Physics

The present work is concerned with the propagation of electro-magneto-thermoelastic plane waves of assigned frequency in a homogeneous isotropic and finitely conducting elastic medium permeated by a primary uniform external magnetic field. We formulate our problem under the theory of Green and Naghdi of type-III (GN-III) to account for the interactions between the elastic, thermal as well as magnetic fields. A general dispersion relation for coupled waves is deduced to ascertain the nature of waves propagating through the medium. Perturbation technique has been employed to obtain the solution of dispersion relation for small thermo-elastic coupling parameter and identify three different types of waves. We specially analyze the nature of important wave components like, phase velocity, specific loss and penetration depth of all three modes of waves. We attempt to compute these wave components numerically to observe their variations with frequency. The effect of presence of magnetic field is analyzed. Comparative results under theories of type GN-I, II and III have been presented numerically in which we have found that the coupled thermoelastic waves are un-attenuated and nondispersive in case of Green-Naghdi-II model which is completely in contrast with the theories of type-I and type-III. Furthermore, the thermal mode wave is observed to propagate with finite phase velocity in case of GN-II model, whereas the phase velocity of thermal mode wave is found to be an increasing function of frequency in other two cases. We achieve significant variations among the results predicted by all three theories.

In our analysis, we show that Efrati et al.'s publication is inconsistent with the mathematics of plate theory. However it is more consistent with the mathematics of shell theory, but with an incorrect strain tensor. Thus, the authors' numerical results imply that a thin object can be stretched substantially with very little force, which is physically unrealistic and mathematically disprovable. All the theoretical work of the authors, i.e. nonlinear plate equations in curvilinear coordinates, can easily be rectified with the inclusion of both a sufficiently differentiable diffeomorphism and a set of external loadings, such as an external strain field.

In our analysis, we show that Howell et al.'s nonlinear beam theory does not depict a representation of the Euler-Bernoulli beam equation, nonlinear or otherwise. The authors' nonlinear beam theory implies that one can bend a beam in to a constant radius of deformation and maintain that constant radius of deformation with zero force. Thus, the model is disproven by showing that it is invalid when the curvature of deformation is constant, while even the linear Euler-Bernoulli beam equation stays perfectly valid under such deformations. To conclude, we derive a nonlinear beam equation by using Ciarlet's nonlinear plate equations and show that our model is valid for constant radius of deformations.

This paper presents a framework for analyzing and designing cylindrical omega-bianisotropic metasurfaces, inspired by mode matching and digital signal processing techniques. Using the discrete Fourier transform, we decompose the the electromagnetic field distributions into orthogonal cylindrical modes and convert the azimuthally varying metasurface constituent parameters into their respective spectra. Then, by invoking appropriate boundary conditions, we set up systems of algebraic equations which can be rearranged to either predict the scattered fields of prespecified metasurfaces, or to synthesize metasurfaces which support arbitrarily stipulated field transformations. The proposed framework facilitates the efficient evaluation of field distributions that satisfy local power conservation, which is one of the key difficulties involved with the design of passive and lossless scalar metasurfaces. It represents a promising solution to circumvent the need for active components, controlled power dissipation, or tensorial surface polarizabilities in many state-of-the art conformal metasurface-based devices. To demonstrate the robustness and the versatility of the proposed technique, we design several devices intended for different applications and numerically verify them using finite element simulations.

We investigate a simple forced harmonic oscillator with a natural frequency varying with time. It is shown that the time evolution of such a system can be written in a simplified form with Fresnel integrals, as long as the variation of the natural frequency is sufficiently slow compared to the time period of oscillation. Thanks to such a simple formulation, we found, for the first time, that a forced harmonic oscillator with a slowly-varying natural frequency is essentially equivalent to diffraction of light.

Optical activity is the ability of chiral materials to rotate linearly-polarized (LP) electromagnetic waves. Because of their intrinsic asymmetry, traditional chiral molecules usually lack isotropic performance, or at best only possess a weak form of chirality. Here we introduce a knotted chiral meta-molecule that exhibits optical activity corresponding to a 90° polarization rotation of the incident waves. More importantly, arising from the continuous multi-fold rotational symmetry of the chiral torus knot structure, the observed polarization rotation behavior is found to be independent of how the incident wave is polarized. In other words, the proposed chiral knot structure possesses two-dimensional (2-D) isotropic optical activity as illustrated in Fig. 1, which has been experimentally validated in the microwave spectrum. The proposed chiral torus knot represents the most optically active meta-molecule reported to date that is intrinsically isotropic to the incident polarization.

We discuss an extension of the velocity Verlet method that accurately approximates the kinetic-energy-conserving charged particle motion that comes from magnetic forcing. For a uniform magnetic field, the method is shown to conserve both particle kinetic energy and magnetic dipole moment better than midpoint Runge-Kutta. We then use the magnetic velocity Verlet method to generate trapped particle trajectories, both in a cylindrical magnetic mirror machine setup, and for dipolar fields like the earth's magnetic field. Finally, the method is used to compute an example of (single) mirror motion in the presence of a magnetic monopole field, where the trajectory can be described in closed form.

I present a chaotic pendulum based on the repulsive force between a random array of point sources of air flow and the conical tip of a rigid pendulum. Source code is provided for generation of random aperture arrays. The chaotic motion was analyzed using machine vision techniques. A computer simulation of this system is also presented, as are the results of some example simulations.

Effective medium theory aims to describe a complex inhomogeneous material in terms of a few important macroscopic parameters. To characterise wave propagation through an inhomogeneous material, the most crucial parameter is the effective wavenumber. For this reason, there are many published studies on how to calculate a single effective wavenumber. Here we present a proof that there does not exist a unique effective wavenumber; instead, there are an infinite number of such (complex) wavenumbers. We show that in most parameter regimes only a small number of these effective wavenumbers make a significant contribution to the wave field. However, to accurately calculate the reflection and transmission coefficients, a large number of the (highly attenuating) effective waves is required. For clarity, we present results for scalar (acoustic) waves for a two-dimensional material filled (over a half space) with randomly distributed circular cylindrical inclusions. We calculate the effective medium by ensemble averaging over all possible inhomogeneities. The proof is based on the application of the Wiener-Hopf technique and makes no assumption on the wavelength, particle boundary conditions/size, or volume fraction. This technique provides a simple formula for the reflection coefficient, which can be explicitly evaluated for monopole scatterers. We compare results with an alternative numerical matching method.

In an interesting recent paper [1] (A. Acharya, Stress of a spatially uniform dislocation density field, J. Elasticity 137 (2019), 151--155), Acharya proved that the stress produced by a spatially uniform dislocation density field in a body comprising a nonlinear elastic material may fail to vanish under no loads. The class of counterexamples constructed in [1] is essentially 2 -dimensional: it works with the subgroup O(2)⊕⟨Id⟩⊂O(3) . The objective of this note is to extend Acharya's result in [1] to O(3) , subject to an additional structural assumption and less regularity requirements.