Related papers: Can large inhomogeneities generate target patterns…
We study linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general (generic) inhomogeneous boundary conditions in Sobolev spaces. We investigate the character of solvability of…
We study the fluctuations of the light emitted by two identical incoherent point sources in a disordered environment. The intensity-intensity correlation function and the speckle contrast, obtained after proper temporal and configurational…
It is pointed out that point defects on graphene are strongly correlated and can not be treated as independent scatters. In particular, for large on-site defect potential, it is shown that defects induce an impurity band with density of…
We study a pattern forming instability in a laser driven optically thick cloud of cold two-level atoms with a planar feedback mirror. A theoretical model is developed, enabling a full analysis of transverse patterns in a medium with…
Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning…
The so-called indentation stiffness tomography technique for detecting the interior mechanical properties of an elastic sample with an inhomogeneity is analyzed in the framework of the asymptotic modeling approach under the assumption of…
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a…
In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
We study the growth of small-scale inhomogeneities of the density of particles floating in weakly nonlinear, small-amplitude, surface waves. Despite the amplitude smallness, the accumulated effect of the long-time evolution may produce…
We review and extend here some recent results on the existence of minimal surfaces and isoperimetric sets in non homogeneous and anisotropic periodic media. We also describe the qualitative properties of the homogenized surface tension,…
Non-topological defects such as grain boundaries abound in pattern forming systems, arising from local variations of pattern properties such as amplitude, wavelength, orientation, etc. We introduce the idea of treating such non-topological…
This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded…
In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the context of homogenized elastic properties of materials. This…
We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects…
Most calibration schemes for reflection-based tissue spectroscopy in the mm-wave/THz-frequency range are based on homogenized, frequency-dependent tissue models where macroscopic material parameters have either been determined by…
In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
The paper contains a review of results on linear systems of ordinary differential equations of an arbitrary order on a finite interval with the most general inhomogeneous boundary conditions in Sobolev spaces. The character of the…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…