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Localized point sources (monopoles) in an acoustical domain are implemented to a three dimensional non-singular Helmholtz boundary element method in the frequency domain. It allows for the straightforward use of higher order surface elements on the boundaries of the problem. It will been shown that the effect of the monopole sources ends up on the right hand side of the resulting matrix system. Some carefully selected examples are studied, such as point sources near and within a concentric spherical core-shell scatterer (with theoretical verification), near a curved focusing surface and near a multi-scale and multi-domain acoustic lens.

Understanding the generation of mechanical stress in drying, particle-laden films is important for a wide range of industrial processes. One way to study these stresses is through the cantilever experiment, whereby a thin film is deposited onto the surface of a thin plate that is clamped at one end to a wall. The stresses that are generated in the film during drying are transmitted to the plate and drive bending. Mathematical modelling enables the film stress to be inferred from measurements of the plate deflection. The aim of this paper is to present simplified models of the cantilever experiment that have been derived from the time-dependent equations of continuum mechanics using asymptotic methods. The film is described using nonlinear poroelasticity and the plate using nonlinear elasticity. In contrast to Stoney-like formulae, the simplified models account for films with non-uniform thickness and stress. The film model reduces to a single differential equation that can be solved independently of the plate equations. The plate model reduces to an extended form of the Föppl-von Kármán (FvK) equations that accounts for gradients in the longitudinal traction acting on the plate surface. Consistent boundary conditions for the FvK equations are derived by resolving the Saint-Venant boundary layers at the free edges of the plate. The asymptotically reduced models are in excellent agreement with finite element solutions of the full governing equations. As the Péclet number increases, the time evolution of the plate deflection changes from $t$ to $t^{1/2}$ , in agreement with experiments.

The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental the equation gives the most complete description of propagating waves as it accounts for the Doppler effect, forward and backward waves, and makes the wave speed to be the same in all inertial frames. To demonstrate these properties, the equation is applied to acoustic wave propagation in an isothermal atmosphere, and to determine Lamb’s cutoff frequency.

International audience; The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields used in the time integration by splitting, for each particle, the time step into sub-steps such that each of these sub-steps corresponds to particle cell residence times. This reduces the spatial discretization error. Given the stochastic nature of the models, a key aspect is to derive estimations of the residence times that do not anticipate the future of the Wiener process. To that effect, the new algorithm relies on a virtual particle, attached to each stochastic one, whose mean conditional behavior provides free-of-statistical-bias predictions of residence times. After consistency checks, this new algorithm is validated on two representative test cases: particle dispersion in a statistically uniform flow and particle dynamics in a non-uniform flow.; L’objectif de ce papier est de proposer un algorithme robuste en pas de temps permettant l’intégration face à face de la trajectoire de particules dans des maillage 3-D non-structurés pour des méthodes lagrangiennes stochastiques. L’idée principale est de mettre à jour de façon dynamique les champs moyens utilisés dans l’intégration temporelle. Pour ce faire, pour chaque particule, on subdivise le pas de temps en sous pas de temps, de façon à ce que chacun de ceux-ci correspondent au temps de résidence de la particule dans une cellule. Ce faisant on réduit l’erreur de discrétisation spatiale. Étant donnée la nature stochastique du modèle, un aspect prépondérant est de pouvoir dériver des estimations du temps de résidence des particules dans les cellules qui n’anticipent pas le futur des processus de Wiener. Dans ce but, le nouvel algorithme est basé sur une particule virtuelle attachée à chaque particule stochastique, dont le comportement conditionné moyen permet d’obtenir des temps de résidence qui ne sont entachés d’aucun biais statistique. Après une vérification de consistance, ce nouvel algorithme est validé sur deux cas de tests représentatifs : une dispersion de polluants dans un écoulement statistiquement uniforme et un écoulement non-uniforme dans lequel on traque la dynamique des particules.

The objective of this paper is to provide a pedagogical framework for the phenomenon of orbital decay of satellites in low Earth orbit. The dynamics of orbital decay are derived considering atmospheric drag as the only dissipative mechanism and using an educational approach suitable for undergraduate calculus-based physics and engineering courses. The resulting non-linear first order differential equation for the altitude as a function of time is solved numerically for the isothermal-barotropic atmospheric model with a {fixed} scale height. The model is validated using the uncontrolled reentry data of the Chinese space station Tiangong-1., Comment: 6 pages, 3 figures

Dispersion curves of elastic waveguides exhibit points where the group velocity vanishes while the wavenumber remains finite. These are the so-called zero-group-velocity (ZGV) points. As the elastodynamic energy at these points remains confined close to the source, they are of practical interest for nondestructive testing and quantitative characterization of structures. These applications rely on the correct prediction of the ZGV points. In this contribution, we first model the ZGV resonances in anisotropic plates based on the appearance of an additional modal solution. The resulting governing equation is interpreted as a two-parameter eigenvalue problem. Subsequently, we present three complementary numerical procedures capable of computing ZGV points in arbitrary nondissipative elastic waveguides in the conventional sense that their axial power flux vanishes. The first method is globally convergent and guarantees to find all ZGV points but can only be used for small problems. The second procedure is a very fast, generally-applicable, Newton-type iteration that is locally convergent and requires initial guesses. The third method combines both kinds of approaches and yields a procedure that is applicable to large problems, does not require initial guesses and is likely to find all ZGV points. The algorithms are implemented in "GEW ZGV computation" (doi: 10.5281/zenodo.7537442)., Added Appendices A, B and D. Some clarifications in the text

