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Existing methods for calculating substructure characteristic modes require treating interconnected metal structures as a single entity to ensure current continuity between different metal bodies. However, when these structures are treated as separate entities, existing methods exhibit inaccuracies, affecting the asses... |
The most general electromagnetic boundary, defined by linear and local boundary conditions, is defined in terms of conditions which can be called generalized impedance boundary conditions. Requiring that the boundary be equivalent to PEC and PMC boundaries for its two eigen-plane waves, which property is known to exis... |
The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle dispersion and propagation across interfaces with remarkable efficiency; but propagating in time is more physical and gives corr... |
In this paper, we consider the dynamics of a heavy homogeneous ball moving under the influence of dry friction on a fixed horizontal plane. We assume the ball to slide without rolling. |
The attraction of the Moon on objects at the surface of the Earth gives rise to a so-called tidal force which is of the order of 1/10,000,000 times the gravitational force of the Earth. For instance, when the Moon is located between the Earth and the Sun (new moon) the distance from a given terrestrial location to the... |
A review article on perturbation theory |
Flattened liquid drops poured on a very hot surface evaporate quite slowly and float on a film of their own vapour. In the cavities of a surface, an unusual type of vibrational motions occurs. |
The Inverse problem for an electromagnetic field produced by a dipole is solved. It is assumed that the field of an arbitrary changing dipole is known. |
The limits of the Second Law of Thermodynamics, which reigns undisputed in the macroscopic world, are investigated at the mesoscopic level, corresponding to spatial dimensions of a few microns. An extremely simple isolated system, modeled after Callen's adiabatic piston, [1] can, under appropriate conditions, be d... |
The influence of material coverings on the antenna bandwidth is investigated for antennas formed by thin electric or magnetic line sources. It is shown that uniform thin layers of arbitrary passive materials (including Veselago, left-handed, or double-negative materials) cannot help to overcome the bandwidth limitatio... |
Dimensional analysis techniques are used to describe (not only qualitatively) some interesting features of two specific physical processes: the kinematics of moving objects on the surface of a planet (e.g. the walking pace of a man on the Moon) and the run-up process of a tsunami wave approaching the shore. |
The complete charge-current density and field strength of an arbitrarily accelerated relativistic point-charge are explicitly calculated. That current includes, apart from the well-established delta-function term which is sufficient for its global conservation, additional contributions depending on the second and thir... |
General relativistic quantum dynamics of twisted (vortex) Dirac particles is constructed. The Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived for a twisted relativistic electron in arbitrary electric and magnetic fields. |
We present a new unified covariant description of electromagnetic field properties for an arbitrary space-time. We derive a complete set of irreducible components describing a six-dimensional electromagnetic field from the Maxwell and metric tensors using the symmetry group SL(2,C). |
An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate non-linear connection and the associated curvature. In the limit of low kinetic ... |
We consider the electrodynamics of electric charges and currents in vacuum and then generalise our results to the description of a dielectric and magnetic material medium : first in spatial algebra (SA) and then in space-time algebra (STA). Introducing a polarisation multivector $\tilde{P} = \boldsymbol{\tilde{p}} -\,... |
Using a dipole interaction model, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metascreen consisting of an array of arbitrarily shaped apertures in a perfectly conducting screen of nonzero thickness. The simple analytical formulas obtained are validated throu... |
We analyze the transformation properties of Faraday law in an empty space and its relationship with Maxwell equations. In our analysis we express the Faraday law via the four-potential of electromagnetic field and the field of four-velocity, defined on a circuit under its deforming motion. |
We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic slider/rigid substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory micro-slip fronts a... |
The classical two-body system with Lorentz-invariant Coulomb interaction V=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stueckelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering... |
Angular momentum balance is examined in the context of the electrodynamics of a spinning charged sphere, which is allowed to possess any variable angular velocity. We calculate the electric and magnetic fields of the (hollow) sphere, and express them as expansions in powers of $\tau/t_c \ll 1$, the ratio of the light-... |
