Dynamics

19 pages, 1069 KB

Open AccessArticle

by Edward Bormashenko, Ramita Sarkar, Mark Frenkel and Shraga Shoval

Dynamics 2025, 5(4), 46; https://doi.org/10.3390/dynamics5040046 - 2 Nov 2025

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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 [...] Read more.

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. Full article

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13 pages, 1327 KB

Open AccessArticle

Application of the Krylov–Bogolyubov–Mitropolsky Method to Study the Effect of Compressive (Tensile) Force on Transverse Oscillations of a Moving Nonlinear Elastic Beam

by Andrii Slipchuk, Petro Pukach and Myroslava Vovk

Dynamics 2025, 5(4), 45; https://doi.org/10.3390/dynamics5040045 - 1 Nov 2025

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Abstract

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, [...] Read more.

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. Full article

(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators: 2nd Edition)

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11 pages, 263 KB

Open AccessArticle

Well-Posedness of Problems for the Heat Equation with a Fractional-Loaded Term and Memory

by Umida Baltaeva, Bobur Khasanov, Omongul Egamberganova and Hamrobek Hayitbayev

Dynamics 2025, 5(4), 44; https://doi.org/10.3390/dynamics5040044 - 14 Oct 2025

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Abstract

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 [...] Read more.

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. Full article

13 pages, 2225 KB

Open AccessCommunication

Experimental Evaluation of Memristor-Enhanced Analog Oscillators: Relaxation and Wien-Bridge Cases

by Luis Manuel Lopez-Jimenez, Esteban Tlelo-Cuautle, Luis Fortino Cisneros-Sinencio and Alejandro Diaz-Sanchez

Dynamics 2025, 5(4), 43; https://doi.org/10.3390/dynamics5040043 - 1 Oct 2025

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Abstract

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 [...] Read more.

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. Full article

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29 pages, 2052 KB

Open AccessArticle

Comparison of Alternative Port-Hamiltonian Dynamics Extensions to the Thermodynamic Domain Toward IDA-PBC-Like Control: Application to a Heat Transfer Model

by Oleksiy Kuznyetsov

Dynamics 2025, 5(4), 42; https://doi.org/10.3390/dynamics5040042 - 1 Oct 2025

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Abstract

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 [...] Read more.

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. Full article

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19 pages, 830 KB

Open AccessArticle

Analysis and Simulation of Dynamic Heat Transfer and Thermal Distribution in Burns with Multilayer Models Using Finite Volumes

by Adriana Sofia Rodríguez-Pérez, Héctor Eduardo Gilardi-Velázquez and Stephanie Esmeralda Velázquez-Pérez

Dynamics 2025, 5(4), 41; https://doi.org/10.3390/dynamics5040041 - 1 Oct 2025

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Abstract

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 [...] Read more.

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. Full article

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20 pages, 4362 KB

Open AccessArticle

PLC Implementation and Dynamics of a V/Heart-Shape Chaotic System

by Abdul-Basset A. Al-Hussein, Fadhil Rahma Tahir, Hamzah Abdulkareem Abbood, Mazin Majid Abdulnabi and Viet-Thanh Pham

Dynamics 2025, 5(4), 40; https://doi.org/10.3390/dynamics5040040 - 1 Oct 2025

Viewed by 1510

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Theory and Applications in Nonlinear Oscillators: 2nd Edition)

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Dynamics, Volume 5, Issue 4 (December 2025) – 7 articles

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