Journal Description
Dynamics
Dynamics
is an international, peer-reviewed, open access journal on physical process. Dynamics is published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, EBSCO, and other databases.
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 12.7 days after submission; acceptance to publication is undertaken in 3.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: APC discount vouchers, optional signed peer review, and reviewer names published annually in the journal.
Latest Articles
Cupolets: History, Theory, and Applications
Dynamics 2024, 4(2), 394-424; https://doi.org/10.3390/dynamics4020022 - 13 May 2024
Abstract
In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to
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In chaos control, one usually seeks to stabilize the unstable periodic orbits (UPOs) that densely inhabit the attractors of many chaotic dynamical systems. These orbits collectively play a significant role in determining the dynamics and properties of chaotic systems and are said to form the skeleton of the associated attractors. While UPOs are insightful tools for analysis, they are naturally unstable and, as such, are difficult to find and computationally expensive to stabilize. An alternative to using UPOs is to approximate them using cupolets. Cupolets, a name derived from chaotic, unstable, periodic, orbit-lets, are a relatively new class of waveforms that represent highly accurate approximations to the UPOs of chaotic systems, but which are generated via a particular control scheme that applies tiny perturbations along Poincaré sections. Originally discovered in an application of secure chaotic communications, cupolets have since gone on to play pivotal roles in a number of theoretical and practical applications. These developments include using cupolets as wavelets for image compression, targeting in dynamical systems, a chaotic analog to quantum entanglement, an abstract reducibility classification, a basis for audio and video compression, and, most recently, their detection in a chaotic neuron model. This review will detail the historical development of cupolets, how they are generated, and their successful integration into theoretical and computational science and will also identify some unanswered questions and future directions for this work.
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(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena—2nd Edition)
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Dynamics of Vortex Structures: From Planets to Black Hole Accretion Disks
by
Elizabeth P. Tito and Vadim I. Pavlov
Dynamics 2024, 4(2), 357-393; https://doi.org/10.3390/dynamics4020021 - 13 May 2024
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Thermo-vortices (bright spots, blobs, swirls) in cosmic fluids (planetary atmospheres, or even black hole accretion disks) are sometimes observed as clustered into quasi-symmetrical quasi-stationary groups but conceptualized in models as autonomous items. We demonstrate—using the (analytical) Sharp Boundaries Evolution Method and a generic
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Thermo-vortices (bright spots, blobs, swirls) in cosmic fluids (planetary atmospheres, or even black hole accretion disks) are sometimes observed as clustered into quasi-symmetrical quasi-stationary groups but conceptualized in models as autonomous items. We demonstrate—using the (analytical) Sharp Boundaries Evolution Method and a generic model of a thermo-vorticial field in a rotating “thin” fluid layer in a spacetime that may be curved or flat—that these thermo-vortices may be not independent but represent interlinked parts of a single, coherent, multi-petal macro-structure. This alternative conceptualization may influence the designs of numerical models and image-reconstruction methods.
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Estimating Spatio-Temporal Building Power Consumption Based on Graph Convolution Network Method
by
Georgios Vontzos, Vasileios Laitsos, Avraam Charakopoulos, Dimitrios Bargiotas and Theodoros E. Karakasidis
Dynamics 2024, 4(2), 337-356; https://doi.org/10.3390/dynamics4020020 - 2 May 2024
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Buildings are responsible for around 30% and 42% of the consumed energy at the global and European levels, respectively. Accurate building power consumption estimation is crucial for resource saving. This research investigates the combination of graph convolutional networks (GCNs) and long short-term memory
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Buildings are responsible for around 30% and 42% of the consumed energy at the global and European levels, respectively. Accurate building power consumption estimation is crucial for resource saving. This research investigates the combination of graph convolutional networks (GCNs) and long short-term memory networks (LSTMs) to analyze power building consumption, thereby focusing on predictive modeling. Specifically, by structuring graphs based on Pearson’s correlation and Euclidean distance methods, GCNs are employed to discern intricate spatial dependencies, and LSTM is used for temporal dependencies. The proposed models are applied to data from a multistory, multizone educational building, and they are then compared with baseline machine learning, deep learning, and statistical models. The performance of all models is evaluated using metrics such as the mean absolute error (MAE), mean squared error (MSE), R-squared (R2), and the coefficient of variation of the root mean squared error (CV(RMSE)). Among the proposed computation models, one of the Euclidean-based models consistently achieved the lowest MAE and MSE values, thus indicating superior prediction accuracy. The suggested methods seem promising and highlight the effectiveness of GCNs in improving accuracy and reliability in predicting power consumption. The results could be useful in the planning of building energy policies by engineers, as well as in the evaluation of the energy management of structures.