It is well known that the three-body problem has few analytical solutions in certain symmetrical constraints; the Lagrangian triangular solution is one of them. This triangular solution has been revisited by <a href="http://R.Broucke" rel="external noopener nofollow" class="link-external link-http">this http URL</a> a... |
We show that a form for the second partial derivative of $1/r$ proposed by Frahm and subsequently used by other workers applies only when averaged over smooth functions. We use dyadic notation to derive a more general form without that restriction. |
This paper considers active cloaking of a square array of evenly spaced pins in a Kirchhoff plate in the presence of flexural waves. Active sources are distributed exterior to the cluster and are represented by the non-singular Green's function for the biharmonic operator. |
We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature profile and heat flow on each branch are computed. |
Open phononic systems including resonators radiating inside an unbounded medium support localized phonons characterized by a complex frequency. In this context, the concept of elastic quasinormal mode (QNM) arises naturally, as in the cases of nanophotonic and plasmonic open systems. |
According to Karl Popper assumptions are statements used to construct theories. During the construction of a theory whether the assumptions are either true or false turn out to be irrelevant in view of the fact that, actually, they gain their scientific value when the deductions derived from them suffice to explain ob... |
The term `sub-wavelength' is commonly used to describe innovative sound-absorbing structures usually labeled as `metamaterials'. Such structures, however, inherently do not bring groundbreaking advancements. |
In his monograph Thermodynamics, I. Müller proves that for incompressible media the volume does not change with the temperature. This Müller paradox yields an incompatibility between experimental evidence and the entropy principle. |
With the rich dynamics studies of single-state processes, the two-state processes attract more and more interests of people, since they are widely observed in complex system and have effective applications in diverse fields, say, foraging behavior of animals. This report builds the theoretical foundation of the proces... |
This paper expounds the modern theory of symplectic reduction in finite-dimensional Hamiltonian mechanics. This theory generalizes the well-known connection between continuous symmetries and conserved quantities, i.e. Noether's theorem. |
It is shown that there is a simple way to get the quantization equation for the electric and magnetic charges of dyons, $e_ig_j-g_ie_j=m(\hbar c)$, which also shed light to the origin of such quantization. |
In their recent paper, Kholmetskii, Missevitch, and Yarman "reanalyze the usual classical derivation of spin-orbit coupling in hydrogenlike atoms" and find a result "in qualitative agreement with the solution of the Dirac-Coulomb equation for hydrogenlike atoms. " However, the authors' result is bas... |
A magnetothermoelastic problem is considered for a nonhomogeneous, isotropic rotating hollow cylinder in the context of three theories of generalized formulations, the classical dynamical coupled (C-D) theory, the Lord and Shulman's (L-S) theory with one relaxation time parameter as well as the Green and Lindsay... |
We analyze a very simple variant of the Lorentz pendulum, in which the length is varied exponentially, instead of uniformly, as it is assumed in the standard case. We establish quantitative criteria for the condition of adiabatic changes in both pendula and put in evidence their substantially different physical behavi... |
Superscattering, induced by degenerate resonances, breaks the fundamental single-channel limit of scattering cross section of subwavelength structures; in principle, an arbitrarily large total cross section can be achieved via superscattering. It thus provides a unique way to strengthen the light-matter interaction at... |
The formation of high-order Bessel beams by a passive acoustic device consisting of an Archimedes' spiral diffraction grating is theoretically, numerically and experimentally reported in this work. These beams are propagation-invariant solutions of the Helmholtz equation and are characterized by an azimuthal varia... |
We assess Coarse Graining by studying different partitions of the phase space of the Baker transformation and the periodic torus automorphisms. It turns out that the shape of autocorrelation functions for the Baker transformation is more or less reproduced. |
A brief summary of the objections to the relational nature of inertial mass, gravitational mass and electric charge is presented. The objections are refuted by showing that the measurement process of comparing an instrument reference clock and a reference rod both obeying the laws of physics to a system obeying the sa... |
The determination of the stiffness center of a machine tool is a major element for knowing the dynamic behavior of this one. This stiffness center can be obtained from a static characterization of the machine tool. |
