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physics.class-ph

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preprint2016arXiv

3D Single-port Labyrinthine Acoustic Metamaterial

In this paper, we report on the design, fabrication, and experimental characterization of a 3D single-port labyrinthine acoustic metamaterial. By using curled perforations with one end closed and with appropriate loss inside, the proposed metamaterial can perfectly absorb airborne sounds in a low frequency band. Both the position and width of the band can be tuned flexibly. A tradeoff is uncovered between the relative absorption bandwidth and thickness of the metamaterial. When the relative absorption bandwidth is as high as 51%, the requirement of deep subwavelength thickness (0.07λ) can still be satisfied.

preprint2016arXiv

The tennis racket effect in a three-dimensional rigid body

We propose a complete theoretical description of the tennis racket effect, which occurs in the free rotation of a three-dimensional rigid body. This effect is characterized by a flip ($π$- rotation) of the head of the racket when a full ($2π$) rotation around the unstable inertia axis is considered. We describe the asymptotics of the phenomenon and conclude about the robustness of this effect with respect to the values of the moments of inertia and the initial conditions of the dynamics. This shows the generality of this geometric property which can be found in a variety of rigid bodies. A simple analytical formula is derived to estimate the twisting effect in the general case. Different examples are discussed.

preprint2017arXiv

Comment on Jackson's analysis of electric charge quantization due to interaction with Dirac's magnetic monopole

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. This paper presents a detailed derivation of Jackson's main result, explains the significance of the missing term, and highlights the close connection between Jackson's findings and Dirac's original argument.

preprint2016arXiv

Modulating heat conduction by stretching or compressing

Recent studies have revealed that the symmetry of interparticle potential plays an important role in one-dimensional heat conduction problem. Here we demonstrate that by stretching or compressing the Fermi-Pasta-Ulam-\b{eta} lattice, one can control the symmetry of the potential, and thus manipulate the decaying behavior of the heat current autocorrelation function (HCAF). In fact, stretching or compressing induces a fast decaying stage (FDS) during which the HCAF decays faster than power-law manners or in a power law manner but faster than ~t -1. The time range as well as the decay amplitude of the HCAF over the FDS increase as the stretching or compressing ratio increase, or as the temperature decreases. As a consequence, the thermal conductivity calculated following the Green-Kubo formula shows a truncation-time independent window, implying a system-size independent conductivity. Stretching or compressing also changes the exponent of the power-law tail of the HCAF. The complicated heat conduction behavior induced by stretching or compressing can be connected to the change of the symmetry of the interparticle potential.

preprint2016arXiv

The (not so simple!) chain fountain

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. This effect was shown to be due to an anomalous reaction force from the top of the pile of beads, a possible origin for this force was proposed in the same paper. Here, we describe some experiments that give a contribution towards the clarification of the origin of this force, and show that the explanation goes far beyond the one proposed before.

preprint2016arXiv

A Positive and Entropy-Satisfying Finite Volume Scheme for the Baer-Nunziato Model

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numeric

preprint2016arXiv

Classical and quantum dynamics of a charged scalar particle in a background of two counterpropagating plane waves

We consider a scalar particle in a background formed by two counter-propagating plane waves. Two cases are studied: i) dynamics at a magnetic node and ii) zero initial transverse canonical momentum. The Lorentz and Klein-Gordon equations are solved for these cases and approximations analysed. For the magnetic node solution (homogeneous, time-dependent electric field), the modified Volkov wavefunction which arises from a high-energy approximation is found to be inaccurate for all energies and the solution itself unstable when photon emission (nonlinear Compton scattering) is included. For the zero initial transverse canonical momentum case, in both quantum and classical cases, forbidden parameter regimes, absent in the plane wave model, are identified.

preprint2016arXiv

Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction

We consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space. In both cases the flexural plate, or Rayleigh surface, waves in the substrate interact with the resonators to create interesting effects such as effective band-gaps for surface waves or filters that transform surface waves into bulk waves; these effects have parallels in the field of optics where such sub-wavelength resonators create metamaterials, and metasurfaces, in the bulk and at the surface respectively. Here we carefully analyse this canonical problem by extracting the dispersion relations analytically thereby examining the influence of both the flexural and compressional resonances on the propagating wave. For an array of resonators atop an elastic half-space we augment the analysis with numerical simulations. Amongst other effects, we demonstrate the striking effect of a dispersion curve that transitions from Rayleigh wave-like to shear wave-like behaviour and the resultant change in displacement from surface to bulk waves.