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Lie Symmetries of the Wave Equation on the Sphere Using Geometry
by
Michael Tsamparlis and Aniekan Magnus Ukpong
Dynamics 2024, 4(2), 322-336; https://doi.org/10.3390/dynamics4020019 - 29 Apr 2024
Abstract
A semilinear quadratic equation of the form defines a metric ; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets: one set containing the Lie derivative of the metric wrt the Lie symmetry generator, and the other set containing the quantities From the first set, it follows that the generators of Lie point symmetries are elements of the conformal algebra of the metric , while the second set serves as constraint equations, which select elements from the conformal algebra of Therefore, it is possible to determine the Lie point symmetries using a geometric approach based on the computation of the conformal Killing vectors of the metric . In the present article, the nonlinear Poisson equation is studied. The metric defined by this equation is 1 + 2 decomposable along the gradient Killing vector . It is a conformally flat metric, which admits 10 conformal Killing vectors. We determine the conformal Killing vectors of this metric using a general geometric method, which computes the conformal Killing vectors of a general decomposable metric in a systematic way. It is found that the nonlinear Poisson equation admits Lie point symmetries only when , and in this case, only the Killing vectors are admitted. It is shown that the Noether point symmetries coincide with the Lie point symmetries. This approach/method can be used to study the Lie point symmetries of more complex equations and with more degrees of freedom.
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Computational Fluid Dynamics Methodology to Estimate the Drag Coefficient of Balls in Rolling Element Bearings
by
Yann Marchesse, Christophe Changenet and Fabrice Ville
Dynamics 2024, 4(2), 303-321; https://doi.org/10.3390/dynamics4020018 - 25 Apr 2024
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The emergence of electric vehicles has brought new issues such as the problem of rolling element bearings (REBs) operating at high speeds. Losses due to these components in mechanical transmissions are a key issue and must therefore be taken into account right from
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The emergence of electric vehicles has brought new issues such as the problem of rolling element bearings (REBs) operating at high speeds. Losses due to these components in mechanical transmissions are a key issue and must therefore be taken into account right from the design stage of these systems. Among these losses, the one induced by the motion of rolling elements, known as drag loss, becomes predominant in high-speed REBs. Although an experimental approach is still possible, it is difficult to isolate this loss in order to study it properly. A numerical approach based on CFD is therefore a possible way forward, even if other issues arise. The aim of this article is to study the ability of such an approach to correctly estimate the drag coefficient associated with the motion of rolling elements. The influence of the numerical domain extension, the mesh refinement, the simplification of the ring shape, and the presence of the cage on the values of the drag coefficient is presented. While it seems possible to compromise on the calculation domain and mesh size, it appears that the other parameters must be taken into account as much as possible to obtain realistic results.
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SPH Simulation of Molten Metal Flow Modeling Lava Flow Phenomena with Solidification
by
Shingo Tomita, Joe Yoshikawa, Makoto Sugimoto, Hisaya Komen and Masaya Shigeta
Dynamics 2024, 4(2), 287-302; https://doi.org/10.3390/dynamics4020017 - 19 Apr 2024
Abstract
Characteristic dynamics in lava flows, such as the formation processes of lava levees, toe-like tips, and overlapped structures, were reproduced successfully through numerical simulation using the smoothed particle hydrodynamics (SPH) method. Since these specific phenomena have a great influence on the flow direction
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Characteristic dynamics in lava flows, such as the formation processes of lava levees, toe-like tips, and overlapped structures, were reproduced successfully through numerical simulation using the smoothed particle hydrodynamics (SPH) method. Since these specific phenomena have a great influence on the flow direction of lava flows, it is indispensable to elucidate them for accurate predictions of areas where lava strikes. At the first step of this study, lava was expressed using a molten metal with known physical properties. The computational results showed that levees and toe-like tips formed at the fringe of the molten metal flowing down on a slope, which appeared for actual lava flows as well. The dynamics of an overlapped structure formation were also simulated successfully; therein, molten metal flowed down, solidified, and changed the surface shape of the slope, and the second molten metal flowed over the changed surface shape. It was concluded that the computational model developed in this study using the SPH method is applicable for simulating and clarifying lava flow phenomena.
