Related papers: Homogeneity and plane-wave limits
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…
We investigate geodesics in non-homogeneous vacuum pp-wave solutions and demonstrate their chaotic behavior by rigorous analytic and numerical methods. For the particular class of solutions considered, distinct "outcomes" (channels to…
We propose a new method for calculating reflection and transmission coefficients for an arbitrarily polarized electromagnetic plane wave incident on a one-dimensional dielectric medium of finite thickness and with dielectric permittivity…
We obtain results on approximation of holomorphic maps by algebraic maps, jet transversality theorems for holomorphic and algebraic maps, and the homotopy principle for holomorphic submersions of Stein manifolds to certain algebraic…
We introduce the stochastic band structure, a method giving the dispersion relation for waves propagating in periodic media or along waveguides, and subject to material loss or radiation damping. Instead of considering an explicit or…
In weakly nonlinear dispersive wave systems, long-time dynamics are typically governed by time resonances, where wave phases evolve coherently due to exact frequency matching. Recent advances in spatio-temporal spectrum measurements,…
We present a coherent and effective theoretical framework to systematically construct numerically exact nonlinear solitary waves from their respective linear limits. First, all possible linear degenerate sets are classified for a harmonic…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
In this paper, we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients, namely, when the bulk modulus and the density of the medium are only bounded. We show that under a Cordes type condition the…
We study homogeneity aspects of metric spaces in which all triples of distinct points admit pairwise different distances; such spaces are called isosceles-free. In particular, we characterize all homogeneous isosceles-free spaces up to…
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
Let $({\mathcal X},d,\mu)$ be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and $H^1_{\rm at}({\mathcal X})$ be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions…
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…
A random distribution of poroelastic spheres in a poroelastic medium obeying Biot's theory is considered. The scattering coefficients of the fast and the slow waves are computed in the low frequency limit using the sealed pore boundary…
The universe is nearly isotropic on very large scales. It is much more difficult to show that the universe is radially homogeneous (independent of distance), or equivalently, that it is isotropic about distant points. This taken as an…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
We consider the scalar Helmholtz equation with variable, discontinuous coefficients, modelling transmission of acoustic waves through an anisotropic penetrable obstacle. We first prove a well-posedness result and a frequency-explicit bound…
Many geologic materials have a composite structure, in which macroscopic mechanical behavior is determined by the properties, shape, and heterogeneous distribution of individual constituents. In particular, sedimentary rocks commonly…
Effects of spatially varying interfacial parameters on the propagation of surface waves are studied. These variations can arise from inhomogeneities in coverage of surface active substances such as amphiphillic molecules at the fluid/gas…