability of each framework for the modeling and control of multiphysics systems with thermodynamic subsystems.

Dynamics doi: 10.3390/dynamics5040041

Authors: Adriana Sofia Rodríguez-Pérez Héctor Eduardo Gilardi-Velázquez Stephanie Esmeralda Velázquez-Pérez

Burns represent a significant medical challenge, and the development of theoretical models has the potential to contribute to the advancement of new diagnostic tools. This study aimed to perform numerical simulations of the Pennes bioheat transfer equation, incorporating heat generation terms due to the body’s immunological response to thermal injury, as well as changes in skin thermal parameters and blood perfusion for each burn type. We propose the incorporation of specific parameters and boundary conditions related to multilayer perfusion into the Pennes bioheat model. Using the proposed layered skin model, we evaluate temperature differences to establish correlations for determining burn depth. In this investigation, 1D and 3D algorithms based on the finite volume method were applied to capture transient and spatial thermal variations, with the resulting temperature distributions demonstrating the ability of the proposed models to describe the expected thermal variations in healthy and burned tissue. This work demonstrates the potential of the finite volume method to approximate the solution of the Pennes biothermal equation. Overall, this study provides a computational framework for analyzing heat transfer in burn injuries and highlights the relevance of mathematical simulations as a tool for future research on infrared thermography in medicine.

Dynamics doi: 10.3390/dynamics5040040

Authors: Abdul-Basset A. Al-Hussein Fadhil Rahma Tahir Hamzah Abdulkareem Abbood Mazin Majid Abdulnabi Viet-Thanh Pham

This paper investigates the nonlinear dynamics behavior and practical realization of a V/Heart-shape chaotic system. Nonlinear analysis contemporary tools, including bifurcation diagram, Lyapunov exponents, phase portraits, power spectral density (PSD) bicoherence, and spectral entropy (SE), are employed to investigate the system’s complex dynamical behaviors. To discover the system’s versatility, two case studies are presented by varying key system parameters, revealing various strange attractors. The system is modeled and implemented using an industrial-grade programmable logic controller (PLC) with structured text (ST) language, enabling robust hardware execution. The dynamics of the chaotic system are simulated, and the results are rigorously compared with experimental data from laboratory hardware implementations, demonstrating excellent agreement. The results indicate the potential usage of the proposed chaotic system for advanced industrial applications, secure communication, and dynamic system analysis. The findings confirm the successful realization of the V-shape and Heart-shape Chaotic Systems on PLC hardware, demonstrating consistent chaotic behavior across varying parameters. This practical implementation bridges the gap between theoretical chaos research and real-world industrial applications.

Dynamics doi: 10.3390/dynamics5030039

Authors: Juanjuan Ma Limei Qi Hongqiang Dong Ting Liu Mei Zeng

Chemical synaptic coupling is crucial in the nervous system. This paper establishes a chemical synaptic Chay neuronal coupling system using the Heaviside function and analyzes the equilibrium point’s type and stability based on the Jacobian matrix. Matcont simulation found that the Hopf bifurcation point transformed into a Bogdanov–Takens bifurcation point under the influence of chemical coupling strength, and a series of saddle-node bifurcation points are generated. The discharge time history of the system and the evolution of single-parameter bifurcation behavior were numerically simulated through a language and Matlab. The parameter matching results indicated that the chemical synaptic reversible potentials and synaptic thresholds were −15 mV and −35 mV, respectively. The bifurcation behavior and its changes under multi-parameter conditions were studied by using various numerical methods such as time series diagrams, bifurcation diagrams, and two-parameter diagrams. The similarity function identified key factors affecting synchrony in a chemical synaptic coupling system. Results indicate that synchrony primarily depends on chemical coupling strength, with other factors providing positive feedback to enhance it. The simulation of the spatiotemporal dynamics in a chemically synaptic coupled network of 2000 ring neurons revealed that altering the maximum conductance at local positions within the network can induce the generation of traveling waves. Strong coupling strengths ensure that the induced traveling waves propagate at greater velocities and can excite and awaken a larger number of neurons in a shorter time frame. The nonlinear properties of chemical synaptic neuronal system offer essential tools and foundations for studying neurobiology and brain dynamics.

Dynamics doi: 10.3390/dynamics5030038

Authors: Fernando C. Pérez-Cárdenas

The Fluctuation Theorem establishes a relationship between microscopic reversibility and macroscopic irreversible phenomena, such as dissipation. In this short paper, we present an elementary derivation of this theorem within the framework of stochastic thermodynamics. Beginning with a brief examination of the time-reversible laws of motion that rule at the microscopic level, we discuss how through coarse-graining we arrive at the principle of detailed balance. This principle, which was originally proved for equilibrium processes, is extended to out-of-equilibrium situations in order to arrive at the Fluctuation Theorem. Though this extension is theoretically sound, one of the main purposes of this paper is to show that the origin of the practical limitations encountered, when applying this theorem to processes lasting longer than a certain duration, can be explained by the paucity of unlikely events that arise in out-of-equilibrium processes. The numerical results from the one-dimensional, one-particle stochastic model that is introduced here agree very well with the Fluctuation Theorem and, at the same time, bring to light the limits of its applicability in relation to the number of simulations or experiments and the duration of the process under study.