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(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena—2nd Edition)
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Auto-Correlation Functions of Chaotic Binary Sequences Obtained by Alternating Two Binary Functions
by
Akio Tsuneda
Dynamics 2024, 4(2), 272-286; https://doi.org/10.3390/dynamics4020016 - 16 Apr 2024
Abstract
This paper discusses the auto-correlation functions of chaotic binary sequences obtained by a one-dimensional chaotic map and two binary functions. The two binary functions are alternately used to obtain a binary sequence from a chaotic real-valued sequence. We consider two similar methods and
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This paper discusses the auto-correlation functions of chaotic binary sequences obtained by a one-dimensional chaotic map and two binary functions. The two binary functions are alternately used to obtain a binary sequence from a chaotic real-valued sequence. We consider two similar methods and give the theoretical auto-correlation functions of the new binary sequences, which are expressed by the auto-/cross-correlation functions of the two chaotic binary sequences generated by a single binary function. Furthermore, some numerical experiments are performed to confirm the validity of the theoretical auto-correlation functions.
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(This article belongs to the Topic Nonlinear Phenomena, Chaos, Control and Applications to Engineering and Science and Experimental Aspects of Complex Systems)
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System Identification Using Self-Adaptive Filtering Applied to Second-Order Gradient Materials
by
Thomas Kletschkowski
Dynamics 2024, 4(2), 254-271; https://doi.org/10.3390/dynamics4020015 - 7 Apr 2024
Abstract
For many engineering applications, it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in
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For many engineering applications, it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches, length scale parameters have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modeling, as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established, there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion, system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach, it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically, it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior.
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(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena—2nd Edition)
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A Versatile Deposition Model for Natural and Processed Surfaces
by
Cihan Ates, Rainer Koch and Hans-Jörg Bauer
Dynamics 2024, 4(2), 233-253; https://doi.org/10.3390/dynamics4020014 - 30 Mar 2024
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This paper introduces a robust deposition model designed for exploring the growth dynamics of deposits on surfaces under practical conditions. The study addresses the challenge of characterizing the intricate morphology of deposits, exhibiting significant visual variations. A generative approach is deployed to create
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This paper introduces a robust deposition model designed for exploring the growth dynamics of deposits on surfaces under practical conditions. The study addresses the challenge of characterizing the intricate morphology of deposits, exhibiting significant visual variations. A generative approach is deployed to create diverse natural and engineered surface textures, governed by probabilistic principles. The model’s formulation addresses key questions related to deposition initiation, nucleation point behaviour, spatial scaling, deposit growth rates, spread dynamics, and surface mobility. A versatile algorithm, relying on six parameters and employing nested loops and Gaussian sampling, is developed. The algorithm’s efficacy is examined through extensive simulations, involving variations in nucleation scaling densities, aggregate scaling scenarios, spread factors, and diffusion rates. Surface statistics are computed for simulated deposits and analyzed using Fast Fourier Transform (FFT). The resulting database enables quantitative comparisons of surfaces generated with different parameters, where the database-derived parallel coordinates offer guidance for selecting optimal model parameters to achieve desired surface morphologies. The proposed approach is validated against urea-derived deposits, exhibiting statistical consistency and agreement with experimental observations. Overall, the model’s adaptable framework holds promise for understanding and predicting deposit growth on surfaces in diverse practical scenarios.
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Dynamics and Stability of Double-Walled Carbon Nanotube Cantilevers Conveying Fluid in an Elastic Medium
by
Vassil M. Vassilev and Galin S. Valchev
Dynamics 2024, 4(2), 222-232; https://doi.org/10.3390/dynamics4020013 - 27 Mar 2024
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The paper concerns the dynamics and stability of double-walled carbon nanotubes conveying fluid. The equations of motion adopted in the current study to describe the dynamics of such nano-pipes stem from the classical Bernoulli–Euler beam theory. Several additional terms are included in the
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The paper concerns the dynamics and stability of double-walled carbon nanotubes conveying fluid. The equations of motion adopted in the current study to describe the dynamics of such nano-pipes stem from the classical Bernoulli–Euler beam theory. Several additional terms are included in the basic equations in order to take into account the influence of the conveyed fluid, the impact of the surrounding medium and the effect of the van der Waals interaction between the inner and outer single-walled carbon nanotubes constituting a double-walled one. In the present work, the flow-induced vibrations of the considered nano-pipes are studied for different values of the length of the pipe, its inner radius, the characteristics of the ambient medium and the velocity of the fluid flow, which is assumed to be constant. The critical fluid flow velocities are obtained at which such a cantilevered double-walled carbon nanotube embedded in an elastic medium loses stability.