We establish, in the framework of the theory of nested figures, the expressions for the gravitational moments $J_{2n}$ of a systems made of ${\cal L}$ homogeneous layers separated by spheroidal surfaces and in relative rotational motion. We then discuss how to solve the inverse problem, which consists in finding the equilibrium configurations (i.e. internal structures) that reproduce ``exactly'' a set of observables, namely the equatorial radius, the total mass, the shape and the first gravitational moments. Two coefficients $J_{2n}$ being constrained per surface, ${\cal L}=1+\frac{n}{2}$ layers ($n$ even) are required to fix $J_2$ to $J_{2n}$. As shown, this problem already suffers from a severe degeneracy, inherent in the fact that two spheroidal surfaces in the system confocal with each other leave unchanged all the moments. The complexity, which increases with the number of layers involved, can be reduced by considering the rotation rate of each layer. Jupiter is used as a test-bed to illustrate the method, concretely for ${\cal L}=2,3$ and $4$. For this planet, the number of possible internal structures is infinite for ${\cal L} > 2$. Intermediate layers can have smaller or larger oblateness, and can rotate slower or faster than the surroundings. Configurations with large and massive cores are always present. Low-mass cores (of the order a few Earth masses) are predicted for ${\cal L} \ge 4$. The results are in good agreement with the numerical solutions obtained from the Self-Consistent-Field method., Accepted for publication in MNRAS, 24 pages

We revisit the classical pursuit curve problem solved by Pierre Bouguer in the 18th century, taking into account that information propagates at a finite speed. To a certain extent, this could be seen as a relativistic correction to that problem, though one does not need Einstein's theory of relativity in order to derive or understand its solution. The discussion of this generalized problem of pursuit constitutes an excellent opportunity to introduce the concept of retarded time without the complications inherent to the study of electromagnetic radiation (where it is usually seen for the first time), which endows the problem with a clear pedagogical motivation. We find the differential equation which describes the problem, solve it numerically, compare the solution to Bouguer's for different values of the parameters, and deduce a necessary and sufficient condition for the pursuer to catch the pursued, complementing previous work by Hoenselaers., 15 pages, 7 figures, submitted to the American Journal of Physics

Dissociative electron attachment, that is, the cleavage of chemical bonds induced by low-energy electrons, is difficult to model with standard quantum-chemical methods because the involved anions are not bound but subject to autodetachment. We present here a new computational development for simulating the dynamics of temporary anions on complex-valued potential energy surfaces. The imaginary part of these surfaces describes electron loss, whereas the gradient of the real part represents the force on the nuclei. In our method, the forces are computed analytically based on Hartree-Fock theory with a complex absorbing potential. $Ab\ initio$ molecular dynamics simulations for the temporary anions of dinitrogen, ethylene, chloroethane, and the five mono- to tetrachlorinated ethylenes show qualitative agreement with experiments and offer mechanistic insights into dissociative electron attachments. The results also demonstrate how our method evenhandedly deals with molecules that may undergo dissociation upon electron attachment and those which only undergo autodetachment., Manuscript: 10 pages, 4 figures. Supplementary Material: 41 pages, 43 figures

A backstepping-based compensator design is developed for a system of $2\times2$ first-order linear hyperbolic partial differential equations (PDE) in the presence of an uncertain long input delay at boundary. We introduce a transport PDE to represent the delayed input, which leads to three coupled first-order hyperbolic PDEs. A novel backstepping transformation, composed of two Volterra transformations and an affine Volterra transformation, is introduced for the predictive control design. The resulting kernel equations from the affine Volterra transformation are two coupled first-order PDEs and each with two boundary conditions, which brings challenges to the well-posedness analysis. We solve the challenge by using the method of characteristics and the successive approximation. To analyze the sensitivity of the closed-loop system to uncertain input delay, we introduce a neutral system which captures the control effect resulted from the delay uncertainty. It is proved that the proposed control is robust to small delay variations. Numerical examples illustrate the performance of the proposed compensator.

A charged particle which is allowed to accelerate must have relativistic behavior because it is coupled to electromagnetic radiation which propagates at the speed of light. We treat the simple steady-state situation of a charged particle moving in a circular orbit with counter-propagating plane waves providing the power which balances the energy radiated away by the accelerating charge. It is emphasized that only an electromagnetic arrangement, such as a Coulomb potential or a constant magnetic field, can provide the relativistic central force for the particle motion., 14 pages

The construction of an analytic orbit theory that takes into account the main effects of the Geopotential is notably simplified when splitting the removal of periodic effects in several stages. Conversely, this splitting of the analytical solution into several transformations reduces the evaluation efficiency for dense ephemeris output. However, the advantage is twofold when the different parts of the mean-to-osculating transformation are composed into a single transformation. To show that, Brouwer's solution is extended to the second order of the zonal harmonic of the second degree by the sequential elimination of short- and long-period terms. Then, the generating functions of the different transformations are composed into a single one, from which a single mean-to-osculating transformation is derived. The new, unique transformation notably speeds up the evaluation process, commonly improving evaluation efficiency by at least one third with respect to the customary decomposition of the analytical solution into three different parts.