Dynamics doi: 10.3390/dynamics5030037

Authors: Vhahangwele Colleen Sigonde Desejo Filipeson Sozinando Bernard Xavier Tchomeni Alfayo Anyika Alugongo

Gear transmission error (GTE) is a critical factor influencing the performance and service life of gear systems, as it directly contributes to vibration, noise generation, and premature wear. The present study introduces a combined theoretical and experimental approach to characterizing GTE in a single-stage spur gear system. A six-degree-of-freedom nonlinear dynamic model was formulated to capture coupled lateral–torsional vibrations, accounting for gear mesh stiffness, bearing and coupling characteristics, and a harmonic transmission error component representing manufacturing and assembly imperfections. Simulations and experiments were conducted under healthy and eccentricity-faulted conditions, where a controlled 890 g eccentric mass induced misalignment. Frequency domain inspection of faulty gear data showed pronounced sidebands flanking the gear mesh frequency near 200 Hz, as well as harmonics extending from 500 Hz up to 1200 Hz, in contrast with the healthy case dominated by peaks confined to 50–100 Hz. STFT analysis revealed dispersed spectral energy and localized high-intensity regions, reinforcing its role as an effective fault diagnostic tool. Experimental findings aligned with theoretical predictions, demonstrating that the integrated modelling and time–frequency framework is effective for early fault detection and performance evaluation of spur gear systems.

Dynamics doi: 10.3390/dynamics5030036

Authors: Maria Eduarda F. Capponero Giovani D. Telli Elizaldo D. dos Santos Liércio A. Isoldi Mateus das Neves Gomes Cesare Biserni Luiz Alberto O. Rocha

The energy potential of sea waves has gained relevance, leading to extensive research on converters. The present work analyzes the contribution of Constructal Design to the development of wave energy converters. Constructal Design utilizes performance indicators to enhance system efficiency by varying the degrees of freedom where flow occurs. Thus, the systematic literature review methodology was applied to gather a collection of documents focused on the research topic. This study identified articles published between 2014 and 2024 by 40 authors affiliated with institutions in Brazil, Italy, and Portugal. The oscillating water column (OWC) converter received the most research attention, followed by the overtopping converter. Analyzing the documents collected for this study, the performance indicators revealed improvements ranging from 1.19 to 839 times, indicating the lowest and highest enhancements observed, respectively. The Constructal Design method has proven highly effective in identifying specific architectures or geometric arrangements that enhance flow configuration and improve the performance of wave energy converters. However, relatively few studies have applied the Constructal Design method to wave energy converters in comparison to other methodologies, presenting a significant opportunity for future research.

Dynamics doi: 10.3390/dynamics5030035

Authors: Gheorghe Maria Daniela Gheorghe Crina Muscalu Andreea Scoban

Currently, D-fructose (DF) is produced through enzymatic isomerization of beta-D-glucose (DG) under disadvantageous conditions (equilibrium conversion of 50%, costly separation, etc.). Alternatively, the two-step Cetus enzymatic process became a promising approach for producing high-purity DF. First, DG is oxidized to keto-glucose (kDG) using commercial pyranose 2-oxidase (P2Ox). To avoid the fast P2Ox inactivation by the in situ produced hydrogen peroxide, catalase is added to decompose this byproduct. The DG oxidation occurs with high conversion and selectivity, leading to kDG free of allergenic aldose compounds. Then, kDG is reduced to DF by using the NADPH cofactor and aldose reductase (ALR). This study aims to evaluate the continuous in situ regeneration of NADPH at the expense of formate decomposition in the presence of formate dehydrogenase (FDH). By adopting a kinetic model from literature, this in silico analysis determines the optimal operation of a batch reactor (BR) used in the Cetus second step to maximize the DF production and minimize the consumption of costly NADPH. Compared to its simple operation, the optimized BR with cofactor regeneration reported a 25% lower NADPH consumption, though the amount of the processed substrate is ca. 3× higher. Also, the costly enzymes (ALR, FDH) consumption is 2× smaller.

Dynamics doi: 10.3390/dynamics5030034

Authors: Maximilian T. Meyer Arno Schindlmayr

Miller’s rule originated as an empirical relation between the nonlinear and linear optical coefficients of materials. It is now accepted as a useful tool for guiding experiments and computational materials discovery, but its theoretical foundation had long been limited to a derivation for the classical Lorentz model with a weak anharmonic perturbation. Recently, we developed a mathematical framework which enabled us to prove that Miller’s rule is equally valid for quantum anharmonic oscillators, despite different dynamics due to zero-point fluctuations and further quantum-mechanical effects. However, our previous derivation applied only to one-dimensional oscillators and to the special case of second- and third-harmonic generation in a monochromatic electric field. Here we extend the proof to three-dimensional quantum anharmonic oscillators and also treat all orders of the nonlinear response to an arbitrary multi-frequency field. This makes the results applicable to a much larger range of physical systems and nonlinear optical processes. The obtained generalized Miller formulae rigorously express all tensor elements of the frequency-dependent nonlinear susceptibilities in terms of the linear susceptibility and thus allow a computationally inexpensive quantitative prediction of arbitrary parametric frequency-mixing processes from a small initial dataset.

