Classical Physics
arXiv:physics.class-ph
Newtonian and relativistic dynamics, classical field theory, classical electromagnetism, thermodynamics.
40 papers
2512.22898Energy transport in the Schrödinger plate
In this paper, we introduce "the Schrödinger plate." This is an infinite two-dimensional linear micro-polar elastic medium, with out-of-plane degrees of freedom, lying on a linear elastic foundation of a special kind. Any free motion of the plate can be corresponded to a solution of the two-dimensional Schrödinger equation for a single particle in the external potential field $V$. The specific dependence of the potential $V$ on the position is taken into account in the properties of the plate elastic foundation. The governing equations of the plate are derived as equations of the two-dimensional constraint Cosserat continuum using the direct approach. The plate dynamics can be described by the classical Germain-Lagrange equation for a plate, but the strain energy is different from the one used in the classical Kirchhoff-Love plate theory. Namely, the Schrödinger plate cannot be imagined as a thin elastic body composed of an isotropic linear material. The main property of the Schrödinger plate is as follows: the mechanical energy propagates in the plate exactly in the same way as the probability density propagates according to the corresponding Schrödinger equation.
2512.22898Dec 2025
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Recovering long-range cumulative response to geometric frustration in quasi-1d systems, mediated by constitutive softness
Cumulative geometric frustration can drive self-limited assembly and morphology selection through size-dependent energetic costs. However, the slenderness of quasi-one-dimensional systems generally suppresses the formation of long-range longitudinal gradients. We show that the suppression of longitudinal gradients can be overcome by tuning the ratio between the longitudinal and transverse (shear) moduli. We demonstrate the recovery of cumulative frustration across distinct quasi-one-dimensional systems, each frustrated through a different mechanism, by the introduction of a soft response mode.
2512.11562Dec 2025
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Revisiting Koehler's experiment of measuring the ratio of the specific heats of air by self-sustained oscillations: a more concise theoretical interpretation
We revisit Koehler's experiment, a clever modification of Ruchardt's experiment designed to measure the ratio of specific heats of gas. The theory of self-sustained oscillations in Koehler's experiment was provided by Koehler (1950). However, its lengthy and dense analysis may pose challenges to readers due to the complexity of the calculations. Following Koehler's approximation for pressure changes, we explicitly present the model equations as piecewise linear differential systems and qualitatively analyze the periodic solutions from a geometric perspective. This concise and transparent approach addresses a fundamental question about Koehler's experiment: why is the oscillation frequency nearly equal to the Ruchardt frequency? Our analysis avoids intricate calculations and will be particularly helpful for teachers and students who encounter Koehler's experiment in general physics laboratory classes.
2511.10012Nov 2025
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Do Discrete Fine-Scale Mechanical Models with Rotational Degrees of Freedom Homogenize Into a Cosserat or a Cauchy Continuum?
This article answers the question of whether homogenization of discrete fine-scale mechanical models, such as particle or lattice models, gives rise to an equivalent continuum that is of Cauchy-type or Cosserat-type. The study employs the machinery of asymptotic expansion homogenization to analyze discrete mechanical models with rotational degrees of freedom commonly used to simulate the mechanical behavior of heterogeneous solids. The proposed derivation has general validity in both stationary (steady-state) and transient conditions (assuming wavelength much larger that particle size) and for arbitrary nonlinear, inelastic fine-scale constitutive equations. The results show that the unit cell problem is always stationary, and the only inertia term appears in the linear momentum balance equation at the coarse scale. Depending on the magnitude of the local bending stiffness, mathematical homogenization rigorously identifies two limiting conditions that correspond to the Cauchy continuum and the Cosserat continuum. A heuristic combination of these two limiting conditions provides very accurate results also in the transition from one limiting case to the other. Finally, the study demonstrates that cases for which the Cosserat character of the homogenized response is significant are associated with non-physically high fine-scale bending stiffness and, as such, are of no interest in practice.
2511.06279Nov 2025
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Coherent control of magnon-polaritons using an exceptional point
The amplitude of resonant oscillations in a non-Hermitian environment can either decay or grow in time, corresponding to a mode with either loss or gain. When two coupled modes have a specific difference between their loss or gain, a feature termed an exceptional point emerges in the excitations' energy manifold, at which both the eigenfrequencies and eigenmodes of the system coalesce. Exceptional points have intriguing effects on the dynamics of systems due to their topological properties. They have been explored in contexts including optical, microwave, optomechanical, electronic and magnonic systems, and have been used to control systems including optical microcavities, the lasing modes of a PT-symmetric waveguide, and terahertz pulse generation. A challenging problem that remains open in all of these scenarios is the fully deterministic and direct manipulation of the systems' loss and gain on timescales relevant to coherent control of excitations. Here we demonstrate the rapid manipulation of the gain and loss balance of excitations of a magnonic hybrid system on durations much shorter than their decay rate, allowing us to exploit non-Hermitian physics for coherent control. By encircling an exceptional point, we demonstrate population transfer between coupled magnon-polariton modes, and confirm the distinctive chiral nature of exceptional point encircling. We then study the effect of driving the system directly through an exceptional point, and demonstrate that this allows the coupled system to be prepared in an equal superposition of eigenmodes. We also show that the dynamics of the system at the exceptional point are dependent on its generalised eigenvectors. These results extend the established toolbox of adiabatic transfer techniques with a new approach for coherent state preparation, and provide a new avenue for exploring the dynamical properties of non-Hermitian systems.
