Physics - Classical Physics Publications (50)

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Physics - Classical Physics Publications

We demonstrate that nonlinearity may play a constructive role in supporting Bloch oscillations in a model which is discrete, in one dimension and continuous in the orthogonal one. The model can be experimentally realized in several fields of physics such as optics and Bose-Einstein condensates. We demonstrate that designing an optimal relation between the nonlinearity and the linear gradient strength provides extremely long-lived Bloch oscillations with little degradation. Read More


A substantial control of dispersion features of the hybrid EH01 and HE11 modes of a circular waveguide which is completely filled by a longitudinally magnetized composite finely-stratified ferrite-semiconductor structure is discussed. A relation between the resonant conditions of such a composite gyroelectromagnetic filling of the circular waveguide and dispersion features of the supported modes are studied. Three distinct frequency bands with the single-mode operation under normal as well as anomalous dispersion conditions of the EH01 mode are identified by solving an optimization problem with respect to the filling factors of the composite medium. Read More


We derive focused laser pulse solutions to the electromagnetic wave equation in vacuum. After reproducing beam and pulse expressions for the well-known paraxial Gaussian and axicon cases, we apply the method to analyse a laser beam with Lorentzian transverse momentum distribution. Whilst a paraxial approach has some success close to the focal axis and within a Rayleigh range of the focal spot, we find that it incorrectly predicts the transverse fall-off typical of a Lorentzian. Read More


In this work, a high-order discontinuous Galerkin (DG) method is used to perform a large-eddy simulation (LES) of a subsonic isothermal jet at high Reynolds number Re D = 10^6 on a fully un-structured mesh. Its radiated acoustic field is computed using the Ffowcs Williams and Hawkings formulation. In order to assess the accuracy of the DG method, the simulation results are compared to experimental measurements and a reference simulation based on a finite volume method. Read More


From the energy-momentum tensors of the electromagnetic field and the mechanical energy-momentum, the equations of energy conservation and balance of electromagnetic and mechanical forces are obtained. The equation for the Abraham force in a dielectric medium with losses is obtained Read More


We show that if a Lagrangian is invariant under a transformation (with the invariance defined in the standard manner), then the equations of motion obtained from it maintain their form under the transformation. We also show that the converse is not true, giving examples of equations of motion that are form-invariant under a transformation, but these equations can be derived from a Lagrangian that is not invariant under such transformation. The conclusions are valid for discrete or continuous systems. Read More


Though commonly used to calculate Q-factor and fractional bandwidth, the energy stored by radiating systems (antennas) is a subtle and challenging concept that has perplexed researchers for over half a century. Here, the obstacles in defining and calculating stored energy in general electromagnetic systems are presented from first principles as well as using demonstrative examples from electrostatics, circuits, and radiating systems. Along the way, the concept of unobservable energy is introduced to formalize such challenges. Read More


This paper shows that the method of uncertainty quantification via the introduction of Stratonovich cylindrical noise in the Hamiltonian formulation introduces stochastic Lie transport into the dynamics in the same form for both electromagnetic fields and fluid vorticity dynamics. Namely, the resulting stochastic partial differential equations (SPDE) retain their unperturbed form, except for an additional term representing induced Lie transport by a set of divergence-free vector fields associated with the spatial correlations of the cylindrical noise. The explanation lies in the method of construction of the Hamiltonian for the Stratonovich stochastic contribution to the motion in both cases, via pairing data correlation vector fields for cylindrical noise with the momentum map for the deterministic motion, which is responsible for the well-known analogy between hydrodynamics and electromagnetism. Read More


Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CW) on the predicted size-dependent surface tensions and nucleation rates for selected $n$-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and compared to the classical nucleation theory and the Peng--Robinson EoS. Read More


Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2- Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Read More


An instructive paradox concerning classical description of energy and momentum of extended physical systems in special relativity theory is explained using an elementary example of two point-like massive bodies rotating on a circle in their center-of-mass frame of reference, connected by an arbitrarily light and infinitesimally thin string. Namely, from the point of view of the inertial observers who move with respect to the rotating system, the sums of energies and momenta of the two bodies oscillate, instead of being constant in time. This result is understood in terms of the mechanism that binds the bodies: the string contributes to the system total energy and momentum no matter how light it is. Read More


In this paper an analytical approach for calculating scattering matrix elements for the case of normal incidence of the plane electromagnetic waves on the square patch-type Frequency Selective Surface (FSS), which is placed at the interface between two dielectric media is proposed. Analytical expressions for the reflection and transmission coefficients are shown to be accurate enough for practical purposes. Read More