Dynamics doi: 10.3390/dynamics5030033

Authors: Thibaut Torres Yasser Diab Christophe Changenet Thomas Touret Bérengère Guilbert

This study aims to develop a new model for windage losses, building upon existing formulation, complemented by dedicated experimental campaigns and a specific methodology designed to isolate and quantify windage losses. The model relies on an analytical approach to flow characterization, incorporating a correction factor accounting for air density reduction. The experimental investigation was carried out on a dedicated test bench and includes both spur and helical gears. The results demonstrate good agreement between the proposed model and the experimental data, with and without the presence of nearby obstacles, such as side flanges, highlighting the model’s robustness across different configurations. The proposed windage loss model reproduces the experimental results with significantly greater accuracy than the original one, yielding relative deviations below 5% compared to almost 20% for spur gears, and below 9% compared to over 21%, and in some cases up to 50%, for helical gears.

Dynamics doi: 10.3390/dynamics5030032

Authors: Shigetoshi Nara Naoya Miyahara Yutaka Yamaguti Ichiro Tsuda

The high-dimensional chaos generated in a neural network consisting of pseudo-neuron devices invented by one of the authors (S.N.) has been successfully applied to control the complex motion of a roving robot, e.g., to solve a maze, as reported in the previous papers. On the basis of successful works and the concept that chaos plays important functional roles in biological systems, in the present paper, we report new experiments to show the functional aspects of chaos via behavioral interactions in an ill-posed context and solve problems with chaotic neural networks. Explicitly, experiments on two roving robots in a maze (labyrinth) are reported, in which both seek to catch each other or one chases and the other flees, mimicking the survival activities of insects in natural environments. The two-dimensional robot motion is controlled with motion control systems, each of which is equipped with a chaotic neural network to generate autonomous and adaptive actions depending on sensor inputs of obstacles and/or target detection information including uncertainty. We report both computer experiments and practical hardware implementations, where for the latter, only the chaotic neural network is run on a desktop computer, the motion signals are coded into two-dimensional space, and sensor signals are transferred via Bluetooth device between robots and computers.

Dynamics doi: 10.3390/dynamics5030031

Authors: Aleksander Stefanov Stanislav Varbev

We derive a new exactly solvable multi-component system of non-linear evolution equations (NLEEs). The system consists of three 1+1-dimensional evolution equations—one first-order and two second-order in the spatial variable. We review their Lax representation, formulate the scattering problem, and derive the soliton-like solutions of the system.

Dynamics doi: 10.3390/dynamics5030030

Authors: Qing Gu Zeqi Wu Yongquan Li Huo Tao Boyu Li Wen Li

This work systematically addresses the dual challenges of non-inertial dynamic coupling and kinematic constraint redundancy encountered in dynamic modeling of serial–parallel–serial hybrid robotic mechanisms, and proposes an improved Newton–Euler modeling method with constraint compensation. Taking the Skiing Simulation Platform with 6-DOF as the research mechanism, the inverse kinematic model of the closed-chain mechanism is established through GF set theory, with explicit analytical expressions derived for the motion parameters of limb mass centers. Introducing a principal inertial coordinate system into the dynamics equations, a recursive algorithm incorporating force/moment coupling terms is developed. Numerical simulations reveal a 9.25% periodic deviation in joint moments using conventional methods. Through analysis of the mechanism’s intrinsic properties, it is identified that the lack of angular momentum conservation constraints on the end-effector in non-inertial frames leads to system controllability degradation. Accordingly, a constraint compensation strategy is proposed: establishing linearly independent differential algebraic equations supplemented with momentum/angular momentum balance equations for the end platform. Co-Simulation results demonstrate that the optimized model reduces the maximum relative error of actuator joint moments to 0.98%, and maintains numerical stability across the entire configuration space. The constraint compensation framework provides a universal solution for dynamics modeling of complex closed-chain mechanisms, validated through applications in flight simulators and automotive driving simulators.

Dynamics doi: 10.3390/dynamics5030029

Authors: Italo Guarneri

Schmidt entropy is used as a common denotation for all Hilbert space entropies that can be defined via the Schmidt decomposition theorem; they include quantum entanglement entropies and classical separability entropies. Exact results about the asymptotic growth in time of such entropies (in the form of Renyi entropies of any order ≥1) are directly derived from the Schmidt decompositions. Such results include a proof that pure point spectra entail boundedness in time of all entropies of order larger than 1; and that slower than exponential transport forbids faster than logarithmic asymptotic growth. Applications to coupled Quantum Kicked Rotors and to Floquet systems are presented.