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Open AccessArticle
Exploiting Domain Partition in Response Function-Based Dynamic Surrogate Modeling: A Continuous Crystallizer Study
by
Alessandro Di Pretoro, Ludovic Montastruc and Stéphane Negny
Dynamics 2024, 4(2), 208-221; https://doi.org/10.3390/dynamics4020012 - 26 Mar 2024
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Given the exponential rise in the amount of data requiring processing in all engineering fields, phenomenological models have become computationally cumbersome. For this reason, more efficient data-driven models have been recently used with the purpose of substantially reducing simulation computational times. However, especially
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Given the exponential rise in the amount of data requiring processing in all engineering fields, phenomenological models have become computationally cumbersome. For this reason, more efficient data-driven models have been recently used with the purpose of substantially reducing simulation computational times. However, especially in process engineering, the majority of the proposed surrogate models address steady-state problems, while poor studies refer to dynamic simulation modeling. For this reason, using a response function-based approach, a crystallization unit case study was set up in order to derive a dynamic data-driven model for crystal growth whose characteristic differential parameters are derived via Response Surface Methodology. In particular, multiple independent variables were considered, and a well-established sampling technique was exploited for sample generation. Then, different sample sizes were tested and compared in terms of accuracy indicators. Finally, the domain partition strategy was exploited in order to show its relevant impact on the final model accuracy. In conclusion, the outcome of this study proved that the proposed procedure is a suitable methodology for dynamic system metamodeling, as it shows good compliance and relevant improvement in terms of computational time. In terms of future research perspectives, testing the proposed procedure on different systems and in other research fields would allow for greater improvement and would, eventually, extend its validity.
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Iterated Crank–Nicolson Method for Peridynamic Models
by
Jinjie Liu, Samuel Appiah-Adjei and Moysey Brio
Dynamics 2024, 4(1), 192-207; https://doi.org/10.3390/dynamics4010011 - 15 Mar 2024
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In this paper, we explore the iterated Crank–Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method was originally developed for hyperbolic advection equations. In peridynamics,
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In this paper, we explore the iterated Crank–Nicolson (ICN) algorithm for the one-dimensional peridynamic model. The peridynamic equation of motion is an integro-differential equation that governs structural deformations such as fractures. The ICN method was originally developed for hyperbolic advection equations. In peridynamics, we apply the ICN algorithm for temporal discretization and the midpoint quadrature method for spatial integration. Several numerical tests are carried out to evaluate the performance of the ICN method. In general, the ICN method demonstrates second-order accuracy, consistent with the Störmer–Verlet (SV) method. When the weight is 1/3, the ICN method behaves as a third-order Runge–Kutta method and maintains strong stability-preserving (SSP) properties for linear problems. Regarding energy conservation, the ICN algorithm maintains at least second-order accuracy, making it superior to the SV method, which converges linearly. Furthermore, selecting a weight of 0.25 results in fourth-order superconvergent energy variation for the ICN method. In this case, the ICN method exhibits energy variation similar to that of the fourth-order Runge–Kutta method but operates approximately 20% faster. Higher-order convergence for energy can also be achieved by increasing the number of iterations in the ICN method.
