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Dynamics, Volume 5, Issue 3 (September 2025) – 11 articles

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24 pages, 5111 KB  
Article
The Use of Gas Dynamics to Estimate the Influence of Flanges on Gear Windage Power Loss
by Thibaut Torres, Yasser Diab, Christophe Changenet, Thomas Touret and Bérengère Guilbert
Dynamics 2025, 5(3), 33; https://doi.org/10.3390/dynamics5030033 - 14 Aug 2025
Viewed by 219
Abstract
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 [...] Read more.
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. Full article
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15 pages, 1864 KB  
Article
Interaction Between Two Independent Chaotic Neural Networks Installed in the Motion Control Systems of Two Roving Robots
by Shigetoshi Nara, Naoya Miyahara, Yutaka Yamaguti and Ichiro Tsuda
Dynamics 2025, 5(3), 32; https://doi.org/10.3390/dynamics5030032 - 14 Aug 2025
Viewed by 212
Abstract
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. [...] Read more.
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. Full article
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19 pages, 905 KB  
Article
Breather and Rogue Wave Solutions of a New Three-Component System of Exactly Solvable NLEEs
by Aleksander Stefanov and Stanislav Varbev
Dynamics 2025, 5(3), 31; https://doi.org/10.3390/dynamics5030031 - 1 Aug 2025
Viewed by 220
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Topic Recent Trends in Nonlinear, Chaotic and Complex Systems)
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19 pages, 1583 KB  
Article
Modeling, Validation, and Controllability Degradation Analysis of a 2(P-(2PRU–PRPR)-2R) Hybrid Parallel Mechanism Using Co-Simulation
by Qing Gu, Zeqi Wu, Yongquan Li, Huo Tao, Boyu Li and Wen Li
Dynamics 2025, 5(3), 30; https://doi.org/10.3390/dynamics5030030 - 11 Jul 2025
Viewed by 281
Abstract
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 [...] Read more.
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. Full article
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10 pages, 248 KB  
Article
Remarks on the Time Asymptotics of Schmidt Entropies
by Italo Guarneri
Dynamics 2025, 5(3), 29; https://doi.org/10.3390/dynamics5030029 - 10 Jul 2025
Viewed by 197
Abstract
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 [...] Read more.
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. Full article
21 pages, 4831 KB  
Article
Aerodynamic Optimization and Thermal Deformation Effects on Mid-Altitude Sounding Rockets: A Computational and Structural Analysis
by Aslam Abdullah, Mohd Fadhli Zulkafli, Muhammad Akmal Abdul Halim, Ramanathan Ashwin Thanneermalai and Bambang Basuno
Dynamics 2025, 5(3), 28; https://doi.org/10.3390/dynamics5030028 - 9 Jul 2025
Viewed by 407
Abstract
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 [...] Read more.
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. Full article
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28 pages, 1358 KB  
Article
Mathematical Theory of Social Conformity II: Geometric Pinning, Curvature–Induced Quenching, and Curvature–Targeted Control in Anisotropic Logistic Diffusion
by Dimitri Volchenkov
Dynamics 2025, 5(3), 27; https://doi.org/10.3390/dynamics5030027 - 7 Jul 2025
Viewed by 708
Abstract
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 [...] Read more.
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. Full article
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19 pages, 332 KB  
Article
Coherent States of the Conformable Quantum Oscillator
by Cresus Fonseca de Lima Godinho, Claudio Maia Porto, Marcos Cardoso Rodriguez and Ion Vasile Vancea
Dynamics 2025, 5(3), 26; https://doi.org/10.3390/dynamics5030026 - 4 Jul 2025
Viewed by 236
Abstract
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 [...] Read more.
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. Full article
11 pages, 945 KB  
Article
Waveguide Arrays: Interaction to Many Neighbors
by Marco A. Tapia-Valerdi, Irán Ramos-Prieto, Francisco Soto-Eguibar and Héctor M. Moya-Cessa
Dynamics 2025, 5(3), 25; https://doi.org/10.3390/dynamics5030025 - 1 Jul 2025
Viewed by 242
Abstract
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 [...] Read more.
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. Full article
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15 pages, 717 KB  
Article
A Combined Separation of Variables and Fractional Power Series Approach for Selected Boundary Value Problems
by Gabriel Antonio Felipe, Carlos Alberto Valentim and Sergio Adriani David
Dynamics 2025, 5(3), 24; https://doi.org/10.3390/dynamics5030024 - 20 Jun 2025
Viewed by 316
Abstract
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 [...] Read more.
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. Full article
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29 pages, 7811 KB  
Article
Dynamic Response of Reinforced Concrete Columns Subjected to Air and Underwater Explosions
by Getu Abyu, Girum Urgessa and Ameen Topa
Dynamics 2025, 5(3), 23; https://doi.org/10.3390/dynamics5030023 - 20 Jun 2025
Viewed by 618
Abstract
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 [...] Read more.
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. Full article
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