# Physics - Classical Physics Publications (50)

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## Physics - Classical Physics Publications

A long elastic cylinder, radius $a$ and shear-modulus $\mu$, becomes unstable given sufficient surface tension $\gamma$. We show this instability can be simply understood by considering the energy, $E(\lambda)$, of such a cylinder subject to a homogenous longitudinal stretch $\lambda$. Although $E(\lambda)$ has a unique minimum, if surface tension is sufficient ($\Gamma\equiv\gamma/(a\mu)>\sqrt{32}$) it looses convexity in a finite region. Read More

We consider a two-state system consisting of a pair of coupled ferromagnetic waveguides. A monotonically increasing bias magnetic field can dynamically manipulate the system to enter a PT-symmetry broken phase and then reenter a symmetric phase. The symmetry recovery is enabled by the presence of accidental degeneracy points when the system has no loss, and each degeneracy point can spawn a pair of exceptional points when asymmetric loss is introduced. Read More

Tsallis' non-extensivity $S_q(AB)=S(A)+S(b)+ 1-q)S(A)S(B)$ entails hidden correlations. We show here that these correlations lead to surprising results for the Tsallis' classical ideal gas and the Harmonic Oscillator. Read More

The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion function. The generalized Fourier transform approach is the extension of the Fourier transform method used for normal diffusion equation. Read More

The accuracy of two equivalent antenna representations, near-field sources and far-field sources, are evaluated for an antenna installed on a simplified platform in a series of case studies using different configurations of equivalent antenna representations. The accuracy is evaluated in terms of installed far-fields and surface currents on the platform. The results show large variations between configurations. Read More

We show that gyrotropic structures with balanced gain and loss that respect anti-linear symmetries exhibit a giant non-reciprocity at the so-called exact phase where the eigenfrequencies of the isolated non-Hermitian set-up are real. The effect occurs in a parameter domain near an exceptional point (EP) degeneracy, where mode-orthogonality collapses. The theoretical predictions are confirmed numerically in the microwave domain, where a non-reciprocal transport above 90dB is demonstrated, and are further verified using lump-circuitry modeling. Read More

The focus of this paper is on the use of transfer functions to comprehend the formation of band gaps in locally resonant acoustic metamaterials. Identifying a recursive approach for any number of serially arranged locally resonant mass in mass cells, a closed form expression for the transfer function is derived. Analysis of the end-to-end transfer function helps identify the fundamental mechanism for the band gap formation in a finite metamaterial. Read More

Recent studies have introduced a new class of two-dimensional acoustic metamaterials whose dispersion and propagation properties results from the use of geometric inhomogeneities in the form of Acoustic Black Holes (ABH). The ABH is an element able to smoothly bend and slow down elastic waves, therefore providing a variety of unconventional dispersion and propagation properties typically observed in more complex multi-material and locally resonant designs. This approach enables thin-walled structural elements having fully embedded acoustic lenses capable of different functionalities such as focusing, collimation, and negative refraction. Read More

Having no any explanations the radiation of high-frequency components of the pulsar in the Crab Nebula can be a manifestation of instability in the nonlinear reflection from the neutron star surface. Reflected radiation it is the radiation of relativistic positrons flying from the magnetosphere to the star and accelerated by the electric field of the polar gap. The discussed instability it is a stimulated scattering by surface waves, predicted more than forty years ago and still nowhere and by no one had been observed. Read More

In this paper the problem is posed of determining the physically-meaningful asymptotic orderings holding for the statistical description of a large $N-$body system of hard spheres,\textit{ i.e.,} formed by $N\equiv\frac{1}{\varepsilon} \gg1$ particles, which are allowed to undergo instantaneous and purely elastic unary, binary or multiple collisions. Read More

There were proposed new formulas for the dielectric medium permittivity distribution along spatial coordinates in the space between a linear TEM-horn's leafs, which were obtained according to the rules of geometric optics in the assumption of the phase center being lumped or distributed. The formulas has been checked by FDTD simulation of an ultra-wideband signal excitation; two cases were studied---when dielectric medium is present, and absent. For these both cases, there was obtained voltage steady-wave ratio, as well as radiation patterns at a set of frequencies up to 20~GHz; the results comparison was performed. Read More

In J.D. Jackson's Classical Electrodynamics textbook, the analysis of Dirac's charge quantization condition in the presence of a magnetic monopole has a mathematical omission and an all too brief physical argument that might mislead some students. Read More

