Related papers: A high-contrast composite with annular inclusions:…
We analyse a problem of two-dimensional linearised elasticity for a two-component periodic composite, where one of the components consists of disjoint soft inclusions embedded in a rigid framework. We consider the case when the contrast…
We study the homogenisation of geometrically nonlinear elastic composites with high contrast. The composites we analyse consist of a perforated matrix material, which we call the "stiff" material, and a "soft" material that fills the pores.…
Diffusion models have demonstrated remarkable capabilities in synthesizing realistic images, spurring interest in using their representations for various downstream tasks. To better understand the robustness of these representations, we…
Spatially periodic elastic metamaterials, comprising hard inclusions within a soft matrix in $d$-dimensional space ($d\geq 2$), exhibit a rich spectrum of physical phenomena. This paper investigates such a model and presents the following…
Acoustic waves propagation of in composite of water with embedded double-layered silicone resin/silver rods is considered. Approximate values of effective dynamical constitutive parameters are obtained. Frequency ranges of simultaneous…
We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…
In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic…
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation…
We analyze the propagation of elastic waves in soft materials subjected to finite deformations. We derive explicit dispersion relations, and apply these results to study elastic wave propagation in (i) nearly incompressible materials such…
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…
This paper studies the behaviour of iterates of weighted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space $H^2$. Questions relating to uniform, strong and weak convergence are…
This paper is concerned with an asymptotic analysis of the dispersion relation for wave propagation in an elastic layer of uniform thickness. The layer is subject to an underlying simple shear deformation accompanied by an arbitrary uniform…
Evaluation of the angular distribution function of particles scattered in an amorphous medium is improved by deforming the integration path in the Fourier integral representation into the complex plane. That allows us to present the…
We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…
We derive exact nonlocal expressions for the effective dielectric constant tensor ${\boldsymbol \varepsilon}_e({\bf k}_I, \omega)$ of disordered two-phase composites and metamaterials from first principles. This formalism extends the…
We analyse a system of partial differential equations describing the behaviour of an elastic plate with periodic moduli in the two planar directions, in the asymptotic regime when the period and the plate thickness are of the same order of…
This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to…
This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear…
Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…
This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is…