preprint2007arXiv

About Superluminal motions and Special Relativity: A Discussion of some recent Experiments, and the solution of the Causal Paradoxes

Some experiments, performed at Berkeley, Cologne, Florence, Vienna, Orsay, Rennes, etc., led to the claim that something seems to travel with a group velocity larger than the speed c of light in vacuum. Various other experimental results seem to point in the same direction: For instance, localized wavelet- type solutions to Maxwell equations have been found, both theoretically and experimentally, that travel with superluminal speed. [Even muonic and electronic neutrinos [it has been proposed] might be "tachyons", since their square mass appears to be negative]. With regard to the first-mentioned experiments, it was recently claimed by Guenter Nimtz that those results with evanescent waves (or tunneling photons) imply superluminal signal and impulse transmission, and therefore violate Einstein causality. In this note we want to stress that, on the contrary, all such results do not place relativistic causality in jeopardy, even if they referred to actual tachyonic motions: In fact, Special Relativity can cope even with superluminal objects and waves. For instance, it is possible (at least in microphysics) to solve also the known causal paradoxes, devised for faster than light

preprint2016arXiv

Equilibrium dynamical correlations in the Toda chain and other integrable models

We investigate the form of equilibrium spatio-temporal correlation functions of conserved quantities, and of energy transport in the Toda lattice and in other integrable models. From numerical simulations we find that the correlations satisfy ballistic scaling with a remarkable collapse of data from different times. We examine special limiting choices of parameter values, for which the Toda lattice tends to either the harmonic chain or the equal mass hard-particle gas. In both these limiting cases, one can obtain the correlations exactly and we find excellent agreement with the direct Toda simulation results. We also discuss a transformation to "normal mode" variables, as commonly done in hydrodynamic theory of non-integrable systems, and find that this is useful, to some extent, even for the integrable system.

preprint2016arXiv

On the accuracy of the Debye shielding

The expression for the Debye shielding in plasma physics is usually derived under the assumptions that the plasma particles are weakly coupled, so their kinetic energy is much larger than the potential energy between them, and that the velocity distributions of the plasma species are Maxwellian. The first assumption also establishes that the plasma parameter ND, the number of particles within a sphere with a Debye radius should be greater than 1, and determines the difference between weakly and strongly coupled plasmas. Under such assumptions, Poisson's equation can be linearised, and a simple analytic expression obtained for the electrostatic potential. However, textbooks rarely discuss the accuracy of this approximation. In this work we compare the linearised solution with the exact one, obtained numerically, and show that the linearisation, which underestimates the exact solution, is reasonably good even for ND ~ 40. We give quantitative criteria to set the limit of the approximation when the number of particles is very small, or the distance to the test charge too short.

preprint2016arXiv

Electromagnetic Force and Momentum

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.

preprint2016arXiv

Rectification Effect on Solitary Waves in the Symmetric Y-shaped Granular Chain

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. The energy rectification efficiency can be improved by adjusting the branch angle and the direction of incident solitary wave. The results have particularly practical significance for the potential design of acoustic diode devices.

preprint2016arXiv

Analytic Materials

The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer $p$. If $p$ takes its maximum value then we have a complete analytic material. Otherwise it is incomplete analytic material of rank $p$. For two-dimensional materials further progress can be made in the identification of analytic materials by using the well-known fact that a $90^\circ$ rotation applied to a divergence free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.

preprint2016arXiv

Formation of high-order acoustic Bessel beams by spiral diffraction gratings

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 variation of the phase along its annular spectrum producing an acoustic vortex in the near field. In our system, the scattering of plane acoustic waves by the spiral grating leads to the formation of the acoustic vortex with zero pressure on-axis and the angular phase dislocations characterized by the spiral geometry. The order of the generated Bessel beam and, as a consequence, the size of the generated vortex can be fixed by the number of arms in the spiral diffraction grating. The obtained results allow to obtain Bessel beams with controllable vorticity by a passive device, which has potential applications in low-cost acoustic tweezers and acoustic radiation force devices.

preprint2016arXiv

Unlimited-Power Reflectors, Absorbers, and Emitters with Conjugately Matched Layers