The decay of scalar variance in isotropic turbulence in a bounded domain is investigated. Extending the study of Touil, Bertoglio and Shao (2002; Journal of Turbulence, 03, 49) to the case of a passive scalar, the effect of the finite size of the domain on the lengthscales of turbulent eddies and scalar structures is ... |
This paper focuses on the oscillation threshold of single reed instruments. Several characteristics such as blowing pressure at threshold, regime selection, and playing frequency are known to change radically when taking into account the reed dynamics and the flow induced by the reed motion. |
We present an elementary deduction of the Newtonian force from Kepler's laws. We relate it to a generalization by Jacobi of the Keplerian motion, where the Euclidean form in the plane is replaced by some function with the same homogeneity. |
In this paper, the growth-induced bending deformation of a thin hyperelastic plate is studied. For a plane-strain problem, the governing PDE system is formulated, which is composed of the mechanical equilibrium equations, the constraint equation and the boundary conditions. |
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. |
A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical problem. |
This paper presents an intuitive, geometrical derivation of the relativistic addition of velocities, and of the electromagnetic interaction between two uniformly moving charged particles, based on 2 spatial + 1 temporal dimensional Minkowski diagrams. We calculate the relativistic addition of velocities by projecting ... |
In this paper anisotropic and dispersive wave propagation within linear strain-gradient elasticity is investigated. This analysis reveals significant features of this extended theory of continuum elasticity. |
It is shown that given an arbitrary canonical transformation and an arbitrary Hamiltonian, there is a naturally defined mapping that sends any solution of the Hamilton-Jacobi (HJ) equation into a solution of the HJ equation corresponding to the new Hamiltonian |
Metre size inertial resonators located in the ground have been theoretically shown to interact with a seismic wave (attenuation, band gaps) to enable protection of surface structures such as buildings. The challenge for Civil Engineering is to both reduce the size of these resonators and to increase their efficiency. |
We propose a classical solution for the kinetic description of matter falling into a black hole, which permits to evaluate both the kinetic entropy and the entropy production rate of classical infalling matter at the event horizon. The formulation is based on a relativistic kinetic description for classical particles ... |
The discontinuity of the vorticity is written as a function of the vector T grad s, (where T is the temperature and s the specific entropy). The expression is obtained thanks to potential equations and independently of the mass conservation and the equation of momentum balance. |
This is the answer to objections put forth in Proceedings of the Zacatecas Workshop "Lorentz Group, CPT and Neutrinos" (World Scientific, Singapore, 2000), pp. 335-341. |
A theory to predict the steady state position of a dissipative, flow-controlled system, as defined by a control volume, is developed based on the Maximum Entropy (MaxEnt) principle of Jaynes, involving minimisation of a generalised free energy-like potential. The analysis provides a theoretical justification of a loca... |
Existing optimization methods are used to calculate the upper-bounds on radiation efficiency with and without the constraint on self-resonance. These bounds are used for the design and assessment of small electric-dipole-type antennas. |
We present numerical results on the transmission properties of the left-handed materials (LHM) and split-ring resonators (SRR). The simulation resultsare in qualitative agreement with experiments. |
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and quantitative analysis. |
We examine the possible trajectories of a classical particle, trapped in a two-dimensional infinite rectangular well, using the Hamilton-Jacobi equation. We observe that three types of trajectories are possible: periodic orbits, open orbits and some special trajectories when the particle gets pocketed. |
When a flat stress-free surface (i.e., the ground in seismological applications) separating air from a isotropic, homogeneous or horizontally-layered, solid substratum is solicited by a SH plane body wave incident in the substratum, the response in the substratum is a single specularly-reflected body wave. When the st... |
Sound synthesis can be developed using physics-based modelling of the musical instruments. These methods need the description of the various parts of sound production mechanism, in particular a model of the acoustic resonator that have to be simple enough due to the real-time constraint. |
We show that the uniformly accelerated reference systems proposed by Einstein when introducing acceleration in the theory of relativity are Fermi-Walker coordinate systems. We then consider more general accelerated motions and, on the one hand we obtain Thomas precession and, on the other, we prove that the only accel... |