Dynamics doi: 10.3390/dynamics5030028

Authors: Aslam Abdullah Mohd Fadhli Zulkafli Muhammad Akmal Abdul Halim Ramanathan Ashwin Thanneermalai Bambang Basuno

Mid-altitude sounding rockets are essential for atmospheric research and suborbital experimentation, where aerodynamic optimization and structural integrity are crucial for achieving targeted apogees. This study uses OpenRocket v23.09 for preliminary flight performance prediction and SolidWorks 2024 to integrate aerodynamic and structural analyses through Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA). SolidWorks Flow Simulation and SolidWorks Simulation are used to assess how nose cone and fin geometries, as well as thermal deformation, influence flight performance. Among nine tested configurations, the ogive nose cone with trapezoidal fins achieved the highest simulated apogee of 2639 m, with drag coefficients of 0.480 (OpenRocket) and 0.401 (SolidWorks Flow Simulation). Thermal–structural analysis revealed a maximum nose tip displacement of 0.7249 mm for the rocket with the ogive nose cone, leading to an increasing drag coefficient of 0.404. However, thermal deformation of the ellipsoid nose cone led to a reduction in the drag coefficient from 0.419 to 0.399, even though it exhibited a slightly higher maximum displacement of 0.7443 mm. Mesh independence was confirmed with outlet velocity deviations below 1% across refinements. These results highlight the importance of integrated CFD–FEA approaches, geometric optimization, and material resilience for enhancing the aerodynamic performance of subsonic sounding rockets.

Dynamics doi: 10.3390/dynamics5030027

Authors: Dimitri Volchenkov

We advance a mathematical framework for collective conviction by deriving a continuum theory from the network-based model introduced by us recently. The resulting equation governs the evolution of belief through a degenerate anisotropic logistic–diffusion process, where diffusion slows as conviction saturates. In one spatial dimension, we prove global well-posedness, demonstrate spectral front pinning that arrests the spread of influence at finite depth, and construct explicit traveling-wave solutions. In two dimensions, we uncover a geometric mechanism of curvature–induced quenching, where belief propagation halts along regions of low effective mobility and curvature. Building on this insight, we formulate a variational principle for optimal control under resource constraints. The derived feedback law prescribes how to spatially allocate repression effort to maximize inhibition of front motion, concentrating resources along high-curvature, low-mobility arcs. Numerical simulations validate the theory, illustrating how localized suppression dramatically reduces transverse spread without affecting fast axes. These results bridge analytical modeling with societal phenomena such as protest diffusion, misinformation spread, and institutional resistance, offering a principled foundation for selective intervention policies in structured populations.

Dynamics doi: 10.3390/dynamics5030026

Authors: Cresus Fonseca de Lima Godinho Claudio Maia Porto Marcos Cardoso Rodriguez Ion Vasile Vancea

The recently proposed conformable deformation of quantum mechanics by a fractional parameter α∈(0,1] has been used to construct a conformable quantum harmonic oscillator, which coincides with the standard quantum oscillator at α=1. We argue that there is a conformable generalization of the uncertainty principle and use it to define the conformable coherent states of the conformable quantum oscillator along the general line of quantum mechanics. We investigate the fundamental physical and mathematical properties of these states in the xα-representation. In particular, we determine these states from the minimum uncertainty, compute their energy, find their conformable time-dependent form, determine the conformable translation operator, and show that conformable coherent states are eigenstates of the conformable annihilation operator. These states reproduce in the α=1 limit of the correspondence principle the coherent states of the standard quantum harmonic oscillator.

Dynamics doi: 10.3390/dynamics5030025

Authors: Marco A. Tapia-Valerdi Irán Ramos-Prieto Francisco Soto-Eguibar Héctor M. Moya-Cessa

We present an analytical framework for describing light propagation in infinite waveguide arrays, incorporating a generalized long-range coupling to achieve a more realistic model. We demonstrate that the resulting solution can be expressed in terms of generalized Bessel-like functions. Additionally, by applying the concept of eigenstates, we borrow from quantum mechanics a basis given in terms of phase states that allows the analysis of the transition from the discrete to the continuum limit, obtaining a relationship between the field amplitudes and the Fourier series coefficients of a given function. We apply our findings to different coupling functions, providing new insights into the propagation dynamics of these systems.

Dynamics doi: 10.3390/dynamics5030024

Authors: Gabriel Antonio Felipe Carlos Alberto Valentim Sergio Adriani David

Fractional modeling has emerged as an important resource for describing complex phenomena and systems exhibiting non-local behavior or memory effects, finding increasing application in several areas in physics and engineering. This study presents the analytical derivation of equations pertinent to the modeling of different systems, with a focus on heat conduction. Two specific boundary value problems are addressed: a Helmholtz equation modified with a fractional derivative term, and a fractional formulation of the Laplace equation applied to steady-state heat conduction in circular geometry. The methodology combines the separation of variables technique with fractional power series expansions, primarily utilizing the Caputo fractional derivative. An important aspect of this paper is its instructional emphasis, wherein the mathematical derivations are presented with detail and clarity. This didactic approach is intended to make the analytical methodology transparent and more understandable, thereby facilitating greater comprehension of the application of these established methods to non-integer-order systems. The final goal is not only to provide a different approach of solving these physical models analytically, but to provide a clear, guided pathway for those engaging in the treatment of fractional differential equations.

