Physics

In this paper, we show that the linear dielectrics and magnetic materials in matter obey a special kind of mathematical property known as Cesàro convergence. Then, we also show that the analytical continuation of the linear permittivity \& permeability to a complex plane in terms of Riemann zeta function. The metamaterials are fabricated materials with a negative refractive index. These materials, in turn, depend on permittivity \& permeability of the linear dielectrics and magnetic materials. Therefore, the Cesàro convergence property of the linear dielectrics and magnetic materials may be used to fabricate the metamaterials.

Metasurfaces have attracted significant research interest owing to their unprecedented control over the spatial distributions of electromagnetic fields. Herein we propose the concept of metasurface tessellation to achieve reconfigurable scattering functions. Square meta-tiles, composed of identical structures, are arranged to fill a surface. The electromagnetic scattering of the tiled surface is determined by the orientation distribution of the meta-tiles. We present three typical cases of meta-tiles consisting of binary elements to realize several distinct scattering patterns. This study provides an alternative method to build reconfigurable and multi-functional metasurface devices without external stimuli and complicated fabrication.

The topologically polarized isostatic lattices discovered by Kane and Lubensky (2014, Nat. Phys. 10, 39-45) challenged the standard effective medium theories used in the modeling of many truss-based materials and metamaterials. As a matter of fact, these exhibit Parity (P) asymmetric distributions of zero modes that induce a P-asymmetric elastic behavior, both of which cannot be reproduced within Cauchy elasticity. Here, we propose a new effective medium theory baptized "microtwist elasticity" capable of rendering polarization effects on a macroscopic scale. The theory is valid for trusses on the brink of a polarized-unpolarized phase transition in which case they necessarily exhibit more periodic zero modes than they have dimensions. By mapping each periodic zero mode to a macroscopic degree of freedom, the microtwist theory ends up being a kinematically enriched theory. Microtwist elasticity is constructed thanks to leading order two-scale asymptotics and its constitutive and balance equations are derived for a fairly generic isostatic truss: the Kagome lattice. Various numerical and analytical calculations, of the shape and distribution of zero modes, of dispersion diagrams and of polarization effects, systematically show the quality of the proposed effective medium theory. Most notably, the theory is capable of producing a continuum version of Kane and Lubensky's topological polarization vector.

Energy storage technologies are of great practical importance in electrical grids where renewable energy sources are becoming a significant component in the energy generation mix. Here, we focus on some of the basic properties of flywheel energy storage systems, a technology that becomes competitive due to recent progress in material and electrical design. While the description of the rotation of rigid bodies about a fixed axis is classical mechanics textbook material, all its basic aspects pertinent to flywheels, like, e.g., the evaluation of stress caused by centripetal forces at high rotation speeds, are either not covered or scattered over different sources of information; so it is worthwhile to look closer at the specific mechanical problems for flywheels, and to derive and clearly analyse the equations and their solutions. The connection of flywheels to electrical systems impose particular boundary conditions due to the coupling of mechanical and electrical characteristics of the system. Our report thus deal with the mechanical design in terms of stresses in flywheels, particularly during acceleration and deceleration, considering both solid and hollow disks geometries, in light of which we give a detailed electrical design of the flywheel system considering the discharge-stage dynamics of the flywheel. We include a discussion on the applicability of this mathematical model of the electrical properties of the flywheel for actual settings. Finally, we briefly discuss the relative advantages of flywheels in electrical grids over other energy storage technologies.