We provide an experimental framework where periodically driven PT-symmetric systems can be investigated. The set-up, consisting of two UHF oscillators coupled by a time-dependent capacitance, demonstrates a cascade of PT-symmetric broken domains bounded by exceptional point degeneracies. |
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other... |
Two previously studied classes of electromagnetic media, labeled as those of Q media and P media, are decomposed according to the natural decomposition introduced by Hehl and Obukhov. Six special cases based on either non-existence or sole existence of the three Hehl-Obukhov components, are defined for both medium cla... |
Several noncovariant formulations of the electromagnetic self-force of extended charged bodies, as have been developed in the context of classical models of charged particles, are compared. The mathematical equivalence of the various dissimilar self-force expressions is demonstrated explicitly by deriving these expres... |
A long-standing controversy concerning the causes of the magnetic field in and around a parallel-plate capacitor is examined. Three possible sources of contention are noted and detailed. |
Dynamic Mode III interfacial fracture in a dissimilar square-cell lattice, composed of two contrasting mass-spring lattice half-planes joined at an interface, is considered. The fracture, driven by a remotely applied load, is assumed to propagate at a constant speed along the interface. |
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an extremely complicated problem. |
This paper presents an analytical approach of the propagation of an acoustic wave through a normally distributed disordered lattice made up of Helmholtz resonators connected to a cylindrical duct. This approach allows to determine analytically the exact transmission coefficient of a weakly disordered lattice. |
It is nearly impossible to separate two interleaved phonebooks when held by their spines. A full understanding of this astonishing demonstration of solid friction in complex assemblies has remained elusive. |
According to the principle of relativity, the equations describing the laws of physics should have the same forms in all admissible frames of reference, i.e., form-invariance is an intrinsic property of correct wave equations. However, so far in the design of metamaterials by transformation methods, the form-invarianc... |
We introduce a reverse engineering approach to drive a RC circuit. This technique is implemented experimentally |
A popular absorbing structure, often referred to as Perfect Metamaterial Absorber, comprising metallic periodic pattern over a thin low-loss grounded substrate is studied by resorting to an efficient transmission line model. This approach allows the derivation of simple and reliable closed formulas describing the abso... |
A specialized high-precision numerical search for equal-mass collisionless three-body periodic free-fall orbits with central symmetry is conducted. The search is based on Newton's method with initial approximations obtained by the grid-search method. |
We present a simple method to obtain the solution of a few orbital problems: the Kepler problem, the modified Kepler problem by the addition of an inverse square potential and linear force. |
In this paper we present a vibration spectrum of a homogenous parallelepiped (HP) under the action of volume and surface forces resulting from the exponent displacements entering the Fourier transforms. Vibration under the action of axial surface tractions and the free vibration are described separately. |
This paper investigates the potential for stabilizing an inverted pendulum without electric devices, using gravitational potential energy. We propose a wheeled mechanism on a slope, specifically, a wheeled double pendulum, whose second pendulum transforms gravity force into braking force that acts on the wheel. |
Metriplectic dynamics couple a Poisson bracket of the Hamiltonian description with a kind of metric bracket, for describing systems with both Hamiltonian and dissipative components. The construction builds in asymptotic convergence to a preselected equilibrium state. |
The paper presents a new macroelement model for shallow foundations. The model is defined through a non-linear constitutive law written in terms of some generalized force and displacement parameters. |
We show that a topology can be defined in the four dimensional space-time of special relativity so as to obtain a topological semigroup for time. The Minkowski 4-vector character of space-time elements as well as the key properties of special relativity are still the same as in the standard theory. |
The concept of an observer and their associated rest space is defined in a pre-metric (i.e., projective-geometric) context that relates to time+space decompositions of the tangent bundle to space-time. The transformation from one observer to another when the two are in a state of relative motion is then defined, and i... |