Dynamics doi: 10.3390/dynamics5030023

Authors: Getu Abyu Girum Urgessa Ameen Topa

This research explores how RC columns respond to blast-induced dynamic effects, with a novel focus on partially submerged scenarios, bridging a gap between air blast and underwater explosion (UNDEX) research. Using advanced finite element modeling in LS-DYNA, the study captures the unique behavior of RC columns under mixed-media conditions, where shockwaves propagate through water and air interfaces. Comprehensive parametric analyses explore the influence of charge size, blast stand-off, and depth of water, revealing distinct dampening mechanisms and structural responses. Key findings include a measurable reduction in peak displacement of partially submerged explosions compared to fully submerged explosions, attributed to the moderating effects of the water–air interface. A total of 60 simulation cases were conducted to systematically analyze partially submerged scenarios, providing robust insights into energy transmission and damage mechanisms. The numerical models, validated against published experimental data by others, demonstrate the accuracy of computational modeling in simulating damage profiles, displacement histories, and energy dissipation trends. This research offers practical implications for designing resilient RC structures in coastal and maritime environments. The results contribute significantly to the field of blast mechanics, advancing our understanding of mixed-media shockwave dynamics and their impact on critical infrastructure.

Dynamics doi: 10.3390/dynamics5020022

Authors: Karel Vokurka

The buoyancy of radially oscillating spark-generated bubbles is studied experimentally. Bubble sizes, defined as the maximum bubble radius, range from 26.6 to 52.1 mm, and the bubbles oscillate at a hydrostatic pressure of 127 kPa in a large expanse of liquid. We found that the position of these bubbles is relatively stable during the first two oscillations. They move upwards only in short time intervals when their size is, due to contraction, close to the minimum volume. The vertical movement, therefore, takes place in the form of steps. The relative heights of these steps, defined as the ratio of step heights to bubble size, increase with bubble size and range from 0.15 to 0.29. No significant deformations in the spherical shape of bubbles are observed during the first two oscillations.

Dynamics doi: 10.3390/dynamics5020021

Authors: Sarp Adali

A variational formulation and variationally consistent boundary conditions were derived for a coupled system of two boron nitride nanotubes (BNNTs), with the piezoelectric and surface effects taken into account in the formulation. The coupling between the nanotubes was defined in terms of Winkler and Pasternak interlayers. The equations governing the vibrations of the coupled system were expressed as a system of four partial differential equations based on nonlocal elastic theory. After deriving the variational principle for the double BNNT system, Hamilton’s principle was expressed in terms of potential and kinetic energies. Next, the differential equations for the free vibration case were presented and the variational form for this case was derived. The Rayleigh quotient was formulated for the vibration frequency, which indicated that piezoelectric and surface effects led to higher vibration frequencies. Next, the variationally consistent boundary conditions were formulated in terms of moment and shear force expressions. It was observed that the presence of the Pasternak interlayer between the nanotubes led to coupled boundary conditions when a shear force and/or a moment was specified at the boundaries.

Dynamics doi: 10.3390/dynamics5020020

Authors: Hong Wang Sunil Subedi Wenbo Jia

To address grid variability caused by renewable energy integration and to maintain grid reliability and resilience, hydropower must quickly adjust its power generation over short time periods. This changing energy generation landscape requires advance technology integration and adaptive parameter optimization for hydropower systems via digital twin effort. However, this is difficult owing to the lack of characterization and modeling for the nonlinear nature of hydroturbines. To solve this issue, this paper first formulates a six-coefficient Kaplan hydroturbine model and then proposes a parametric optimization tuning framework based on the Nelder–Mead algorithm for adaptive dynamic learning of the six-coefficients so as to build models that describe the turbine. To assess the performance of the proposed optimal parametric tuning technique, operational data from a real-world Kaplan hydroturbine unit are collected and used to model the relationship between the gate opening and the generated power production. The findings show that the proposed technique can effectively and adaptively learn the unknown dynamics of the Kaplan hydroturbine while optimally tune the unknown coefficients to match the generated power output from the real hydroturbine unit with an inaccuracy of less than 5%. The method can be used to provides optimal tuning of parameters critical for controller design, operational optimization and daily maintenance for hydroturbines in general.

Dynamics doi: 10.3390/dynamics5020019

Authors: Carmine Maria Pappalardo Giuseppe Isola Angela Donadio Rosario La Regina Valentino Paolo Berardi Domenico Guida

This research work aims to design and develop a dynamic vibration absorber that effectively reduces the vibrations of a flexible structure subjected to external loads. The analysis presented in this paper initially focuses on identifying the resonance frequencies of a typical structural system, which serves as the case study, since these frequencies are critical to dampening due to their potential to cause excessively large vibration amplitudes. Following this, the optimal parameters of the vibration absorber, including the mass, stiffness, and damping characteristics of the proposed design, were determined. Additionally, this paper proposes and examines the use of viscous-type damping, which is achieved through piston–cylinder systems connected to the structural components of the analyzed frame structure. Thus, the main contributions of this work include the analytical dimensioning, the technical design, and the virtual prototyping of a dynamic absorber constructed using a guyed mast structure capable of significantly reducing mechanical vibrations. This design solution ultimately enhances the strength and durability of the frame structure represented in the case study under external excitation, particularly in the worst-case scenario of seismic action. Furthermore, a key aspect of this study is implementing a new numerical procedure for identifying the system equivalent stiffness coefficient based on its mass and modal parameters, which is particularly useful in engineering applications. The numerical experiments conducted in this work support the effectiveness of the proposed design solution, devised specifically for the dynamic vibration absorber developed in this paper.