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Open AccessArticle
A Novel Scalable Quantum Protocol for the Dining Cryptographers Problem
by
Peristera Karananou and Theodore Andronikos
Dynamics 2024, 4(1), 170-191; https://doi.org/10.3390/dynamics4010010 - 8 Mar 2024
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This paper presents an innovative entanglement-based protocol to address the Dining Cryptographers problem, utilizing maximally entangled tuples as its core. This protocol aims to provide scalability in terms of both the number of cryptographers n and the
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This paper presents an innovative entanglement-based protocol to address the Dining Cryptographers problem, utilizing maximally entangled tuples as its core. This protocol aims to provide scalability in terms of both the number of cryptographers n and the amount of anonymous information conveyed, represented by the number of qubits m within each quantum register. The protocol supports an arbitrary number of cryptographers n, enabling scalability in both participant count and the volume of anonymous information transmitted. While the original Dining Cryptographers problem focused on a single bit of information—whether a cryptographer paid for dinner—the proposed protocol allows m, the number of qubits in each register, to be any arbitrarily large positive integer. This flexibility allows the transmission of additional information, such as the cost of the dinner or the timing of the arrangement. Another noteworthy aspect of the introduced protocol is its versatility in accommodating both localized and distributed versions of the Dining Cryptographers problem. The localized scenario involves all cryptographers gathering physically at the same location, such as a local restaurant, simultaneously. In contrast, the distributed scenario accommodates cryptographers situated in different places, engaging in a virtual dinner at the same time. Finally, in terms of implementation, the protocol accomplishes uniformity by requiring that all cryptographers utilize identical private quantum circuits. This design establishes a completely modular quantum system where all modules are identical. Furthermore, each private quantum circuit exclusively employs the widely used Hadamard and CNOT quantum gates, facilitating straightforward implementation on contemporary quantum computers.
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Open AccessArticle
Phase Diagram of Nuclear Pastas in Neutron Star Crusts
by
Jorge A. Muñoz and Jorge A. López
Dynamics 2024, 4(1), 157-169; https://doi.org/10.3390/dynamics4010009 - 22 Feb 2024
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Two neural networks were trained to predict, respectively, the Euler characteristic and the curvature of nuclear pastas in neutron star crust conditions generated by molecular dynamics simulations of neutron star matter with 0.1 < x < 0.5, 0.040 fm−3 < ρ <
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Two neural networks were trained to predict, respectively, the Euler characteristic and the curvature of nuclear pastas in neutron star crust conditions generated by molecular dynamics simulations of neutron star matter with 0.1 < x < 0.5, 0.040 fm−3 < ρ < 0.085 fm−3 (0.68 × 1014 g/cm3 < ρ < 1.43 × 1014 g/cm3), and 0.2 MeV < T < 4.0 MeV, where x is proton content, the density is , and the temperature is T. The predictions of the two networks were combined to determine the nuclear pasta phase that is thermodynamically stable at a given x, , and T, and a three-dimensional phase diagram that extrapolated slightly the regions of existing molecular dynamics data was computed. The jungle gym and anti-jungle gym structures are prevalent at high temperature and low density, while the anti-jungle gym and anti-gnocchi structures dominate at high temperature and high density. A diversity of structures exist at low temperatures and intermediate density and proton content. The trained models used in this work are open access and available at a public repository to promote comparison to pastas obtained with other models.
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Development and Validation of a Compressible Reacting Gas-Dynamic Flow Solver for Supersonic Combustion
by
Anvar Gilmanov, Ponnuthurai Gokulakrishnan and Michael S. Klassen
Dynamics 2024, 4(1), 135-156; https://doi.org/10.3390/dynamics4010008 - 11 Feb 2024
Abstract
An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and
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An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and turbulence–combustion interaction. The comparisons of the simulation results with experimental and computational data confirm the fidelity of this solver for problems involving multicomponent high-speed reactive flows. The gas dynamics of turbulence–chemistry interaction are modeled using a partially stirred reactor formulation and provide promising results to better understand the complex physics involved in supersonic combustors. A time-scale analysis based on local Damköhler numbers reveals different regimes of turbulent combustion. In the core of the jet flow, the Damköhler number is relatively high, indicating that the reaction time scale is smaller than the turbulent mixing time scale. This means that the combustion is controlled by turbulent mixing. In the shear layer, where the heat release rate and the scalar dissipation rate have the highest value, the flame is stabilized due to finite rate chemistry with small Damköhler numbers and a limited fraction of fine structure. This solver allows three-dimensional gas dynamic simulation of high-speed multicomponent reactive flows relevant to practical combustion applications.
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(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)
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Physical Reservoir Computing Enabled by Solitary Waves and Biologically Inspired Nonlinear Transformation of Input Data
by
Ivan S. Maksymov
Dynamics 2024, 4(1), 119-134; https://doi.org/10.3390/dynamics4010007 - 8 Feb 2024
Cited by 1
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Reservoir computing (RC) systems can efficiently forecast chaotic time series using the nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardware counterparts of traditional RC algorithms and more-efficient RC-like
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Reservoir computing (RC) systems can efficiently forecast chaotic time series using the nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardware counterparts of traditional RC algorithms and more-efficient RC-like schemes. Inspired by the nonlinear processes in a living biological brain and using solitary waves excited on the surface of a flowing liquid film, in this paper, we experimentally validated a physical RC system that substitutes the effect of randomness that underpins the operation of the traditional RC algorithm for a nonlinear transformation of input data. Carrying out all operations using a microcontroller with minimal computational power, we demonstrate that the so-designed RC system serves as a technically simple hardware counterpart to the ‘next-generation’ improvement of the traditional RC algorithm.