**Affiliations:**

^{1}University of Georgia

Derivation of the Lorentz transformation without the use of Einstein's Second Postulate is provided along the lines of Ignatowsky, Terletskii, and others. This is a write-up of the lecture first delivered in PHYS 4202 E&M class during the Spring semester of 2014 at the University of Georgia. The main motivation for pursuing this approach was to develop a better understanding of why the faster-than-light neutrino controversy (OPERA experiment, 2011) was much ado about nothing. Read More

We introduce a corrective function to compensate errors in contact area computations coming from mesh discretization. The correction is based on geometrical arguments and requires only one additional quantity to be computed: the length of contact/non-contact interfaces. The new technique enables us to evaluate accurately the true contact area using a coarse mesh for which the shortest wavelength in the surface spectrum reaches the grid size. Read More

In this paper, we proposed the GLHUA double layer cloak; proved the properties of GLHUA double layer cloak; Using GL no scattering inversion and the pre cloak condition 6.1 to 6.4 in paper [1], we create GLHUA outer layer cloak radial relative parameter and angular relative parameter theoretically. Read More

The discovery that the band structure of electronic insulators may be topologically non-trivial has unveiled distinct phases of electronic matter with novel properties. Recently, mechanical lattices have been found to have similarly rich structure in their phononic excitations, giving rise to protected uni-directional edge modes whose existence was demonstrated in lattices of interacting gyroscopes and coupled pendula. In all these cases, however, as well as in other topological metamaterials, the underlying structure was finely tuned, be it through periodicity, quasi-periodicity or isostaticity. Read More

We demonstrate both numerically and experimentally that geometric frustration in two-dimensional periodic acoustic networks consisting of arrays of narrow air channels can be harnessed to form band gaps (ranges of frequency in which the waves cannot propagate in any direction through the system). While resonant standing wave modes and interferences are ubiquitous in all the analyzed network geometries, we show that they give rise to band gaps only in the geometrically frustrated ones (i.e. Read More

The rectification effect on the propagation of solitary waves in the symmetric Y-shaped granular chain is numerically investigated in this Letter. A heterojunction with mass mismatch occurs at the position of Y-junction by adjusting the branch angle. And the heavy-light heterojunction is more favorable for the solitary wave passing. Read More

In this paper we revisit the classification of the gauge transformations in the Euler top system using the generalized classical Hamiltonian dynamics of Nambu. In this framework the Euler equations of motion are bi-Hamiltonian and $SL(2, \mathbb{R})$ linear combinations of the two Hamiltonians leave the equations of motion invariant, although belonging to inequivalent Lie-Poisson structures. Here we give the explicit form of the Hamiltonian vector fields associated to the components of the angular momentum for every single Lie-Poisson structure including both the asymmetric rigid bodies and its symmetric limits. Read More

In two space dimensions and one time dimension a wave changes its shape even in the absence of a dispersive medium. However, this anomalous dispersive behavior in empty two-dimensional space does not occur if the wave dynamics is described by a linear homogeneous wave equation in two space dimensions and {\it two} time dimensions. Wave propagation in such a space can be realized in a three-dimensional anisotropic metamaterial in which one of the space dimensions has a negative permittivity and thus serves as an effective second time dimension. Read More

The optical theorem is an important tool for scattering analysis in acoustics, electromagnetism, and quantum mechanics. We derive an extended version of the optical theorem for the scattering of elastic waves by a spherical inclusion embedded in a linear elastic solid using a vector spherical harmonics representation of the waves. The sphere can be a rigid, empty cavity, elastic, viscoelastic, or layered material. Read More

Using GL no scattering full wave modeling and inversion, we create a GLHUA pre cloak electromagnetic (EM) material in the virtual sphere that makes the sphere is invisible. The invisible sphere is called GLHUA sphere. In GLHUA sphere, the Pre cloak relative parameter is not less than 1; the parameters and their derivative are continuous across the boundary r=R2 and the parameters are going to infinity at origin r=0. Read More

**Affiliations:**

^{1}LMT,

^{2}I2M,

^{3}IJLRA,

^{4}LMT

In this paper, we propose a factorization of a fourth-order harmonic tensor into second-order tensors. We obtain moreover explicit equivariant reconstruction formulas, using second-order covariants, for transverse isotropic and orthotropic harmonic fourth-order tensors, and for trigonal and tetragonal harmonic fourth-order tensors up to a cubic fourth order covariant remainder. Read More

We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the thermodynamic limit of the given model. Read More