2511.038995Nov 2025
View2511.02865Comment on "Absence of a consistent classical equation of motion for a mass-renormalized point charge"
Here we comment on the paper by Arthur D. Yaghjian, Phys. Rev. E 78, 046606 (2008) (arXiv:0805.0142). The author provides an equation of motion for a point charged particle in a certain regime of system parameters (on the other hand, claiming that in a different regime the classical equation of motion does not exist). The solutions of this equation (in the regime where it exists) presented in the paper show instantaneous jumps in the particle's velocity. We show that such jumps, in the case of a point particle, would generate infinite energy in the radiated electromagnetic field. Therefore, we claim that the point-particle limit used by the author is incorrect.
2511.028651Nov 2025
View2511.00571Path-Dependent Energy Lagrangian for Irreversible Thermomechanical Systems
We present a minimal Path-Dependent Energy Lagrangian (PDEL) that generates, from a single action, the balance equations of mechanics and the entropy/heat equation for irreversible thermomechanical systems. The reversible part is the Helmholtz free energy, while irreversible effects enter through a history integral of channel powers. A single upper-limit/tangential variation rule makes the same instantaneous power appear as a dissipative force in the mechanical/internal-variable equations and as a positive source in the entropy/heat equation, closing the first law without double counting and guaranteeing nonnegative entropy production under mild monotonicity assumptions. PDEL preserves the classical Lagrangian mechanics while subsuming standard dissipative models (Kelvin--Voigt viscosity, diffusion) and their viscous heating, and clarifies the reversible character of thermo-mechanical cross terms. The formulation offers a compact alternative to Rayleigh/Onsager appendices and GENERIC/metriplectic brackets, with limited algebraic complexity and straightforward extension to multiphysics.
2511.00571Nov 2025
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On the perturbed harmonic oscillator and celestial mechanics
We study the influence of perturbations in the three dimensional isotropic harmonic oscillator problem considering different perturbing force laws and apply our results in the context of celestial mechanics, particularly in the movement of stars in stellar clusters. We use a method based on the Runge-Lenz tensor, so that our results are valid for any eccentricity of the unperturbed orbits of the oscillator. To establish basic concepts, we start by considering two cases, namely: a Larmor and a keplerian perturbation; and show that, in both cases, the perturbed orbits will precess. After that, we consider the more general problem of a central perturbation with any power-law dependence, that also only causes precession. Then, we consider precessionless perturbations caused by an Euler force and by the non-central dragging forces of the form $\boldsymbol{δF}=-γ_nv^{n-1}\boldsymbol{v}$, where $\boldsymbol{v}$ is the velocity of the particle and $γ_n\geq0$. We demonstrate that, in the case of a linear drag $(n=1)$, the orbits eccentricities remains constant. In contrast to what occurs in the well-known Kepler problem, for $n>1$ the orbit becomes increasingly eccentric. In the case $n=-3$, where the force is interpreted as a Chandrasekhar friction, we show that the eccentricity diminishes over time. We finish this work by making a few comments about the relevance of the main results.
2510.25981Oct 2025
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Approaching the Thermodynamic Limit of an Ideal Gas
For a gas confined in a container, particle-wall interactions produce modifications to the partition function involving the average surface density of gas particles. While such correlations have a vanishing effect in the thermodynamic limit, examining them is beneficial for a sharper understanding of how the limit is attained. We contrast a classical and a quantum model of particle-wall correlations within the canonical ensemble.