We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Read More


Scattering of obliquely incident electromagnetic waves from periodically space-time modulated slabs is investigated. It is shown that such structures operate as nonreciprocal harmonic generators and spatial-frequency filters. For oblique incidences, low frequency harmonics are filtered out in the form of surface waves, while high-frequency harmonics are transmitted as space waves. Read More


We study the dynamics of pairs of connected masses in the plane, when nonholonomic (knife-edge) constraints are realized by forces of viscous friction, in particular its relation to constrained dynamics, and its approximation by the method of matching asymptotics of singular perturbation theory when the mass to friction ratio is taken as the small parameter. It turns out that long term behaviors of the frictional and constrained systems may differ dramatically no matter how small the perturbation is, and when this happens is not determined by any transparent feature of the equations of motion. The choice of effective time scales for matching asymptotics is also subtle and non-obvious, and secular terms appearing in them can not be dealt with by the classical methods. Read More


This paper explores in details the capabilities of two model reduction techniques - the Spectral Reduced Order Model (Spectral-ROM) and the Proper Generalised Decomposition (PGD) - to numerically solve moisture diffusion problems. Both techniques assume separated tensorial representation of the solution by a finite sum of function products. The Spectral-ROM fixes a set of spatial basis functions to be the Chebyshev polynomials and then, a system of ordinary differential equations is built to compute the temporal coefficients of the solution using the Galerkin projection method, while the PGD aims at computing directly the basis of functions by minimising the residual. Read More


Faraday's Law of induction is often stated as "a change in magnetic flux causes an EMF"; or, more cautiously, "a change in magnetic flux is associated with an EMF"; It is as well that the more cautious form exists, because the first "causes" form is incompatible with the usual expression $V = - \partial_t \Phi$. This is not, however, to deny the causality as reasonably inferred from experimental observation - it is the equation for Faraday's Law of induction which does not represent the claimed cause-and-effect relationship. Here I investigate a selection of different approaches, trying to see how an explicitly causal mathematical equation, which attempts to encapsulate the "a change in magnetic flux causes . Read More


This research is on the dynamics of electrostatically actuated radial-contour mode microring resonators. The governing equation of motion is derived by the minimization of the Hamiltonian and generalized to include the viscous damping effect. The Galerkin method is used to discretize the distributed-parameter model of the considered ring resonator. Read More


We report on the experimental observation of topologically protected edge waves in a two-dimensional elastic hexagonal lattice. The lattice is designed to feature K point Dirac cones that are well separated from the other numerous elastic wave modes characterizing this continuous structure. We exploit the arrangement of localized masses at the nodes to break mirror symmetry at the unit cell level, which opens a frequency bandgap. Read More


In this paper, we investigate the main algebraic properties of the maximally superintegrable system known as "Perlick system type I". All possible values of the relevant parameters, $K$ and $\beta$, are considered. In particular, depending on the sign of the parameter $K$ entering in the metrics, the motion will take place on compact or non compact Riemannian manifolds. Read More


In this paper, we investigate both experimentally and theoretically the dynamics of a liquid plug driven by a cyclic forcing inside a cylindrical rigid capillary tube. First, it is shown that depending on the type of forcing (flow rate or pressure cycle), the dynamics of the liquid plug can either be stable and periodic, or conversely accelerative and eventually leading to the plug rupture. In the latter case, we identify the source of the instability to be a combination of a flow memory resulting from liquid film deposition on the walls and a lubrication effect, i. Read More


Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. Read More


We are concerned with a novel sensor-based gesture input/instruction technology which enables human beings to interact with computers conveniently. The human being wears an emitter on the finger or holds a digital pen that generates a time harmonic point charge. The inputs/instructions are performed through moving the finger or the digital pen. Read More


We relate the large time asymptotics of the energy statistics in open harmonic networks to the variance-gamma distribution and prove a full Large Deviation Principle. We consider both Hamiltonian and stochastic dynamics, the later case including electronic RC networks. We compare our theoretical predictions with the experimental data obtained by Ciliberto et al. Read More


We report the results of an extended search for planar Newtonian periodic three-body orbits with vanishing angular momentum, that has led to more than 150 new topologically distinct orbits, which is more than three-fold increase over the previously known ones. Each new orbit defines an infinite family of orbits with non-vanishing angular momenta. We have classified these orbits in ten algebraically defined sequences. Read More


We theoretically show that an externally driven dipole placed inside a cylindrical hollow waveguide can generate a train of ultrashort and ultrafocused electromagnetic pulses. The waveguide encloses vacuum with perfect electric conducting walls. A dipole driven by a single short pulse, which is properly engineered to exploit the linear spectral filtering of the cylindrical hollow waveguide, excites longitudinal waveguide modes that are coherently re-focused at some particular instances of time. Read More