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Open AccessArticle
Analysis of Wind Turbine Wake Dynamics by a Gaussian-Core Vortex Lattice Technique
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Apurva Baruah and Fernando Ponta
Dynamics 2024, 4(1), 97-118; https://doi.org/10.3390/dynamics4010006 - 1 Feb 2024
Cited by 3
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The development and deployment of the next generation of wind energy systems calls for simulation tools that model the entire wind farm while balancing accuracy and computational cost. A full-system wind farm simulation must consider the atmospheric inflow, the wakes and consequent response
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The development and deployment of the next generation of wind energy systems calls for simulation tools that model the entire wind farm while balancing accuracy and computational cost. A full-system wind farm simulation must consider the atmospheric inflow, the wakes and consequent response of the multiple turbines, and the implementation of the appropriate farm-collective control strategies that optimize the entire wind farm’s output. In this article, we present a novel vortex lattice model that enables the effective representation of the complex vortex wake dynamics of the turbines in a farm subject to transient inflow conditions. This work extends the capabilities of our multi-physics suite, CODEF, to include the capability to simulate the wakes and the high-fidelity aeroelastic response of multiple turbines in a wind farm. Herein, we compare the results of our GVLM technique with the LiDAR measurements obtained at Sandia National Laboratories’ SWiFT facility. The comparison shows remarkable similarities between the simulation and field measurements of the wake velocity. These similarities demonstrate our model’s capabilities in capturing the entire wake of a wind turbine at a significantly reduced computational cost as compared to other techniques.
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New Types of Derivative Non-linear Schrödinger Equations Related to Kac–Moody Algebra
by
Aleksander Aleksiev Stefanov
Dynamics 2024, 4(1), 81-96; https://doi.org/10.3390/dynamics4010005 - 18 Jan 2024
Abstract
We derive a new system of integrable derivative non-linear Schrödinger equations with an L operator, quadratic in the spectral parameter with coefficients belonging to the Kac–Moody algebra . The construction of the fundamental analytic solutions of L is
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We derive a new system of integrable derivative non-linear Schrödinger equations with an L operator, quadratic in the spectral parameter with coefficients belonging to the Kac–Moody algebra . The construction of the fundamental analytic solutions of L is outlined and they are used to introduce the scattering data, thus formulating the scattering problem for the Lax pair .
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(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)
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Non-Symmetry in the Shock Refraction at a Closed Interface as a Recovery Mechanism
by
Anna Markhotok
Dynamics 2024, 4(1), 57-80; https://doi.org/10.3390/dynamics4010004 - 10 Jan 2024
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The possibility of a shock wave recovery at a discrete closed interface with a heated gas has been investigated. A two-dimensional model applied to conditions of optical discharges featuring spherical, elliptical, and drop-like configurations demonstrated that non-symmetry in the shock refraction contributes to
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The possibility of a shock wave recovery at a discrete closed interface with a heated gas has been investigated. A two-dimensional model applied to conditions of optical discharges featuring spherical, elliptical, and drop-like configurations demonstrated that non-symmetry in the shock refraction contributes to the specific mechanism of recovery other than simply its compensation. Even though the full restoration of the hypersonic flow state does not occur in a strict sense of it, clear reverse changes toward the initial shape of the shock front eventually take place, thus creating an appearance of a full recovery seen in experiments. From analysis of different interface symmetries, the factors determining the recovery dynamics are identified. The results are directly applicable to the problem of energy deposition into a hypersonic flow; however, it can be useful anywhere else where the flow modifications following the interaction are important. The dimensionless form of the equations allows applications on any scale other than that demonstrated for the optical discharges.
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Multiplicative Renormalization of Stochastic Differential Equations for the Abelian Sandpile Model
by
Dimitri Volchenkov
Dynamics 2024, 4(1), 40-56; https://doi.org/10.3390/dynamics4010003 - 4 Jan 2024
Abstract
The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling
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The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes.
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(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)
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