2510.24552Oct 2025
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Tracking the normal modes of an overpass highway bridge using Distributed Acoustic Sensing
Distributed Acoustic Sensing (DAS) of ambient vibrations is a promising technique in the context of structural health monitoring of civil engineering structures. The methodology uses Rayleigh backscattered light from small deformations at different locations of the sensed fiber-optic cable, turning it into a large array of equally distributed strain sensors. In this paper, we demonstrate the feasibility of using DAS technology to record dynamic strain used for modal identification through the Operational Modal Analysis (OMA) of a strut-frame bridge overpassing the A8 highway in southeastern France. Modal identification using DAS data is successful despite its predominantly axial sensitivity (along fiber), though the help of three-component seismometers is useful for discriminating the main motion direction of each identified mode. The identification of 1 bridge's normal modes with unprecedented spatial resolution is obtained from the lowest (transverse and longitudinal) modes to high-order modes that present significant vertical motion. In addition, strong seasonal effects are observed in both the absolute frequency values and the modal shapes of the first transverse and longitudinal modes of the bridge, comparing ambient vibration testing and DAS surveys carried out in the summer and winter periods.
2510.24212Oct 2025
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An extensive search for stable periodic orbits of the equal-mass zero angular momentum three-body problem
A special 2D initial conditions' domain of the equal-mass zero angular momentum planar three-body problem, which has been formerly studied, is analyzed to deepen the knowledge of the stability regions in it. The decay times in the domain are carefully computed. Four stability regions are established. 971 verified initial conditions for linearly stable periodic collisionless orbits are found. Many of these identified initial conditions are new ones. The periodic orbits of each stability region are characterized by a certain pattern in their syzygy sequences. Additional computations show that the orbits found should be considered as candidates for KAM-stable orbits.
2510.22802Oct 2025
View2511.01889Coulomb force between two Dirac monopoles
The model of magnetic monopoles that was proposed by Paul Dirac in 1931 has long been a subject of theoretical interest in physics because of its potential to explain the quantization of electric charge. While much attention has been given to non-Dirac monopoles, Dirac's model, which involves an infinitely thin solenoid known as a Dirac string, presents subtleties in the interaction between monopoles. In this paper, we show that the force between two Dirac monopoles obeys a Coulomb-like interaction law. This derivation offers an instructive exercise in fundamental electromagnetism concepts and is appropriate for undergraduate and early graduate-level students.
2511.01889Oct 2025
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The swinging counterweight trebuchet. On internal friction
Mechanical energy is lost to friction during a shot with a trebuchet. The losses are mainly due to sliding friction at the bearings for the throwing arm and at the hinge for the swinging counterweight, but the aerodynamic force on the sling also contributes. Generalized forces for these sliding and aerodynamic frictions are derived and included in the equations for the internal movement of the engine. The equations are solved by the use of perturbation theory and calculated losses are compared with results from an experimental engine of small dimensions. Scaling to full-size trebuchets is discussed.
2510.21869Oct 2025
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Lattice-induced sound trapping in biperiodic metasurfaces of acoustic resonators
A referential example of a physical system that supports bound states in the continuum (BICs) with an infinite quality factor ($Q$-factor) is a subwavelength lattice of discrete scatterers (resonators) whose response can be significantly modified by exploiting lattice interactions. In this work, we explore the multipole interference mechanism for realizing accidental acoustic BICs (trapped modes) at the $Γ$-point (in-plane Bloch wave vector $\mathbf{k}_{\parallel} = \mathbf{0}$) in biperiodic lattices of acoustic resonators with one resonator per unit cell. To do so, we expand the pressure field from the lattice into a series of scalar zonal ($m = 0$) spherical multipoles, carried by a normally incident plane wave, and formulate analytical conditions on the resonator's multipole moments under which an eigenmode becomes a BIC. The conditions allow us to determine the lattice constant and frequency values that enable the formation of the axisymmetric BIC due to the destructive interference of radiation from zonal multipole moments of a certain parity, although each moment radiates individually. By employing the T-matrix method for acoustic metasurfaces, we numerically investigate the BIC resonance in various structures, including finite arrays, and also the transformation of such resonances into high-$Q$ quasi-BIC regimes, which can be excited by a plane wave at normal incidence.
2510.17750Oct 2025
View2510.17054Note on Jackson's formalism of gauge transformation
An outline is given of the derivation of two inhomogeneous wave equations in an influential 2002 AJP paper of Jackson on the transformation from the Lorenz gauge to other electromagnetic gauges. The derivation shows that, contrary to a statement in the paper, the function satisfying one of the equations is not associated with the Coulomb-gauge vector potential but is associated with the Lorenz-gauge vector potential instead.
2510.17054Oct 2025
View2510.11663The vector potential of a steady azimuthal current density. Once again
We give an integral expression for the vector potential of a time-independent, steady azimuthal current density. Our derivation is substantially simpler and somewhat more general than others given in the literature. As an illustration, we recover the results for the vector potential of a circular current loop as an orthogonal expansion in spherical and cylindrical coordinates. Additionally, we obtain closed analytical expressions for the vector potential and the magnetic induction of a circular current loop in terms of Legendre functions of the second kind, that are simpler than the results in terms of complete elliptic integrals given in textbooks.