The penetration of a fast projectile into a resistant medium is a complex process that is suitable for simple modeling, in which basic physical principles can be profitably employed. This study connects two different domains: the fast motion of macroscopic bodies in resistant media and the interaction of charged subatomic particles with matter at high energies, which furnish the two limit cases of the problem of penetrating projectiles of different sizes. These limit cases actually have overlapping applications; for example, in space physics and technology. Read More


A generalized magnetothermoelasticity, in the context of Lord-Shulman theory, is employed to investigate the interaction of a homogeneous and isotropic perfect conducting half space with rotation. The Laplace transform for time variable is used to formulate a vector-matrix differential equation which is then solved by eigenvalue method. The continuous solution of displacement component while the discontinuous solutions of stress components, temperature distribution, induced magnetic and electric field have been analyzed in an approximate manner using assymptotic expansion for small time. Read More


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's (G-L) theory with two relaxation time parameters. The inner surface of the cylinder is subjected to a time dependent exponential thermal shock at its inner boundary. The inner and outer surfaces of the hollow cylinder are assumed to be traction free and the temperature gradient vanishes at its outer surface. Read More


We study the orbit of a single particle moving under the Yukawa potential and observe the precessing ellipse type orbits. The amount of precession can be tuned through the coupling parameter $\alpha$. With a suitable choice of the coupling parameter; we can get a closed bound orbit. Read More


We derive the spectral decomposition of the Lippmann-Schwinger equation for electrodynamics, obtaining the fields as a sum of eigenmodes. The method is applied to cylindrical geometries. Read More


In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease known as "slow dynamics" occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. Read More


This paper presents a topology optimization framework for structural problems subjected to transient loading. The mechanical model assumes a linear elastic isotropic material, infinitesimal strains, and a dynamic response. The optimization problem is solved using the gradient-based optimizer Method of Moving Asymptotes (MMA) with time-dependent sensitivities provided via the adjoint method. Read More


First-order perturbative calculation of the frequency-shifts caused by special relativity is performed for a charged particle confined in a Penning trap. The perturbed motion is approximated by the Jacobian elliptic functions which describe the periodic orbit repeating itself sinuously with a period that exceeds $2\pi$. We find relativistic corrections to amplitudes of oscillating modes as well as shifts of eigenfrequencies which depend on amplitudes. Read More


We study, both numerically and analytically, the time needed to observe the breaking of an FPU $\alpha$-chain in two or more pieces, starting from an unbroken configuration at a given temperature. It is found that such a "chopping" time is given by a formula that, at low temperatures, is of the Arrhenius-Kramers form, so that the chain does not break up on an observable time-scale. The result explains why the study of the FPU problem is meaningful also in the ill-posed case of the $\alpha$-model Read More


Besides the defining space-time symmetries (homogeneity and isotropy) of inertial frames, the derivation of Lorentz transformation requires postulating the principle of relativity and the existence of a finite speed limit. In this article, we point out that the existence of a finite speed limit can be readily inferred from the nature of allowed inertial frames. We also show that the principle of relativity can be obtained from the defining space-time symmetries of every inertial frame. Read More


The problem of determining those multiplets of forces, or sets of force multiplets, acting at a set of points, such that there exists a truss structure, or wire web, that can support these force multiplets with all the elements of the truss or wire web being under tension, is considered. The two-dimensional problem where the points are at the vertices of a convex polygon is essentially solved: each multiplet of forces must be such that the net anticlockwise torque around any vertex of the forces summed over any number of consecutive points clockwise past the vertex must be non-negative; and one can find a truss structure that supports under tension, and only supports, those force multiplets in a convex polyhedron of force multiplets that is generated by a finite number of force multiplets each satisfying the torque condition. Progress is also made on the problem where only a subset of the points are at the vertices of a convex polygon, and the other points are inside. Read More


We consider $d\times d$ tensors $A(x)$ that are symmetric, positive semi-definite, and whose row-divergence vanishes identically. We establish sharp inequalities for the integral of $(\det A)^{\frac1{d-1}}$. We apply them to models of compressible inviscid fluids: Euler equations, Euler--Fourier, relativistic Euler, Boltzman, BGK, etc. Read More


Homogeneity of space and time, spatial isotropy, principle of relativity and the existence of a finite speed limit (or its variants) are commonly believed to be the only axioms required for developing the special theory of relativity (Lorentz transformations). In this paper it is shown, however, that Lorentz transformation cannot actually be derived without the explicit assumption of time isotropy (time-reversal symmetry) which is logically independent of the other postulates of relativity. Postulating time isotropy also restores the symmetry between space and time in the postulates of relativity. Read More