The Curzon-Ahlborn efficiency has long served as the definite upper bound for the thermal efficiency at maximum output power, and has thus shaped the development of finite-time thermodynamics. In this letter, we repeal the ruling consensus according to which it has a genuine universal character and pertains to linear irreversible thermodynamics. We demonstrate that the Curzon-Ahlborn efficiency should instead properly be associated with a particular case of nonlinear heat engines. Read More

The optimal currents on arbitrarily shaped radiators with respect to the minimum quality factor Q are found using a simple and efficient procedure. The solution starts with a reformulation of the problem of minimizing quality factor Q as an alternative, so-called dual, problem. Taking advantage of modal decomposition and group theory, it is shown that the dual problem can easily be solved and always results in minimal quality factor Q. Read More

In this paper we study a system which consists in an elastic medium carrying transverse waves and one punctual high elastic medium density, called concretion. We compute the equation of motion for the concretion as well as the wave equation of this classical and theoretical system. Afterwards we always consider the case in which the concretion is not the wave source any more. Read More

Electromagnetic scattering from moving bodies, being inherently time-dependent phenomenon, gives rise to a generation of new frequencies, which could characterize the motion. While a standard linear path leads to a constant Doppler shift, accelerating scatterers could generate a micro-Doppler frequency comb. Here, a spectra produced by rotating objects, was studied and observed in a bi-static lock in detection scheme. Read More

Permalloy nanoparticles containing bacterial cellulose hydrogel obtained after reduction was compressed into a xerogel flexible sheet by hot pressing at 60 C at different pressures. The permalloy nanoparticles with an ordered structure have a bimodal size distribution centered around 25 nm and 190 nm. The smaller nanoparticles are superparamagnetic while the larger particles are ferromagnetic at room temperature. Read More

Both the radiation efficiency and bandwidth of electrically small antennas are dramatically reduced as the size decreases. Fundamental limitations on the bandwidth of small antennas have been thoroughly treated in the past. However, upper bounds on radiation efficiency have not been established even though it is also of significant importance. Read More

A method for evaluating finite trigonometric summations is applied to a system of N coupled oscillators under acceleration. Initial motion of the nth particle is shown to be of the order ${{T}^{2n+2}}$ for small time T and the end particle in the continuum limit is shown to initially remain stationary for the time it takes a wavefront to reach it. The average velocities of particles at the ends of the system are shown to take discrete values in a step-like manner. Read More

Sound propagation within certain non-relativistic condensed matter models obeys a relativistic wave equation despite such systems admitting entirely non-relativistic descriptions. A natural question that arises upon consideration of this is, "do devices exist that will experience the relativity in these systems?" We describe a thought experiment in which 'acoustic observers' possess devices called sound clocks that can be connected to form chains. Careful investigation shows that appropriately constructed chains of stationary and moving sound clocks are perceived by observers on the other chain as undergoing the relativistic phenomena of length contraction and time dilation by the Lorentz factor, with c the speed of sound. Read More

Given a sufficiently long bead chain in a cup, if we pull the end of the chain over the rim of the cup, the chain tends to continuously flow out of the cup, under gravity, in a common siphon process. Surprisingly enough, under certain conditions, the chain forms a fountain in the air! This became known as the Mould effect, after Steve Mould who discovered this phenomenon and made this experiment famous on YouTube, in a video that went viral. The reason for the emergence of this fountain remains unclear. Read More

This article was published as Sec.4 of the "Roadmap on Structured Light" in Journal of Optics 19 (2017) 013001. Section 4 describes the essential elements of the classical theory of electromagnetic force and momentum. Read More

We present the mathematical framework of an athlete modelled as a system of coupled rigid bodies to simulate platform and springboard diving. Euler's equations of motion are generalised to non-rigid bodies, and are then used to innovate a new dive sequence that in principle can be performed by real world athletes. We begin by assuming shape changes are instantaneous so that the equations of motion simplify enough to be solved analytically, and then use this insight to present a new dive (513XD) consisting of 1. Read More

We introduce the concept of a metasurface system able to route space wave via surface waves. This concept may be used to laterally shift or modulate the beam width of scattered waves. We propose two corresponding synthesis techniques, one that is exact but leads to practically challenging material parameters and one that is approximate but leads to simpler material parameters. Read More

