Related papers: On a coupled-physics transmission eigenvalue probl…
The structure, thermodynamics and slow activated dynamics of the equilibrated metastable regime of glass-forming fluids remains a poorly understood problem of high theoretical and experimental interest. We apply a highly accurate…
We study a supersolid in the context of a Gross-Pitaevskii theory with a non-local effective potential. We employ a homogenisation technique which allows us to calculate the elastic moduli, supersolid fraction and other state variables of…
We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic…
This paper is concerned with the invisibility cloaking in electromagnetic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. Our study is…
We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires…
This paper investigates the problem of time-harmonic acoustic scattering in an inhomogeneous medium with a complex topological structure. Specifically, the medium is anisotropic and contains several disjoint sound-soft obstacles. This model…
This paper investigates the singularities at the vertex of multiply connected angular inhomogeneities for heat conduction and elastic deformation. With the aid of Eshelby's equivalent inclusion method (EIM), each inhomogeneity is simulated…
The paper deals with three evolution problems arising in the physical modelling of acoustic phenomena of small amplitude in a fluid, bounded by a surface of extended reaction. The first one is the widely studied wave equation with acoustic…
In this work, we consider not only a discontinuous boundary-value problem with retarded argument and four supplementary transmission conditions at the two points of discontinuities but also, eigenparameter-dependent boundary conditions and…
The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in…
Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville…
Elastic wave propagation is a century-old problem. Unlike on a flat manifold, analytical solution is not well established for a curved manifold. In this study we take a step towards building an analytical framework for solving the elastic…
We study the eigenvalue problem for some special class of anti-triangular matrices. Though the eigenvalue problem is quite classical, as far as we know, almost nothing is known about properties of eigenvalues for anti-triangular matrices.…
We study the reflection of an acoustic plane wave from a steadily sliding planar interface with velocity strengthening friction or a shear band in a confined granular medium. The corresponding acoustic impedance is utterly different from…
The goal of this paper is to develop numerical methods computing a few smallest elastic interior transmission eigenvalues, which are of practical importance in inverse elastic scattering theory. The problem is challenging since it is…
There is recent interest in the inter and intra element interactions of metamaterial unit cells. To calculate the effects of these interactions which can be substantial, an ab initio general coupled mode equation, in the form of an…
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…
Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional…
We apply a homogenization process to the acoustic velocity potential wave equation. The study of various examples shows that the resulting effective properties are different from those of the homogenized pressure wave equation for the same…
We revisit the problem of extraordinary transmission of acoustic (electromagnetic) waves through a slit in a rigid (perfectly conducting) wall. We use matched asymptotic expansions to study the pertinent limit where the slit width is small…