In this paper, we undertake to present a self-contained and thorough analysis of the gravitational three body problem, with anticipated application to the Great Inequality of Jupiter and Saturn. The analysis of the three body Lagrangian is very convenient in heliocentric coordinates with Lagrange multipliers, the coordinates being the vector-sides $\vec{r}_i,\,i=1,2,3$ of the triangle that the bodies form. In two dimensions to begin with, the equations of motion are formulated into a dynamical system for the polar angles $\theta_i$, angular momenta $\ell_i$ and eccentricity vectors $\vec{e}_i$. The dynamical system is simplified considerably by change of variables to certain auxiliary vector $\vec{f}_i=\hat{r}_i+\vec{e}_i$. We then begin to formulate the Hamiltonian perturbation theory of the problem, now in three dimensions. We first give the geometric definitions for the Delaunay action-angle variables of the two body problem. We express the three body Hamiltonian in terms of Delaunay variables in each sector $i=1,2,3$, revealing that it is a nearly integrable Hamiltonian. We then present the KAM theory perturbative approach that will be followed in future work, including the modification that will be required because the Hamiltonian is degenerate.

Resonant modes determine the response of electromagnetic devices, including dielectric and plasmonic resonators. Relying on the degrees of freedom that metamaterials provide, this contribution shows how to design, at will, the resonant modes of a dielectric object placed in an unbounded space. Specifically, the proposed method returns in analytical form the spatial distribution of the dielectric susceptibility tensor for which the object exhibits resonances at prescribed frequencies and spatial distribution of the polarization. Together with the synthesis of the material, two key concepts are introduced: the controlled tunability of the resonant modes and the number of essential modes, i.e. the number of modes that uniquely characterize the spatial distribution of the dielectric susceptibility. Moreover, this approach can be applied to design the resonant modes of any system where the constitutive relationship is linear and local.

We demonstrate electromechanical coupling between a superfluid mechanical mode and a microwave mode formed by a patterned microfluidic chip and a 3D cavity. The electric field of the chip-cavity microwave resonator can be used to both drive and detect the motion of a pure superflow Helmholtz mode, which is dictated by geometric confinement. The coupling is characterized using a coherent measurement technique developed for measuring weak couplings deep in the sideband unresolved regime. The technique is based on two-probe optomechanically induced transparency/amplification using amplitude modulation. Instead of measuring two probe tones separately, they are interfered to retain only a signal coherent with the mechanical motion. With this method, we measure a vacuum electromechanical coupling strength of $g_0 = 2\pi \times 23.3$ $\mathrm{\mu}$Hz, three orders of magnitude larger than previous superfluid electromechanical experiments., Comment: 13 pages, 6 figures, submitted to Appl. Phys. Lett., out for peer review, revtex

Crack front waves (FWs) are dynamic objects that propagate along moving crack fronts in 3D materials. We study FW dynamics in the framework of a 3D phase-field framework that features a rate-dependent fracture energy $\Gamma(v)$ ($v$ is the crack propagation velocity) and intrinsic lengthscales, and quantitatively reproduces the high-speed oscillatory instability in the quasi-2D limit. We show that in-plane FWs feature a rather weak time dependence, with decay rate that increases with $d\Gamma(v)/dv\!>\!0$, and largely retain their properties upon FW-FW interactions, similarly to a related experimentally-observed solitonic behavior. Driving in-plane FWs into the nonlinear regime, we find that they propagate slower than predicted by a linear perturbation theory. Finally, by introducing small out-of-plane symmetry-breaking perturbations, coupled in- and out-of-plane FWs are excited, but the out-of-plane component decays under pure tensile loading. Yet, including a small anti-plane loading component gives rise to persistent coupled in- and out-of-plane FWs., Comment: 5 pages, 6 figures + references + Supplemental Materials (movies can be downloaded using a link in the PDF)

It is sometimes claimed that the twin "paradox" requires general relativity for a resolution. This paper presents a simple, exact resolution using only special relativity and the equivalence principle. Two earlier approximate solutions are considered, along with some background review to render the article self-contained. It is hoped that this material will be suitable for classroom instruction., 18 pages, six figures

This paper discusses the wing inertial effects on stability of pitch motion of hovering insects. The paper also presents a dynamic model appropriate for using averaging techniques and discusses the pitch stability results derived from the model. The model is used to predict the body angle of five insect species during hover, which are in good agreement with the available experimental results from different literature. The results suggest that the wing inertia forces have a considerable effect on pitch dynamics of insect flight and should not be ignored in dynamic analysis of hovering insects. The results also suggest that, though the pitch stability of hovering insects is open-loop stable, it may not be vibrationally stabilized. Instead, the pitch stability is a balance of the moment of insect's weight and the aerodynamic moment due to flapping kinematics with a nonzero mean stroke angle. Experiments with a flapping wing device confirm this results. To clearly explain the used model and clarify the difference between vibrational and non-vibrational stabilization, first this paper discusses the vibrational control of a three-degree-of-freedom force-input pendulum with its pivot moving in a vertical plane., 21 pages, 9 figures, 4 tables

The design of devices based on acoustic or optical fields requires the fabrication of cavities and structures capable of efficiently trapping these waves. A special type of cavity can be designed to support resonances with a theoretically infinite quality factor, named bound states in the continuum or BICs. The experimental measurement of such modes is still a challenging problem, as they are, by definition, not accessible from external perturbations. Therefore, current reported works rely on indirect measurements that are based on the traces left by these modes on external properties of one-dimensional systems. Here we report on the theoretical design and experimental realization of a two-dimensional, fully open acoustic resonator supporting BICs. This BIC, whose symmetry is chosen during design by properly tailoring the geometrical properties of the system, is completely accessible and allows for the direct measurement of the whole pressure field and properties. We experimentally demonstrate its existence with high quality factor and field enhancement properties.