This study is motivated by the observation, based on photographs from the Cassini mission, that Saturn's rings have a fractal structure in radial direction. Accordingly, two questions are considered: (1) What Newtonian mechanics argument in support of that fractal structure is possible? (2) What kinematics model of such fractal rings can be formulated? Both challenges are based on taking Saturn's rings' spatial structure as being statistically stationarity in time and statistically isotropic in space, but statistically non-stationary in space. An answer to the first challenge is given through the calculus in non-integer dimensional spaces and basic mechanics arguments (Tarasov (2006) \textit{Celest. Read More

**Affiliations:**

^{1}IMAGINE,

^{2}IMAGINE

A pose of a rigid object is usually regarded as a rigid transformation, described by a translation and a rotation. In this article, we define a pose as a distinguishable static state of the considered object, and show that the usual identification of the pose space with the space of rigid transformations is abusive, as it is not adapted to objects with proper symmetries. Based solely on geometric considerations, we propose a frame-invariant metric on the pose space, valid for any physical object, and requiring no arbitrary tuning. Read More

Locally resonant metamaterials are characterized by bandgaps at wavelengths that are much larger than the lattice size, enabling low-frequency vibration attenuation. Typically, bandgap analyses and predictions rely on the assumption of traveling waves in an infinite medium, and do not take advantage of modal representations typically used for the analysis of the dynamic behavior of finite structures. Recently, we developed a method for understanding the locally resonant bandgap in uniform finite metamaterial beams using modal analysis. Read More

In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. Read More

The efficient way to transfer input potential energy to the kinetic energy of a racket or bat was analyzed by two coupled harmonic triple pendulums. We find the most efficient way to transfer energy based on the kinetic chain process. Using control parameters, such as the release times, lengths and masses of the triple pendulum, we optimize the kinetic chain process. Read More

The force on electric and magnetic dipoles moving in vacuo is discussed in the general case of time-variable non-uniform fields and time-variable dipole moments, to first order in v/c and neglecting radiation reaction. Emphasis is given to the symmetry between electric and magnetic dipoles, justifying in general Amp\`ere's equivalence principle, and showing that the difference between gilbertian and amperian dipoles (in vacuo) is only a question of interpretation. The expression for the force can be expressed in a variety of different forms, and each term of each form is susceptible of specific physical interpretations. Read More

The integral law of thermal radiation by finite size emitters is studied. Two geometrical characteristics of a radiating body or a cavity, its volume and its boundary area, define two terms in its radiance. The term defined by the volume corresponds to the Stefan-Boltzmann law. Read More

In a Letter for relativistic analysis of dielectric Einstein-box thought experiment (T. Ramos, G. F. Read More

In this work, Gibbs paradox was discussed from the view of observer. The limitations of real observer are analyzed quantitatively. The entropy of mixing was found to be determined by both the identification ability and the information already in hand of an observer. Read More

Variable mass systems are a classic example of open systems in classical mechanics. The reaction forces due to mass variation propel ships, balloons, and rockets. Unlike free constant mass systems, the angular momentum of these systems is not of constant magnitude due to the change in mass. Read More

We present a novel propagation medium using a pair of non-identical coupled transmission lines. The medium is referred to as `butterfly' structure and is composed of four coupled transmission lines. These four coupled transmission lines generate higher-order dispersion modes by coupling the modes supported on each of the transmission lines. Read More

Energy dissipation is an unavoidable phenomenon of physical systems that are directly coupled to an external environmental bath. The ability to engineer the processes responsible for dissipation and coupling is fundamental to manipulate the state of such systems. This is particularly important in oscillatory states whose dynamic response is used for many applications, e. Read More

In this paper, using GILD and GL no scattering modeling and inversion method, we find a class of the nonzero solution of the zero scattering nonlinear inversion equation and use it to create our GLHUA cloak with relative EM parameter not less than 1 for each layer with any thickness. major new ingredients are: (1) In the outer layer, R1 < r < R2, the relative radial electric permittivity and radial magnetic permeability equal to 1; the relative angular electric permittivity and magnetic permeability are equal to 0.5((H/C)^(Alpha)+(C/H)^(Alpha)),C=R2-R1, H= r-R1; (2) In the inner layer cloak R0 < r < R1 , the relative radial electric permittivity and radial magnetic permeability equal to 1; the relative angular electric permittivity and magnetic permeability are equal to 0. Read More

This paper gives a method that maps the static magnetic field due to a system of parallel current-carrying wires to a complex function. Using this function simplifies the calculation of the magnetic field energy density and inductance per length in the wires, and we reproduce well-known results for this case. Read More