Dynamics doi: 10.3390/dynamics5020018

Authors: Boutros Azizi Habib Eslami Kais Jribi

An analytical study of the nonlinear response of imperfect stiffened doubly curved shells made of functionally graded material (FGM) is presented. The formulation of the problem is based on the first-order shear deformation shell theory in conjunction with the von Kármán geometrical nonlinear strain–displacement relationships. The nonlinear equations of the motion of stiffened double-curved shells based on the extended Sanders’s theory were derived using Galerkin’s method. The material properties vary in the direction of thickness according to the linear rule of mixture. The effect of both longitudinal and transverse stiffeners was considered using Lekhnitsky’s technique. The fundamental frequencies of the stiffened shell are compared with the FE solutions obtained by using the ABAQUS 6.14 software. A stepwise approximation technique is applied to model the functionally graded shell. The resulting nonlinear ordinary differential equations were solved numerically by using the fourth-order Runge–Kutta method. Closed-form solutions for nonlinear frequency–amplitude responses were obtained using He’s energy method. The effect of power index, functionally graded stiffeners, geometrical parameters, and initial imperfection on the nonlinear response of the stiffened shell are considered and discussed.

Dynamics doi: 10.3390/dynamics5020017

Authors: Dario Handrick Mattie Eckenrode Junsoo Lee

This paper presents a comprehensive review of tethered unmanned aerial vehicles (UAVs), focusing on their challenges and potential applications across various domains. We analyze the dynamic characteristics of tethered UAV systems and address the unique challenges they present, including complex tether dynamics, impulsive forces, and entanglement risks. Additionally, we explore application-specific challenges in areas such as payload transportation and ground-connected systems. The review also examines existing tethered UAV testbed designs, highlighting their strengths and limitations in both simulation and experimental settings. We discuss advancements in multi-UAV cooperation, ground–air collaboration through tethers, and the integration of retractable tether systems. Moreover, we identify critical future challenges in developing tethered UAV systems, emphasizing the need for robust control strategies and innovative solutions for dynamic and cluttered environments. Finally, the paper provides insights into the future potential of variable-length tethered UAV systems, exploring how these systems can enhance versatility, improve operational safety, and expand the range of feasible applications in industries such as logistics, emergency response, and environmental monitoring.

Dynamics doi: 10.3390/dynamics5020016

Authors: Christina Durón Hannah Kravitz Moysey Brio

In this work, we introduce an edge centrality measure for the Helmholtz equation on metric graphs, a particular flow network, based on spectral edge energy density. This measure identifies influential edges whose removal significantly changes the energy flow on the network, as indicated by statistically significant p-values from the two-sample Kolmogorov–Smirnov test comparing edge energy densities in the original network to those with a single edge removed. We compare the proposed measure with eight vertex centrality measures applied to a line graph representation of each metric graph, as well as with two edge centrality measures applied directly to each metric graph. Both methods are evaluated on two undirected and weighted metric graphs—a power grid network adapted from the IEEE 14-bus system and an approximation of Poland’s road network—both of which are multigraphs. Two experiments evaluate how each measure’s edge ranking impacts the energy flow on the network. The results demonstrate that the proposed measure effectively identifies influential edges in metric graphs that significantly change the energy distribution.

Dynamics doi: 10.3390/dynamics5020015

Authors: Gianluca Megna Luciano Cantone Andrea Bracciali

Buffer stops have always been installed on blind tracks to mitigate the hazards associated with overruns due to insufficient or wrong braking. Conventional buffer stops fixed to the rails may absorb only limited energy while Energy-Absorbing Buffers Stops (EABS) dissipate higher energy hydraulically and/or by friction from sliding blocks clamped to the rail head. The assessment of EABS performances in terms of maximum stopping distance and maximum allowed deceleration is usually performed by using the common kinematic rules of motion and considering the overrunning train as a single mass hitting the buffer stop. This paper studies the dynamic characteristics of the collision of entire trains with a friction EABS applying a Longitudinal Train Dynamics (LTD) approach. Several realistic scenarios using the UIC approved TrainDy software were simulated considering various train compositions, with different types of vehicles (locomotives, freight wagons and passenger coaches) and different kinds of buffers. The results show that high dynamic loads are exerted on the vehicles within the train, while the average deceleration and the stopping distance are not greatly influenced when compared with a simpler Finite Element Method (FEM) approach that does not consider the train composition. The progressive application of the EABS braking force increases the stopping distance but can reduce the peak deceleration of about 50%. The results may be used to tune the design parameters of friction EABS according to the currently available specifications and standards for rolling stock structural assessment considering that no international standards for EABS exist currently.