Ionic electro-active polymer (Nafion for example) can be used as sensor or actuator. To this end, a thin film of the water-saturated material is sandwiched between two electrodes. Water saturation causes a quasi-complete dissociation of the polymer and the release of small cations. The application of an electric field across the thickness results in the bending of the strip. Conversely, a voltage can be detected between the two electrodes when the strip is bent. This phenomenon involves multiphysics couplings of electro-mechanical-chemical type. We have previously modeled this system and determined its constitutive equations using the thermodynamics of linear irreversible processes.We applied this model to the case of a cantilevered PEA strip subjected to a continuous voltage between its two faces (static case). The applied forces and the tip displacement are calculated using a beam model in large displacements. We have also studied the force to be exercised on the free end to prevent its displacement (blocking force).Numerical simulations were performed in the case of Nafion. We have drawn the profiles of cations concentration, pressure, electric field and potential in the thickness of the strip. These quantities, which are almost constant in the central part of the strip, vary drastically near the electrodes. The obtained values of the tip displacement and the blocking force are in good agreement with the experimental data published in the literature. These two quantities are linear functions of the imposed electrical potential ; the tip displacement varies as the length square, and the blocking force is proportional to the width and inversely proportional to the length.

Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient contributions arising in this highly-nonlinear and coupled problem within a classical finite element setting. The formulation accounts for all material and geometric nonlinearities, as well as the coupling between the mechanical, electrical and micromorphic fields. The highly-nonlinear system of governing equations are derived using the Dirichlet principle and solved using the finite element method. A series of numerical examples serve to elucidate the theory and to provide insight into this fascinating effect.

An analytical solution of the Helmholtz equation for electromagnetic field distribution in a resonant cavity with elliptic cross-section is found. We compare the frequencies of the eigenmodes with numerical and experimental values for a metallic cavity and find an excellent matching. We focus our analysis on the microwave frequency region, and show how the ellipticity of the cavity (ratio of the minor and major axes length b/a ) influences several mode frequencies and also the Q -factor of the cavity. By doing so, we demonstrate how the elliptic geometry splits the degeneracy of certain modes of the circular cylindric cavity.

In this paper we study the motion of a finite composite cylindrical annulus made of generalized neo-Hookean solids that is subject to periodic shear loading on the inner boundary. Such a problem has relevance to several problems of technological significance, for example blood vessels can be idealized as finite anisotropic composite cylinders. Here, we consider the annulus to be comprised of an isotropic material, namely a generalized neo-Hookean solid and study the effects of annular thickness on the stress distribution within the annulus. We solve the governing partial differential equations and examine the stress response for the strain hardening and strain softening cases of the generalized neo-Hookean model. We also solve the problem of the annular region being infinite in length, that reduces the problem to a partial differential equation in only time and one spatial dimension. When the thickness of the annulus is sufficiently large, the solutions to the problems exhibit very interesting boundary layer structure in that the norm of the strain has a large gradient in a narrow region adjacent to one of the boundaries, with the strain being relatively uniform outside the narrow region. We also find that beyond a distance of two times the annular wall thickness from the ends of the cylinder the solutions for the infinite length cylinder match solutions for the finite length cylinder implying that end effects are not felt in most of the length of a sufficiently long annulus.

A symmetric top or gyroscope can start its motion with different initial values. One can not decide the motion type only by looking at these initial values. For example, in a motion, precession angular velocity can be negative at the beginning, but the top's overall precession can be positive; or initially, the gyroscope spins in one direction, but in a later stage one can find it while spinning in the other direction. On the other hand, if one knows different properties and types of motion, one can know what will happen. In this work, we have studied the classification of motion type by using constants of motion. We have also studied changes in dynamic variables. We have given examples of different types of motion and solved them numerically.

The widespread phenomena of multistability is a problem involving rich dynamics to be explored. In this paper, we study the multistability of a generalized nonlinear forcing oscillator excited by f(x)cosωt . We take Doubochinski's Pendulum as an example. The so-called "amplitude quantization", i.e., the multiple discrete periodical solutions, is identified as self-adaptive subharmonic resonance in response to nonlinear feeding. The subharmonic resonance frequency is found related to the symmetry of the driving force: odd subharmonic resonance occurs under even symmetric driving force and vice versa. We solve the multiple periodical solutions and investigate the transition and competition between these multi-stable modes via frequency response curves and Poincare maps. We find the irreversible transition between the multistable modes and propose a multistability control strategy.