In this study, we systematically investigated the mechanical response of monolayer molybdenum ditelluride (MoTe2) using molecular dynamics simulations. The tensile behavior of the trigonal prismatic phase (2H phase) MoTe2 under uniaxial strain was simulated in both the armchair and zigzag directions. We also investigated the crack formation and propagation in both armchair and zigzag directions at 10K and 300K to understand the fracture behavior of monolayer MoTe2. The crack simulations show clean cleavage for the armchair direction and the cracks were numerous and scattered in the case of the zigzag direction. Finally, we investigated the effect of temperature on Young's modulus and fracture stress of monolayer MoTe2. The results show that at a strain rate of 10^-4 ps^-1, the fracture strength of 2H-MoTe2 in the armchair and zigzag direction at 10K is 16.33 GPa (11.43 N/m) and 13.71429 GPa (9.46 N/m) under a 24% and 18% fracture strain, respectively. The fracture strength of 2H-MoTe2 in the armchair and zigzag direction at 600K is 10.81 GPa (7.56 N/m) and 10.13 GPa (7.09 N/m) under a 12.5% and 12.47% fracture strain, respectively. Although experimental results on MoTe2 are limited for a wide range of temperatures, we have found that Young's modulus agrees with existing literature for pristine MoTe2. For 2H-MoTe2 in both armchair and zigzag directions, the fracture stresses, fracture strengths, and Young's modulus decrease as the temperature rises, resulting from the increased atomic thermal vibrations., 16 Pages, 6 Figures

We show how to utilize magnetostriction to synchronize two mechanical vibration modes in a cavity magnomechanical system. The dispersive magnetostrictive interaction provides necessary nonlinearity required for achieving synchronization. Strong phase correlation between two mechanical oscillators can be established, leading to the synchronization robust against thermal noise. We develop a theoretical framework to analyze the synchronization by solving the constraint conditions of steady-state limit cycles. We determine that the strong cavity-magnon linear coupling can enhance and regulate the synchronization, which offers a new path to modulate synchronization. The work reveals a new mechanism for achieving and modulating synchronization and indicates that cavity magnomechanical systems can be an ideal platform to explore rich synchronization phenomena., comments welcome

The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with analytic and algebraic approaches. In the algebraic solution, creation and annihilation operators are introduced to factorize the Hamiltonian. This work presents an algebraic solution for the simple harmonic oscillator in the context of Classical Mechanics, exploring the Hamiltonian formalism. In this solution, similarities between the canonical coordinates in a convenient basis for the classical problem and the corresponding operators in Quantum Mechanics are highlighted. Moreover, the presented algebraic solution provides a straightforward procedure for the quantization of the classical harmonic oscillator, motivating and justifying some operator definitions commonly used to solve the correspondent problem in Quantum Mechanics.

Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in such structures. Here we report the existence of branched flows of flexural waves in such waveguides. The location of high amplitude motion, away from the launch location, scales as a power law with respect to the variance and linearly with respect to the correlation length of the spatial variation in the bending stiffness. These scaling laws are then theoretically derived from the ray equations. Numerical integration of the ray equations also exhibit this behaviour-consistent with finite element numerical simulations as well as the theoretically derived scaling. There appears to be a universality for the exponents in the scaling with respect to similar observations in the past for other types of waves, as well as flexural and hence dispersive waves in elastic plates., 9 pages, 10 figures, supplementary information attached as separate file

A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and positions, is presented. Methods for incorporating constraints are critically assessed. General theory, as well as explicitly worked out variational principles for a dissipative system (due to Lorenz) and a system with anholonomic constraints (due to Pars) are demonstrated. Conditions under which a (family of) dual Hamiltonian flow(s), as well as a constant(s) of motion, may be associated with a conservative or dissipative, and possibly constrained, primal system naturally emerge in this work.

Unidirectional and backscattering-free propagation of sound waves is of fundamental interest in physics, and highly sought-after in engineering. Current strategies utilize topologically protected chiral edge modes in bandgaps, or complex mechanisms involving active constituents or nonlinearity. Here we propose a new class of passive, linear, one-way edge states based on spin-momentum locking of Rayleigh waves in two-dimensional media in the limit of vanishing bulk modulus, which provides $100\%$ unidirectional and backscattering-free edge propagation at a broad range of frequencies instead of residing in gaps between bulk bands. We further show that such modes are characterized by a new topological winding number that is analogous to discrete angular momentum eigenvalues in quantum mechanics. These passive and backscattering-free edge waves have the potential to enable a new class of phononic devices in the form of lattices or continua that work in previously inaccessible frequency ranges.

