Related papers: The equivalent medium theory within the linear res…
Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…
We study the optimal diffusive transmission and absorption of broadband or polychromatic light in a disordered medium. By introducing matrices describing broadband transmission and reflection, we formulate an extremal eigenvalue problem…
We present a general method based on nonlinear response theory to obtain effective interactions between ions in an electron gas which can also be applied to other systems where an adiabatic separation of time-scales is possible. Nonlinear…
We develop a multiple scattering theory for the absorption of waves in disordered media. Based on a general expression of the average absorbed power, we discuss the possibility to maximize absorption by using structural correlations of…
The convergence between effective medium theory and pore-network modelling is examined. Electrical conductance on two and three-dimensional cubic resistor networks is used as an example of transport through composite materials or porous…
We reconsider the refraction of evanescent waves at an interface between air and negative index medium under the assumption that negative index medium is necessarily dispersive and lossy. We show that all evanescent waves in air will be…
We consider the porous medium equation with a power-like reaction term, posed on Riemannian manifolds. Under certain assumptions on $p$ and $m$ in (1.1), and for small enough nonnegative initial data, we prove existence of global in time…
We derive a family of similarity solutions to the nonlinear non-equilibrium Marshak wave problem for an inhomogeneous planar medium which is coupled to a time dependent radiation driving source. We employ the non-equilibrium gray diffusion…
We apply the equivalent theory to orthorhombic anisotropic materials and provide a general unit-cell design criterion for achieving a length-independent retrieval of the effective material parameters from a single layer of unit cells. We…
We present a detailed, microscopic transport theory for light in strongly scattering disordered systems whose constituent materials exhibit linear absorption or gain. Starting from Maxwell's equations, we derive general expressions for…
In this paper we establish in the fast diffusion range the higher integrability of the spatial gradient of weak solutions to porous medium systems. The result comes along with an explicit reverse H\"older inequality for the gradient. The…
We consider solvability of the generalized reaction-diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction-diffusion…
In this paper we develop a model to describe the diffusion process in a porous medium. For the observed decrease in current yield, we propose other causes than difference in diffusivity, which we consider unaltered by the porous medium. The…
We explore the mathematical theory to rigorously describe the response of media with linear time-varying, generally dispersive, electromagnetic constitutive parameters. We show that even when the temporal inhomogeneity takes place on a time…
A two-photon emission of a medium with periodically time-dependent refractive index is considered. The emission results from the zero-point fluctuations of the medium. Usually this emission is very weak. However, it can be strongly enhanced…
Recently, we showed that dielectric mesoscale spheres support super-resonance effect, i.e. high-order Mie resonance modes with giant field enhancement. The presence of the surrounding medium leads to a significant influence in the intensity…
The diffuse intensity propagating in turbid media is sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects can be described by a stationary diffusion…
The purpose of this paper is to provide equations to model the evolution of effective diffusion over a Riemannian fiber bundle (under the hypothesis of infinite diffusion rate along compact fibers). These equations are obtained by…
We analyse the superluminal propagation of narrow-band pulses at resonances in dissipative media. The output waveform is an attenuated, undistorted, time-advanced version of the input which can be interpreted as the result of the…
In this paper, we consider a long-wave equivalent medium to a finely parallel-layered inhomogeneous medium, obtained using the Backus average. Following the work of Postma and Backus, we show explicitly the derivations of the conditions to…