Related papers: Effective Multipoles in Random media
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…
We present a formulation for deriving effective medium properties of infinitely periodic two-dimensional metamaterial lattice structures beyond the static and quasi-static limits. We utilize the multipole expansions, where the polarization…
It is shown that conserved charges associated with a specific subclass of gauge symmetries of Maxwell electrodynamics are proportional to the well known electric multipole moments. The symmetries are residual gauge transformations surviving…
Modeling time-harmonic Maxwell problems in heterogeneous media presents significant mathematical and computational challenges. Due to the inherent non-elliptic structure and non-coercive nature of Maxwell equations, conventional methods…
Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…
A dynamical effective medium theory is presented for quantum spins and higher multipoles such as quadrupole moments. The theory is a generalization of the spherical model approximation for the Ising model, and is accurate up to O(1/z_n)…
The maximum achievable rate or mutual informa- tion of multidimensional rotationally invariant distributions in the presence of additive white Gaussian noise is analyzed. A simple expression for the special case of multisphere distributions…
The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational…
Many models in natural and social sciences are comprised of sets of inter-acting entities whose intensity of interaction decreases with distance. This often leads to structures of interest in these models composed of dense packs of…
Spontaneous emission and Lamb shift of atoms in absorbing dielectrics are discussed. A Green's-function approach is used based on the multipolar interaction Hamiltonian of a collection of atomic dipoles with the quantised radiation field.…
The theory of self-consistent effective interactions in nuclei is extended for a system with a velocity dependent mean potential. By means of the field coupling method, we present a general prescription to derive effective interactions…
The multipole expansion can be formulated in spherical and Cartesian coordinates. By constructing an explicit map linking both formulations in isotropic media, we discover a lack of equivalence between them in anisotropic media. In…
Dyadic Green functions for time-harmonic fields in a homogeneous, isotropic, dielectric-magnetic medium, moving with constant velocity, are derived by first implementing a simple transformation and then using the dyadic Green functions…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
This article is concerned with the time-harmonic electromagnetic (EM) scattering from a generic inhomogeneous medium. It is shown that if there is a right corner on the support of the medium, then it scatters every pair of incident EM…
A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented here provides the ability to model the macroscopic dynamics…
The microcanonical partition function for self-gravitational system in three dimensional case has been found. Used approach from the field theory of statistical description of the system was tailored to gravitational interacting particles…
A free massive scalar field in inhomogeneous random media is investigated. The coefficients of the Klein-Gordon equation are taken to be random functions of the spatial coordinates. The case of an annealed-like disordered medium, modeled by…