We present an optimized design of our recently realized helical disc dynamo. Like the original set-up, the optimized dynamo consists of a flat multi-arm spiral coil and a co-axially placed disc which is connected to the former by sliding liquid metal contacts. In contrast to the original set-up, the disc and the coil in the optimized design have different sizes. This allows the disc to capture more of the high-density magnetic flux generated in the inner part of the coil and to avoid the reverse flux in the outer part of the coil. By optimizing the coil and dics radii, the critical magnetic Reynolds number can be reduced from ${\mathit Rm}\approx34.6$ when the disc and coil have equal inner and outer radii with the ratio $r_{i}/r_{o}\approx0.36$ to ${\mathit Rm}\approx11.6.$ This lowest possible disc dynamo threshold is attained when the disc and coil have relatively narrow widths. Using a slightly suboptimal but more practical set-up with the inner and outer radii of the disc and coil equal to to $(0.3,0.9)$ and $(0.74,1),$ respectively, self-excitation is expected at ${\mathit Rm}\approx14.6.$, 11 pages, 3 figures (to appear in Magnetohydrodynamics). arXiv admin note: text overlap with arXiv:1306.0142

We present a general formalism for the analysis of mechanical lattices with microstructure using the concept of effective mass. We first revisit a classical case of microstructure being modeled by a spring-interconnected mass-in-mass cell. The frequency-dependent effective mass of the cell is the sum of a static mass and of an added mass, in analogy to that of a swimmer in a fluid. The effective mass is derived using three different methods: momentum equivalence, action equivalence, and dynamic condensation. These methods are generalized to mechanical systems with arbitrary microstructure. As an application, we calculate the effective mass of a $1$D composite lattice with microstructure modeled by a chiral spring-interconnected mass-in-mass cell. A reduced (condensed) model of the full lattice is then obtained by lumping the microstructure into a single effective mass. A dynamic Bloch analysis is then performed using both the full and reduced lattice models, which give the same spectral results. In particular, the frequency bands follow from the full lattice model by solving a linear eigenvalue problem, or from the reduced lattice model by solving a smaller nonlinear eigenvalue problem. The range of frequencies of negative effective mass falls within the bandgaps of the lattice. Localized modes due to defects in the microstructure have frequencies within the bandgaps, inside the negative-mass range. Defects of the outer, or macro stiffness yield localized modes within each bandgap, but outside the negative-mass range. The proposed formalism can be applied to study the odd properties of coupled micro-macro systems, e.g., active matter.

We present a generalized FDTD scheme to simulate moving electromagnetic structures with arbitrary space-time configurations. This scheme is a local adaptation and 2+1-dimensional extension of the uniform and 1+1-dimensional scheme recently reported in [1]. The local adaptation, which is allowed by the inherently matched nature of the generalized Yee cell to the conventional Yee cell, extends the range of applicability of the scheme in [1] to moving structures that involve multiple and arbitrary velocity profiles while being fully compatible with conventional absorbing boundary conditions and standard treatments of medium dispersion. We show that a direct application of the conventional FDTD scheme predicts qualitatively correct spectral transitions but quantitatively erroneous scattering amplitudes, we infer from this observation generalized, hybrid - physical and auxiliary (non-physical) - fields that automatically satisfy moving boundary conditions in the laboratory frame, and accordingly establish local update equations based on the related Maxwell's equations and constitutive relations. We finally validate and illustrate the proposed method by three canonical examples - a space-time interface, a space-time wedge and a space-time accelerated interface - whose combination represent arbitrary space-time configurations. The proposed scheme fills an important gap in the open literature on computational electromagnetics and offers an unprecedented, direct solution for moving structures in commercial software platforms., 13 pages, 9 figures

We devise an end-to-end communication channel model that describes the performance of RIS-assisted MIMO wireless links. The model borrows the impedance (interaction) matrix formalism from the Method of Moments and provides a physics-based communication model. In configurations where the transmit and receive antenna arrays are distant from the RIS beyond a wavelength, a reduced model provides accurate results for arbitrary RIS unit cell geometry. Importantly, the simplified model configures as a cascaded channel transfer matrix whose mathematical structure is compliant with widely accepted, but less accurate, system level RIS models. A numerical validation of the communication model is presented for the design of binary RIS structures with scatterers of canonical geometry. Attained results are consistent with path-loss models: For obstructed line-of-sight between transmitter and receiver, the channel capacity of the (optimised) RIS-assisted link scales as $R^{-2}$, with $R$ RIS-receiver distance at fixed transmitter position. Our results shows that the applicability of communication models based on mutual impedance matrices is not restricted to canonical minimum scattering RIS unit cells., Submitted to IEEE Transactions on Antennas and Propagation; 15 pages, 11 figures

The Euler-Poisson equations for the Lagrange top are derived on the basis of a variational problem with kinematic constraints. The Hamiltonian structure of these equations is established using the intermediate formalism presented in the recent work arXiv:2302.12423. General solution to the equations of motion is reduced to the calculation of four elliptic integrals. Several solutions in terms of elementary functions are presented. The case of precession without nutation has a surprisingly rich relationship between the rotation and precession rates, and is discussed in detail., 15 pages, misprints corrected. arXiv admin note: text overlap with arXiv:2304.10371