Dynamics doi: 10.3390/dynamics5020014

Authors: Rui Zhang Qingyuan Yang Hui Li Dazheng Zhang Siyu Zheng Shengyou Yang

As high-speed train operations increase, the aerodynamic pressure generated by these trains can jeopardize the structural integrity of sound barriers, potentially compromising train safety and the stability of nearby facilities. This paper investigates the unique aerodynamic pressures and load distribution of various types of sound barriers. We analyze the aerodynamic pressure distribution on sound barriers in relation to high-speed trains by utilizing Computational Fluid Dynamics (CFDs) analysis. We explore the theoretical foundations, design of the computational domain, and settings for boundary conditions. The findings indicate that high-speed trains generate both overpressure from compression waves and under pressure from expansion waves. As the barriers become more open, peak aerodynamic pressure and fluctuations decrease. Notably, the highest pressure occurs at the entrance of the barriers. The accuracy of the model is validated with data from a CRH series train traveling at 350 km/h. This paper offers valuable insights to enhance our understanding and improve sound barrier design for a quieter future.

Dynamics doi: 10.3390/dynamics5020013

Authors: Majid Aleyaasin

This paper uses the flexural vibration of cantilever beams as a benchmark problem to test mesh-free and finite element methods in structural dynamics. First, a symbolic analysis of the “kernel collocation” type mesh-free method is carried out, in which the collocation function satisfies the boundary conditions. This enables both Finite Element (FE) and mesh-free results to be compared with exact analytical ones. Thereafter, the natural frequencies and Frequency Response Function (FRF), in terms of the beam parameters, are determined and compared with the analytical results, that exist in the literature. It is shown that by adjusting the parameters of the kernel function, we can find identical peaks to those of the analytical method. The finite element method is also employed to solve this problem, and the first three natural frequencies were computed in terms of the beam parameters. When comparing the two methods, we see that by increasing the number of elements in the FEM we can always achieve better accuracy, but we will obtain twice the number of modal frequencies. However, the mesh-free method with the same number of nodes does not provide these extra frequencies. From this benchmark problem, it is concluded that the accuracy of the mesh-free methods always depends on the adjustment of the kernel function. However, the FEM is advantageous because it does not require such adjustments.

Dynamics doi: 10.3390/dynamics5020012

Authors: North Yates Fernando Ponta Alayna Farrell

One concern in the field of Horizontal Axis Wind Turbines (HAWTs) is what control strategies are needed to handle gust pulses in the wind to prevent extreme oscillations of the blades to reduce fatigue stress, prevent blade rupture, and extend the turbine’s operational life. In order to design innovative control strategies to modify the blade’s oscillatory response, it is crucial to establish the fundamental vibrational behavior of the blades when excited by gust pulses of different frequencies and amplitudes present in the fluctuating wind inflow. In a series of previous works, the authors presented a novel Reduced-Order Characterization (ROC) technique that provided an energy-based characterization of the fundamental modes of oscillation of wind turbine rotors when excited by combinations of wind gust pulses of different frequencies and amplitudes. The main focus of the present work is to extend these original notions of energy-based ROC to a universal technique expressed in terms of non-dimensional quantities that could be applied to turbines of any size, operating in any set of wind conditions, as long as they share geometrical and material similarity. The ROC technique provides a simple formula that is capable of predicting the dominant vibrational modes of a blade with sufficient precision to be useful in the determination of a control decision that can be computed in real time, an aspect of fundamental importance in dealing with rapid fluctuations in wind conditions.

Dynamics doi: 10.3390/dynamics5020011

Authors: Edward Bormashenko

The Ramsey approach is applied to analyses of the kinematics of systems built of non-relativistic, motile point masses/particles. This approach is based on colored graph theory. Point masses/particles serve as the vertices of the graph. The time dependence of the distance between the particles determines the coloring of the links. The vertices/particles are connected with orange links when particles move away from each other or remain at the same distance. The vertices/particles are linked with violet edges when particles converge. The sign of the time derivative of the distance between the particles dictates the color of the edge. Thus, a complete, bi-colored Ramsey temporal graph emerges. The suggested coloring procedure is not transitive. The coloring of the links is time-dependent. The proposed coloring procedure is frame-independent and insensitive to Galilean transformations. At least one monochromatic triangle will inevitably appear in the graph emerging from the motion of six particles due to the fact that the Ramsey number R3,3=6. This approach is extended to the analysis of systems containing an infinite number of moving point masses. An infinite monochromatic (violet or orange) clique will necessarily appear in the graph. Applications of the introduced approach are discussed. The suggested Ramsey approach may be useful for the analysis of turbulence seen within the Lagrangian paradigm.

Dynamics doi: 10.3390/dynamics5010010

Authors: Daniela Gheorghe Gheorghe Maria Laura Renea Crina Muscalu

In recent years, inulin enzymatic hydrolysis has become a very promising alternative for producing fructose on a large scale. Genetically modified chicory was used to extract inulin of industrial quality. By using an adequate kinetic model from the literature, this study aimed to determine the optimal operating alternatives of a batch (BR) or fed-batch (FBR) reactor used for the hydrolysis of inulin to fructose. The operation of the FBR with a constant or variable/dynamic feeding was compared to that of the BR to determine which best maximizes reactor production while minimizing enzyme consumption. Multi-objective optimal solutions were also investigated by using the Pareto-optimal front technique. Our in-silico analysis reveals that, for this enzymatic process, the best alternative is the FBR operated with a constant control variable but using the set-point given by the (breakpoint) of the Pareto optimal front under the imposed technological constraints. This set point reported the best performances, regarding all the considered opposite economic objectives. Also, the FBR with a constant, but NLP optimal feeding, reported fairly good performances.