In order to ensure the fastest wireless energy transfer from a source to the user one needs to maximize the channel capacity for power transport. In communications technologies, the concept of MIMO (multiple input, multiple output) exploits the idea of sending signals via many different rays which may reach the receiver. However, if we are concerned with the task of energy transfer, still only one mode is exploited, even if multiple antennas are used to send power to the receiver. In the near-field scenario, this is the magnetic dipole mode of receiving coil antennas. In the far-field scenario, this is the propagating plane wave TEM mode. Recently, it was shown that using special artificial materials it is possible to ensure that all electromagnetic modes of free space are conjugately matched to the modes of a material body and, thus, all modes deliver power to the body in the most effective way. Such a fascinating feature is acquired because the conjugate matching does not concern only the propagating modes but, most importantly, is applied to all evanescent modes. However, coupling to higher-order (mostly evanescent) modes is weak and disappears in the limit of an infinite planar

preprint2016arXiv

Space-Wave Routing via Surface Waves Using a Metasurface System

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. The concept is experimentally verified in an electromagnetic periscope. Additionally, we propose two other potential applications namely a beam expander and a multi-wave refractor.

preprint2016arXiv

Bistable Circuit Behaviour as a 2 level (stable/metastable) potential energy system

A novel model of analyzing Schmitt trigger as 2 level (metastable/stable) energy system is presented. The energy of the 2 level system is identified. In an MOS implementation, this arises from the electrostatic potential energy of the electrons on the gate to source capacitance of the cross coupled MOS transistors. The electrostatic energy, upon co-ordinate transformation, (incorporating the nonlinear MOS device behaviour and cross coupling), yields an expression for the 2 level system energy. The 2 level system, described under the transformed co-ordinate, is simulated. Simulation on the dynamics of the system shows a metastsable state and two stable states, corresponding to the a maximum(metastable) energy and a minimum(stable) energy, as predicted by the energy expression in the model. This result agrees with earlier attempt based on nonlinear dynamic system approach, whereby the potential is interpreted from the point of view of the gradient of vector field. In addition, the model gives physical design insight on how the change in circuit parameters (such as gm, R), affects the energy characteristics, hence leads to effective design of such 2 level system.

preprint2016arXiv

Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation

Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed $c$ depending on position $\mathbf{r}$. In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path $\ell^*$, scattering phase function $f$ and anisotropy factor $g$. Discarding the operator term in the wave equation is shown to have a significant impact on $f$ and $g$, yet limited to the low-frequency regim

preprint2016arXiv

Force on slowly moving variable electric or magnetic dipoles in vacuo

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 Ampère'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. Terms not described in the literature are pointed out. A possible experiment for verifying the (dual-Lorentz) force of an electric field on a magnetic current (and then "hidden momentum") is proposed.

preprint2015arXiv

Optomechanical reference accelerometer

We present an optomechanical accelerometer with high dynamic range, high bandwidth and read-out noise levels below 8 $μ$g/$\sqrt{\mathrm{Hz}}$. The straightforward assembly and low cost of our device make it a prime candidate for on-site reference calibrations and autonomous navigation. We present experimental data taken with a vacuum sealed, portable prototype and deduce the achieved bias stability and scale factor accuracy. Additionally, we present a comprehensive model of the device physics that we use to analyze the fundamental noise sources and accuracy limitations of such devices.

preprint2016arXiv

On the Angular Momentum of Rockets, Balloons, and Other Variable Mass Systems

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. In this paper, we show that the angular momentum vector for such a system has a fixed direction in space and, thus, is partially conserved for both rigid and flexible, torque-free, variable mass systems. A potential use of this result is that it provides a suitable stationary reference frame against which the orientation of variable mass system could be measured.

preprint2016arXiv

Definite solution of the two capacitor paradox (and two water bucket paradox)

In this work we suggest very simple solution of the two capacitors paradox in the completely ideal (without any electrical resistance or inductive) electrical circuit. Namely, it is shown that electrical field energy loss corresponds to works done by electrical fields of both capacitors by movement of the electrical charge. It is all and nothing more (some dissipation processes, e.g. Joule heating and electromagnetic wave emission effects) is necessary. Additionally, we shortly demonstrate a simple mechanical analogy of mentioned paradox and its solution. Concretely we consider two water buckets connected by a valve where is a seeming loss of the gravitational potential energy that can be explained by the work in the gravitational field.

preprint2016arXiv

The Square-Shoulder-Asakura-Oosawa model

A new model for a colloidal size-asymmetric binary mixture is proposed: The Square-Shoulder-Asakura-Oosawa. This belongs to the larger class of non-additive hard-spheres models and has the property that its effective pair formulation is exact whenever the solvent particle fits inside the interstitial region of three touching solute particles. Therefore one can study its properties from the equivalent one-component effective problem. Some remarks on the phase diagram of this new model are also addressed.

368 works