The interaction of a solenoid with a passing charged particle can be treated within classical or quantum physics. If charged particles pass around both sides of a solenoid, there is an experimentally-observed Aharonov-Bohm deflection of the double-slit particle interference pattern between charges passing on opposite sides. Such a deflection can be obtained by a classical force calculation. Although the magnitude of the angular deflection agrees between the classical force calculation and the quantum topological theory, the direction of the predicted deflection is opposite. Here we point out the simple basis for the direction of the deflection based upon classical electrodynamics and based upon quantum theory, and we mention analogues, both the electrostatic deflection of the particle interference pattern and the optical analogue of the classical calculation. The deflection direction involves an experimental question which is addressed rarely if ever., 12 pages

High-order harmonics are ubiquitous in nature and present in electromagnetic, acoustic, and gravitational waves. They are generated by periodic nonlinear processes or periodic high-frequency pulses. However, this periodicity is often inexact, such as that in chirped (frequency-swept) optical waveforms or interactions with nonstationary matter -- for instance, reflection from accelerating mirrors. Spectra observed in such cases contain complicated sets of harmonic-like fringes. We encountered such fringes in our experiment on coherent extreme ultraviolet generation via BISER, and could not interpret them using currently available knowledge. Here, we present a comprehensive theory based on interference of harmonics with different orders fully explaining the formation of these fringes, which we call alloharmonics. Like atomic spectra, the complex alloharmonic spectra depend on several integer numbers and bear a unique imprint of the emission process, which the theory can decipher, avoiding confusion or misinterpretation. We also demonstrate the alloharmonics in simulations of gravitational waves emitted by binary black hole mergers. Further, we predict the presence of alloharmonics in the radio spectra of pulsars and in optical frequency combs, and propose their use for measurement of extremely small accelerations necessary for testing gravity theories. The alloharmonics phenomenon generalizes classical harmonics and is critical in research fields such as laser mode locking, frequency comb generation, attosecond pulse generation, pulsar studies, and future gravitational wave spectroscopy., 29 pages, 9 figures, 3 tables

We solve analytically the differential equations for a skier on a circular hill and for a particle on a loop-the-loop track when the hill or track is endowed with a coefficient of kinetic friction $\mu$. For each problem, we determine the exact "phase diagram" in the two-dimensional parameter plane., Comment: LaTeX2e, 22 pages (main text plus two appendices) including 10 figures. Version 2 is much revised, thanks to helpful comments by referees. To be published in the American Journal of Physics

We investigate the nonlinear effect of a pendulum with the upper end fixed to an elastic rod which is only allowed to vibrate horizontally. The pendulum will start rotating and trace a delicate stationary pattern when released without initial angular momentum. We explain it as amplitude modulation due to nonlinear coupling between the two degrees of freedom. Though the phenomenon of conversion between radial and azimuthal oscillations is common for asymmetric pendulums, nonlinear coupling between the two oscillations is usually overlooked. In this paper, we build a theoretical model and obtain the pendulum's equations of motion. The pendulum's motion patterns are solved numerically and analytically using the method of multiple scales. In the analytical solution, the modulation period not only depends on the dynamical parameters, but also on the pendulum's initial releasing positions, which is a typical nonlinear behavior. The analytical approximate solutions are supported by numerical results. This work provides a good demonstration as well as a research project of nonlinear dynamics on different levels from high school to undergraduate students., Comment: 19 pages, 6 figures

The article determine a relativistic tensor of the second rank containing the vectors of the electric and magnetic polarization of the medium, based on the Maxwell equations and the determination of the charge density and polarization current of a structural microparticle. Using this tensor and the electromagnetic field tensor, the relativistic lagrangian of the interaction an electromagnetic field with a structural microparticle is obtained, taking into account the polarization of its structural elements. Based on the induced moments, the relativistic lagrangian of the interaction an electromagnetic field with a structural microparticle is constructed with considering the electric and magnetic polarizabilities., 10 pages

Solving physics problems for which we know the equations, boundary conditions and symmetries can be done by deep learning. The constraints can be either imposed as terms in a loss function or used to formulate a neural ansatz. In the present case study, we calculate the induced field inside and outside a dielectric cube placed in a uniform electric field, wherein the dielectric mismatch at edges and corners of the cube makes accurate calculations numerically challenging. The electric potential is expressed as an ansatz incorporating neural networks with known leading order behaviors and symmetries and the Laplace's equation is then solved with boundary conditions at the dielectric interface by minimizing a loss function. The loss function ensures that both Laplace's equation and boundary conditions are satisfied everywhere inside a large solution domain. We study how the electric potential inside and outside a quasi-cubic particle evolves through a sequence of shapes from a sphere to a cube. The neural network being differentiable, it is straightforward to calculate the electric field over the whole domain, the induced surface charge distribution and the polarizability. The neural network being retentive, one can efficiently follow how the field changes upon particle's shape or dielectric constant by iterating from any previously converged solution. The present work's objective is two-fold, first to show how an a priori knowledge can be incorporated into neural networks to achieve efficient learning and second to apply the method and study how the induced field and polarizability change when a dielectric particle progressively changes its shape from a sphere to a cube.