Dynamics doi: 10.3390/dynamics5010009

Authors: Stylianos Vasileios Kontomaris Gamal M. Ismail Vassilis Alimisis Christos Dimas Anna Malamou

Solving nonlinear oscillations is challenging, as solutions to the corresponding differential equations do not exist in most cases. Therefore, numerical methods are usually employed to calculate the precise oscillation frequency. In addition, many interesting mathematical approaches leading to approximate solutions have also been developed. This paper focuses on a classic case of a nonlinear oscillator: the oscillator with an odd-power polynomial restoring force. This case encompasses nearly all scenarios of undamped nonlinear oscillations. The idea is to combine two well-known strategies from the literature: He’s approximation, which is simple to apply and valid for small amplitudes, and the analytical solutions for oscillations with power-law restoring forces. It is shown that by combining these approaches, a universal equation accurate for any amplitude is derived. Many tests of the proposed method’s accuracy are presented using polynomials of various degrees and classic examples, such as the rotating pendulum, cubic–quintic Duffing oscillators, and oscillators with cubic and harmonic restoring forces. In addition, a novel ‘electrical analogue’ of the oscillation with a polynomial-type restoring force is introduced to demonstrate that the methods presented in this paper can be applied in real industrial applications.

Dynamics doi: 10.3390/dynamics5010008

Authors: Edward B. Ang Jaime P. Honra

Global climate change has renewed interest in wind energy adoption and integration for on-grid and off-grid applications. Savonius wind turbines offer substantial advantages for small-scale energy generation in low-wind speed conditions, like urban environments, but suffer from low efficiency. This study focused on the numerical characterization of a novel compact three-blade Savonius rotor design with modified pointed deflectors to promote better flow attachment and enhance airflow guidance directionality. Computational Fluid Dynamics (CFD) was employed to identify the flow characteristics and optimal tip speed ratios for maximum power and torque coefficients under two different uniform low-wind-speed conditions. A Finite Element Analysis-Computational Fluid Dynamics (FEA-CFD) coupled analysis method was also utilized to determine the aerodynamic and structural characteristics of the design in ABS plastic. Flow visualization and FEA-CFD coupled analysis highlighted the novel tip deflectors’ exceptional performance in directing wind flow and pressure toward the concave side of the approaching blades, enhancing drag differential and rotor efficiency. Modest power and low torque coefficients and the optimal TSR values under different uniform low-wind-speed conditions were also identified. The work provided valuable insights on the turbine performance of the novel design and guidance on potential future improvements.

Dynamics doi: 10.3390/dynamics5010007

Authors: Akihiro Nishiyama Shigenori Tanaka Jack Adam Tuszynski

In this paper, we introduce waveguide Quantum Electrodynamics (wQED) for the description of tryptophans in microtubules representing data qubits for information storage and, possibly, information processing. We propose a Hamiltonian in wQED and derive Heisenberg equations for qubits and photons. Using the Heisenberg equations, we derive time-evolution equations for the probability of qubits and the distribution of photons both at zero and finite temperature. We then demonstrate the resultant sub-radiance with small decay rates, which is required to achieve robust data qubits for information storage by coupling tryptophan residues containing data qubits with water molecules as Josephson quantum filters (JQFs). We also describe an oscillation processes of qubits in a tubulin dimer through the propagation of excitations with changing decay rates of JQFs. Data qubits are found to retain initial values by adopting sub-radiant states involving entanglement with water degrees of freedom.

Dynamics doi: 10.3390/dynamics5010006

Authors: Egor S. Rodionov Andrey Ya. Cherepanov Alfiya G. Fazlitdinova Timur T. Sultanov Victor G. Lupanov Polina N. Mayer Alexander E. Mayer

A novel method to measure dynamic flow stress and corresponding strain rates obtained from Taylor tests using profiled samples with a reduced cylindrical head part was applied to study the dynamic characteristics of similar commercial 7075 and V95T1 aluminum alloys. The measured dynamic flow stress is verified using a classical Taylor’s approach with uniform cylinders and compared with the literature data. Our study shows that the dynamic flow stress of 7075 alloy, which is 786 MPa at strain rates of (4–8) × 103 s−1, exceeds the value of 624 MPa for V95T1 alloy at strain rates of (2–6) × 103 s−1 by 25%. The threshold impact velocity resulting in fracture of the 4 mm head part of the profiled samples is 116–130 m/s for 7075 alloy and only 108 m/s for V95T1 alloy. The fracture pattern is also different between the alloys with characteristic shear-induced cracks oriented at 45° to the impact direction in the case of V95T1 alloy and perpendicular to the breaking off head part in the case of 7075 alloy. On the other hand, the compressive fracture strain of V95T1 alloy, which is 0.29–0.36, exceeds that of 7075 alloy, which is 0.27–0.33, by approximately 8%. Thus, V95T1 aluminum alloy exhibits less strength but is more ductile, while 7075 aluminum alloy exhibits more strength but is simultaneously more brittle.