Related papers: Effective Multipoles in Random media
We extend the nonequilibrium dynamical mean field (DMFT) formalism to inhomogeneous systems by adapting the "real-space" DMFT method to Keldysh Green's functions. Solving the coupled impurity problems using strong-coupling perturbation…
We study the radiative decay rate and Purcell effect for a finite-size dipole emitter placed in a homogeneous uniaxial medium. We demonstrate that the radiative rate is strongly enhanced when the signs of the longitudinal and transverse…
We present a method to constrain local charge multipoles within density-functional theory. Such multipoles quantify the anisotropy of the local charge distribution around atomic sites and can indicate potential hidden orders. Our method…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
We establish spectral expansions of homogeneous and isotropic random fields taking values in the $3$-dimensional Euclidean space $E^3$ and in the space $\mathsf{S}^2(E^3)$ of symmetric rank $2$ tensors over $E^3$. The former is a model of…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such…
We report on an extended version of the one-dimensional model proposed by Constant \emph{et al.} [Phys. Rev. Lett 82(8), 1668 (1999)] to study phase matching of high-order harmonic generation in absorbing and dispersive medium. The model -…
In this paper, a fast multipole method (FMM) is proposed to compute long-range interactions of wave sources embedded in 3-D layered media. The layered media Green's function for the Helmholtz equation, which satisfies the transmission…
Divergence-form operators with stationary random coefficients homogenize over large scales. We investigate the effect of certain perturbations of the medium on the homogenized coefficients. The perturbations that we consider are rare at the…
In this contribution we present the first formulation of a heterogeneous multiscale method for an incompressible immiscible two-phase flow system with degenerate permeabilities. The method is in a general formulation which includes…
Light-matter interaction models invariably rely on the multipole expansion of the electromagnetic potentials generated by complex charge distributions. These multipoles are typically taken to be traceless, however, for a correct evaluation…
We consider a reaction-diffusion-advection problem in a perforated medium, with nonlinear reactions in the bulk and at the microscopic boundary, and low diffusion scaling. The microstructure changes in time; the microstructural evolution is…
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…
The efficient use of a multipole expansion of the far field for rapid numerical modeling and optimization of the optical response from ordered and disordered arrays of various structural elements is complicated by the ambiguity in choosing…
Heavy particles suspended in turbulent flow possess inertia and are ejected from violent vortical structures by centrifugal forces. Once piled up along particle paths, this small-scale mechanism leads to an effective large-scale drift. This…
The present work develops a rigorous framework for collective dipole oscillations in dense dielectric media by extending the Lorentz oscillator model to include both quadratic (second order) and cubic (third order) nonlinear restoring…
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…
In this paper we study the multipole expansion of the long-wavelength effective action for radiative sources in ($d$+1) spacetime dimensions. We present detailed expressions for the multipole moments for the case of scalar-,…
The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency $\omega$,…