In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit over time. Since the Hamiltonian orbits generalize the exponential maps, this approach allows us to learn the underlying manifold of the graph in training, in contrast to most of the existing literature that assumes a fixed graph embedding manifold with a closed exponential map solution. Our proposed node embedding strategy can automatically learn, without extensive tuning, the underlying geometry of any given graph dataset even if it has diverse geometries. We test Hamiltonian functions of different forms and verify the performance of our approach on two graph node embedding downstream tasks: node classification and link prediction. Numerical experiments demonstrate that our approach adapts better to different types of graph datasets than popular state-of-the-art graph node embedding GNNs. The code is available at \url{https://github.com/zknus/Hamiltonian-GNN}.

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the equations of motion follows a simple principle which generalizes the holonomic case. Furthermore, attention is paid to the fact that the kinematic variables retain their velocity meaning, without resorting to the pseudo-velocity technique. Particular situations are examined in which the modeling of the constraints can be carried out in several ways to evaluate their effective equivalence. Numerous examples, many of which taken from the most recurring ones in the literature, are provided in order to illustrate the proposed theory.

Following the discovery of moir\'e-driven superconductivity in twisted graphene multilayers, twistronics has spurred a surge of interest in tailored broken symmetries through angular rotations, enabling new properties from electronics to photonics and phononics. Analogously, in monoclinic polar crystals a nontrivial angle between non-degenerate dipolar phonon resonances can naturally emerge due to asymmetries in their crystal lattice, and its variations are associated with intriguing polaritonic phenomena, including axial dispersion, i.e., a rotation of the optical axis with frequency, and microscopic shear effects that result in asymmetric loss distributions. So far these phenomena were restricted to specific mid-infrared frequencies, difficult to access with conventional lasers, and fundamentally limited by the degree of asymmetry and the strength of light-matter interactions available in natural crystals. Here, we leverage twistronics to demonstrate giant axial dispersion and loss asymmetry of hyperbolic waves in elastic metasurfaces, by tailoring the angle between coupled pairs of anisotropic metasurfaces. We show extreme control over elastic wave dispersion via the twist angle, and leverage the resulting phenomena to demonstrate reflection-free negative refraction, as well as the application of axial dispersion to achieve diffraction-free non-destructive testing, whereby the angular direction of a hyperbolic probe wave is encoded into its frequency. Our work welds the concepts of twistronics, non-Hermiticity and extreme anisotropy, demonstrating the powerful opportunities enabled by metasurfaces for tunable, highly directional surface acoustic wave propagation, of great interest for applications ranging from seismic mitigation to on-chip phononics and wireless communications, paving the way towards their translation into emerging photonic and polaritonic metasurface technologies.

Motions of a material point along a set of parabolas are studied, taking into account the forces of Coulomb friction. The obtained results are compared with similar motions along the cycloid. The analysis is carried out using numerical calculations in the Mathcad program., 12 pages, 7 figures

The theory of point-particles in classical electrodynamics has a well-known problem of infinite self-energy, and the same is true of quantum electrodynamics. Instead of concluding that there is no such thing as a true point-particle, it is shown here how to remove the infinities by supposing that the electromagnetic field tensor has a symmetric part. This does not change the physics, as the equation of motion and the antisymmetric part of the retarded fields appearing in the equation of motion are unaffected. The symmetric part of the field tensor is not observable and therefore it need not be gauge-invariant, whereas the antisymmetric part is observable, gauge-invariant, and satisfies both the Maxwell Equations and the field equations governing the whole field tensor. This approach goes well beyond prior efforts at classical renormalization, and also entails a new derivation of the Lorentz-Abraham-Dirac (LAD) equation of motion., 15 pages, shortening title, adding acknowledgments, expanding Appendix, making some stylistic revisions

This paper presents the calculation of the electrical power transported by the electromagnetic fields of two parallel wires carrying opposite DC currents. The Poynting vector is developed in bipolar coordinates and symbolically integrated over different surfaces. For perfectly conducting wires, the purely longitudinal power in the space surrounding the wires is proved to be equal to that which is produced by the battery (and consumed by the load resistor). For resistive wires, the longitudinal power transported by the fields is shown to diminish according to the distance traveled, and the loss is proved to be equal to the power entering the wires via the fields at their surfaces., 23 pages, 9 figures, preliminary draft for 3rd version in review process, American Journal of Physics

Computer simulation of the time evolution in a classical system is a standard numerical method, used in numerous scientific articles in Natural Science. Almost all the simulations are performed by discrete Molecular Dynamics (MD). The algorithm used in MD was originally formulated by I. Newton at the beginning of his book $Principia$. Newton's discrete dynamics is exact in the same sense as Newton's analytic counterpart Classical Mechanics. Both dynamics are time-reversible, symplectic, and have the same dynamic invariances. There is no qualitative difference between the two kinds of dynamics. This is due to the fact, that there exists a ''shadow Hamiltonian'' nearby the Hamiltonian $H(\textbf{q},\textbf{p})$ for the analytic dynamics, and where its dynamics can be obtained by an asymptotic expansion from $H(\textbf{q},\textbf{p})$, and where the positions generated by MD are located on the analytic trajectories for the shadow Hamiltonian. It is only possible to obtain the solution of Newton's classical differential equations for a few simple systems, but the exact discrete Newtonian dynamics can be obtained for almost all complex classical systems. Some examples are given here: The emergence and evolution of a planetary system. The emergence and evolution of planetary systems with inverse forces. The emergence and evolution of galaxies in the expanding Universe., 9 figures