2510.11663Oct 2025
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Advanced creep modelling for polymers: A variable-order fractional calculus approach
Polymer-based plastics exhibit time-dependent deformation under constant stress, known as creep, which can lead to rupture or static fatigue. A common misconception is that materials under tolerable static loads remain unaffected over time. Accurate long-term deformation predictions require experimental creep data, but conventional models based on simple rheological elements like springs and dampers often fall short, lacking the flexibility to capture the power-law behaviour intrinsic to creep processes. The springpot, a fractional calculus-based element, has been used to provide a power-law relationship; however, its fixed-order nature limits its accuracy, particularly when the deformation rate evolves over time. This article introduces a variable-order (VO) springpot model that dynamically adapts to the evolving viscoelastic properties of polymeric materials during creep, capturing changes between glassy, transition and rubbery phases. Model parameters are calibrated using a robust procedure for model identification based on the cross-entropy (CE) method, resulting in physically consistent and accurate predictions. This advanced modelling framework not only overcomes the limitations of the fixed-order models but also establishes a foundation for applying VO mechanics to other viscoelastic materials, providing a valuable tool for predicting long-term material performance in structural applications.
2510.11765Oct 2025
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The Effective Radius of an Electric Point Charge in Nonlinear Electrodynamics
Motivated by the century-old problem of modeling the electron as a pointlike particle with finite self energy, we develop a new class of nonlinear perturbations of Maxwell's electrodynamics inspired by, but distinct from, the Born--Infeld theory. A hallmark of our construction is that the effective radius of an electric point charge can be reduced arbitrarily by tuning a coupling parameter, thereby achieving scales far below the Born--Infeld bound and consistent with the experimentally undetected size of the electron. The models preserve finite self energy for point charges while energetically excluding monopoles and dyons, a robustness that appears intrinsic to this class of nonlinear theories. Two complementary behaviors are uncovered: In the non-polynomial perturbations, the Maxwell limit is not recovered as the coupling vanishes, whereas in polynomial models the self energy diverges correctly, meaning that the Maxwellian ultraviolet structure is reinstated. A further subtlety emerges in the distinction between the prescribed source charge, imposed through the displacement field, and the measurable free charge arising from the induced electric field. In particular, the free charge and the self energy contained within any ball around the point charge tend to zero in the strong-nonlinearity or zero effective-radius limit, rendering a pointlike structure locally undetectable, both electrically and energetically. These findings highlight how nonlinear field equations reconcile theoretical prescription with experimental measurement and suggest a classical rationale for the effective invisibility of the electron substructure.
2510.11733Oct 2025
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Multi-scale friction coefficient: From roughness to system computation using deep learning
The presence of surface defects (roughness, surface imperfections, profiles, etc.) in a contact inevitably leads to the modification of its local properties, such as the coefficient of friction. In railway wheelsets, this surface condition is crucial as it dictates appropriate fatigue design for the final use. However, these local phenomena are not well understood and require a real step back. Therefore, the aim of this paper is to propose a multiscale numerical strategy to better understand these phenomena. The multiscale strategy is divided into two steps. Initially, an analysis by the Discrete Element Method (DEM) modelling the interaction of generated rough surfaces is carried out to determine the coefficient of friction. In a second step, the results of DEM are introduced into a structural calculation where the enrichment of the coefficient of friction is done on each finite element contact. Given the wide variety of potential surface defects (size, distribution, height, etc.), a large number of DEM simulations is performed. A specially developed deep learning program is then used to account for these dispersions. The application targeted in this paper is the fitting of a wheel on a railway axle.
2510.01741Oct 2025
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Harnessing Oscillatory Dynamics for Reprogrammable Mechanical Functionality
A long-standing goal in the field of "mechanical computing" is the creation of truly reprogrammable mechanical structures, where the function of each unit can be dynamically defined, modified, and accessed on demand, much like rewriting data on a hard drive. Prior efforts have largely focused on bistable building blocks, which mimic binary states, but robust and efficient methods for programming large arrays of such units remain limited. In this study, we introduce a new approach for defining and reconfiguring the state of mechanical bits. Specifically, we investigate arrays of pendula whose boundary conditions break symmetry, effectively transforming them into mechanical bits. When actuation times are short compared to the natural oscillation periods, the state of each pendulum can be controlled solely by adjusting the timing of global boundary conditions. This mechanism enables rapid reprogramming, arbitrary information writing, and even the construction of a "mechanical piano" capable of generating user-defined note and chord sequences within only a few oscillation cycles. Because it integrates seamlessly with diverse functionalities, our strategy establishes a scalable framework for reprogrammable mechanical systems and can be readily generalized to other oscillatory systems like membranes or beams.
2509.26317Sep 2025
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