Field patterns, first proposed by the authors in [Milton, Mattei. Proc R Soc A. 2017], are orderly patterns of characteristic lines that arise in specific space-time microstructures whose geometry in one spatial dimension plus time is somehow commensurate to the slope of the characteristic lines. Read More


We show that for an infinite, uniformly charged plate no well defined electric field exists in the framework of electrostatics, for it cannot be defined as a mathematically consistent limit of a solution for a finite plate. We discuss an infinite wire and an infinite stripe as examples of infinite charge distributions for which the electric field can be determined as a limit in a formal, mathematical way. We also propose the didactic framework that can help students to understand the subtleties related to the problems of limits in electrostatics. Read More


Conventional wireless power transfer systems consist of a microwave power generator and transmitter located at one place and a microwave power receiver located at a distance. Here we show that wireless power transfer can be realized as a single distributed microwave generator with an over-the-air feedback, so that the microwave power is generated directly at the place where the energy needs to be delivered. We demonstrate that the use of this paradigm increases efficiency and dramatically reduces sensitivity to misalignments, variations in load and power, and possible presence of obstacles between the source and receiver. Read More


It has been argued in [EPL {\bf 90} (2010) 50004], entitled {\it Essential discreteness in generalized thermostatistics with non-logarithmic entropy}, that "continuous Hamiltonian systems with long-range interactions and the so-called q-Gaussian momentum distributions are seen to be outside the scope of non-extensive statistical mechanics". The arguments are clever and appealing. We show here that, however, some mathematical subtleties render them unconvincing Read More


The synthesis of non-magnetic 2D dielectric cloaks as proper solutions of an inverse scattering problem is addressed in this paper. Adopting the relevant integral formulation governing the scattering phenomena, analytic and numerical approaches are exploited to provide new insights on how frequency and direction of arrival of the incoming wave may influence the cloaking mechanism in terms of permittivity distribution within the cover region. In quasi-static (subwavelength) regime a solution is analytically derived in terms of homogeneous artificial dielectric cover with $\varepsilon<\varepsilon_0$ which is found to be a necessary and sufficient condition for achieving omnidirectional cloaking. Read More


This paper proposes the use of the Spectral method to simulate diffusive moisture transfer through porous materials, which can be strongly nonlinear and can significantly affect sensible and latent heat transfer. An alternative way for computing solutions by considering a separated representation is presented, which can be applied to both linear and nonlinear diffusive problems, considering highly moisture-dependent properties. The Spectral method is compared with the classical implicit Euler and Crank-Nicolson schemes. Read More


In this article, we present the general form of the full electromagnetic Green function suitable for application in bulk material physics. In particular, we show how the seven adjustable parameter functions of the free Green function translate into seven corresponding parameter functions of the full Green function. Furthermore, for both the fundamental response tensor and the electromagnetic Green function, we discuss the reduction of the Dyson equation on the four-dimensional Minkowski space to an equivalent, three-dimensional Cartesian Dyson equation. Read More


The angle of rotation of any target about the radar line of sight (LOS) is known as the polarization orientation angle. The orientation angle is found to be non-zero for undulating terrains and man-made targets oriented away from the radar LOS. This effect is more pronounced at lower frequencies (eg. Read More


The paper considers a process of escape of classical particle from a one-dimensional potential well by virtue of an external harmonic forcing. We address a particular model of the infinite-range potential well that allows independent adjustment of the well depth and of the frequency of small oscillations. The problem can be conveniently reformulated in terms of action-angle variables. Read More


A rattleback is a rigid, semi-elliptic toy which exhibits unintuitive behavior; when it is spun in one direction, it soon begins pitching and stops spinning, then it starts to spin in the opposite direction, but in the other direction, it seems to spin just steadily. This puzzling behavior results from the slight misalignment between the principal axes for the inertia and those for the curvature; the misalignment couples the spinning with the pitching and the rolling oscillations. It has been shown that under the no-slip condition and without dissipation the spin can reverse in both directions, and Garcia and Hubbard obtained the formula for the time required for the spin reversal $t_r$ [Proc. Read More


Using a separable Buchwald representation in cylindrical coordinates, we show how under certain conditions the coupled equations of motion governing the Buchwald potentials can be decoupled and then solved using well-known techniques from the theory of PDEs. Under these conditions, we then construct two parametrized families of particular solutions to the Navier-Lame equation. In this paper, we specifically construct solutions having 2pi-periodic angular parts. Read More