The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation of a mechanical problem to fewer degrees of freedom, a process known as dynamical reduction. However, extant reductions are either non-general, or hide the problem's symmetry or include unexplained definitions. This paper presents a dynamical reduction that avoids these issues, and hence is general and natural. Any three-body configuration defines a triangle, and its orientation in space. Accordingly, we decompose the dynamical variables into the geometry (shape + size) and orientation of the triangle. The geometry variables are shown to describe the motion of an abstract point in a curved 3d space, subject to a potential-derived force and a magnetic-like force with a monopole charge. The orientation variables are shown to obey a dynamics analogous to the Euler equations for a rotating rigid body, only here the moments of inertia depend on the geometry variables, rather than being constant. The reduction rests on a novel symmetric solution to the center of mass constraint inspired by Lagrange's solution to the cubic. The formulation of the orientation variables is novel and rests on a little known generalization of the Euler-Lagrange equations to non-coordinate velocities. Applications to global features, to the statistical solution and to special exact solutions are presented. A generalization to the four-body problem is presented., 32 pages, 2 figures. v2: added the sections "Hill-like region in geometry space" and "quotes from previous works", and made more minor changes

The current need of improving performance in terms of control and aerodynamic efficiency of ammunitions leads to the necessity of performing accurate flying geometry characterizations. Therefore, new investigation methods are developed in order to increase the aerodynamic knowledge. Free flight measurements experiments are the most common way to obtain dynamic aerodynamic coefficients. However, they do not always allow neither easy nor perfect measurements conditions. Currently ISL develops a stereovision method based wind-tunnel measurements methodology for investigation of a 3-axis free rotation model. This methods has been applied to the DREV-ISL reference model in order to compare coefficients obtained by this method with numerical results.

We study the characteristics of azimuthally propagating electromagnetic fields in a cylindrical cavity. It is found that under certain conditions, the transverse components of the electromagnetic field are singular at the center of the cavity but the corresponding electromagnetic field remains of finite energy. The solutions are arranged in branches each of which starts from a root of $J_1(x)=0$ for the TE modes and a root of $J_0(x)=0$ for the TM modes. The lowest (dominant) branch starts from a resonance that corresponds to the solution $x=0$ of $J_1(x)=0$. Its energy has a logarithmic singularity in a lossless structure. The singular solutions with finite energy can be observed experimentally by forcing them to resonate in a cavity with inserted metallic wedges. They can also be excited by transient sources. The singular electromagnetic field of these waves is strong enough to ionize the air. Whether these transient singular fields can initiate lightning, a phenomenon that is still not understood, is a very interesting question. It is also worth investigating whether the lowest resonance is excited in violently energetic cosmological phenomena such as cosmic jets.

Relaxation modulus and creep compliance corresponding to fractional anti-Zener and Zener models are calculated and restrictions on model parameters narrowing thermodynamical constraints are posed in order to ensure relaxation modulus and creep compliance to be completely monotone and Bernstein function respectively, that a priori guarantee the positivity of stored energy and dissipated power per unit volume, derived in time domain by considering the power per unit volume. Both relaxation modulus and creep compliance for model parameters obeying thermodynamical constraints, proved that can also be oscillatory functions with decreasing amplitude. Model used in numerical examples of relaxation modulus and creep compliance is also analyzed for the asymptotic behavior near the initial time instant and for large time., The manuscript is under review in the Applied Mathematical Modeling

We first present a way to formulate the equations of motion for a nonholonomic system with nonlinear constraints with respect to the velocities. The formulation is based on the Cetaev condition which aims to extend the practical method of virtual displacements from the holonomic case to the nonlinear nonholonomic one. The condition may appear in a certain sense artificial and motivated only to coherently generalize that concerning the holonomic case. In the second part we show that for a specific category of nonholonomic constraints (homogeneous functions with respect to the generalized velocities) the Cetaev condition reveals the same physical meaning that emerges in systems with holonomic constraints. In particular the aspect of the mechanical energy associable to the system is analysed.

Modern geometric approaches to analytical mechanics rest on a bundle structure of the configuration space. The connection on this bundle allows for an intrinsic splitting of the reduced Euler–Lagrange equations. Hamel’s equations, on the other hand, provide a universal approach to non-holonomic mechanics in local coordinates. The link between Hamel’s formulation and geometric approaches in local coordinates has not been discussed sufficiently. The reduced Euler–Lagrange equations as well as the curvature of the connection are derived with Hamel’s original formalism. Intrinsic splitting into Euler–Lagrange and Euler–Poincaré equations and inertial decoupling is achieved by means of the locked velocity. Various aspects of this method are discussed.

When a spatially localized stress is applied to a growing one-dimensional interface, the interface deforms. This deformation is described by the effective surface tension representing the stiffness of the interface. We present that the stiffness exhibits divergent behavior in the large system size limit for a growing interface with thermal noise, which has never been observed for equilibrium interfaces. Furthermore, by connecting the effective surface tension with a space-time correlation function, we elucidate the mechanism that anomalous dynamical fluctuations lead to divergent stiffness., Comment: 6 pages, 4 figures (Supplemental Material: 11 pages, 8 figures)