The influence of radiation reaction (RR) on multiphoton Thomson scattering by an electron colliding head-on with a strong laser beam is investigated in a new regime, in which the momentum transferred on average to the electron by the laser pulse approximately compensates the one initially prepared. This equilibrium is... |
Hysteretic damping is often modeled by means of linear viscoelastic approaches such as "nearly constant Attenuation (NCQ)" models. These models do not take into account nonlinear effects either on the stiffness or on the damping, which are well known features of soil dynamic behavior. |
In this letter, an approach for designing a tunable and steerable antenna is presented. The antenna model is based on a wideband bow-tie radiating element mounted above an active Artificial Magnetic Conductor (AMC). |
A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-nonlinear regime. The fully-discrete scheme utilizes the Galerkin / finite-element method based on smooth periodic splines in space, and an... |
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. We show that for higher orders, it is more efficient to have fields represented in terms of symmetric and trace free moments. |
New method of analysing the free and heavy symmetric tops using Euler's equations to perform extraction from the body frame to the lab frame. Subsequent to extraction, the lab frame equations are solved by space phasor method. |
A novel directional coupler with a left-handed material (LHM) layer between two single-mode waveguides of usual material is introduced. The coupling system is analyzed with the supermode theory. |
A least action principle for damping motion has been previously proposed with a Hamiltonian and a Lagrangian containing the energy dissipated by friction. Due to the space-time nonlocality of the Lagrangian, mathematical uncertainties persist about the appropriate variational calculus and the nature (maxima, minima an... |
The electromagnetic (EM) radiation force-per-length exerted on a pair of electrically-conducting cylindrical particles of circular and non-circular cross-sections is examined using a formal semi-analytical method based on boundary matching in cylindrical coordinates. Initially, the scattering coefficients of the parti... |
On simple example is shown that a model of mechanically extended source of radiation in classical electrodynamics indeed has some problems with radiation reaction force. So one cannot, in general case, state, that the present situation with classical dynamics of mechanically extended sources of radiation is "very ... |
We analyze the deformation and energetics of a thin elastic cylindrical tube compressed between two plates which are parallel to the tube axis. The deformation is studied theoretically using exact numerical simulations and the variational approach. |
We present new aspects of the electromagnetic field by introducting the natural potentials. These natural potentials are suitable for constructing the first order distortions of the metric tensor of Complex Relativity - the theory combining the General Relativity with the electromagnetic equations. |
One-dimensional motion of Sommerfeld sphere in the case of potential barrier is numerically investigated. The effect of classical tunneling is found out - Sommerfeld sphere overcomes the barrier and finds itself in the forbidden, from classical point of view, area. |
In this work we examine the electrostatic screening potential due to a point charge located off-centre in a spherical dielectric cavity. This potential is expanded for the case in which the dielectric constant $\epsilon$ is large, several methods of finding the terms in the expansion are investigated, and closed-form ... |
If matter is suddenly put under a high pressure, for example a pressure of 100 Mb =10^14 dyn/cm^2, it can undergo a transformation into molecular excited states, bound by inner electron shells, with keV potential well for the electrons. If this happens, the electrons can under the emission of X-rays go into the ground... |
In the year 2002 publications of A.V.M. Khachatourian and A.O. Wistrom were released, in which the existence of an electrostatic torque has been claimed. This moment of force should act in a three sphere configuration, where one sphere is held at a constant electric potential. |
Various issues concerned with the design and sensitivity of the Anderson bridge are discussed. We analyse the circuit using the tools of Network Analysis to determine the conditions under which the balance may be obtained with greater sensitivity and discuss how to obtain these under practical circumstances in an unde... |
Free will is an old philosophical enigma that has been recently revived by neuropsychology. We restrict ourselves to the problem that determinism seems to allow only an illusion of freedom but random decissions do not contain any freedom either. |
Polarization radiation arising when a charged particle moves uniformly in vacuum nearby the media possessing a finite permittivity $\epsilon (\omega) = \epsilon^{\prime} + i \epsilon^{\prime \prime}$ and sharp boundaries is considered. The method is developed in which polarization radiation is represented as a field o... |
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