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Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two…
The paper deals with the homogenization of reaction-diffusion equations with large reaction terms in a multi-scale porous medium. We assume that the fractures and pores are equidistributed and that the coefficients of the equations are…
We consider a diffusion on a bounded domain, assuming that the system is irreducible inside the domain and that the diffusion has varying degree of degeneracy on the domain's boundary. The long-term statistical properties of typical…
Several basic properties of homogeneous planar Whispering Gallery dielectric resonators are investigated through a general approach. In particular the values for the minimum and maximum allowed radius, defined by irradiation and dielectric…
We investigate the dynamics of an overdamped Brownian particle moving in a washboard potential with space dependent friction coefficient. Analytical expressions have been obtained for current and diffusion coefficient. We show that the…
We study the problem of lateral diffusion on a static, quasi-planar surface generated by a stationary, ergodic random field possessing rapid small-scale spatial fluctuations. The aim is to study the effective behaviour of a particle…
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…
While diffusion models excel at generating high-quality images, their tendency to memorize training data poses significant privacy and copyright risks. In this work, we for the first time identify that memorization induces internal…
We report a detailed experimental study of vector modulation instability in highly birefringent optical fibers in the anomalous dispersion regime. We prove that the observed instability is mainly induced by vacuum fluctuations. The detuning…
A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain…
Discrete diffusion models are a class of generative models that construct sequences by progressively denoising samples from a categorical noise distribution. Beyond their rapidly growing ability to generate coherent natural language, these…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
In the case of diffusions on $\mathbb R^d$ with constant diffusion matrix, without assuming reversibility nor hypoellipticity, we prove that the contractivity of the deterministic drift is equivalent to the constant rate contraction of…
The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian…
We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly…
We study theoretically the concept of homogenization in optics using an ensemble of randomly distributed resonant stationary atoms with density $\rho$. The ensemble is dense enough for the usual condition for homogenization, viz.…
We investigate the long time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant $D$. We consider two cases: (a) The particle is pulled forward by a small external constant…
A homogenization problem of infinite dimensional diffusion processes indexed by ${\mathbf Z}^d$ having periodic drift coefficients is considered. By an application of the uniform ergodic theorem for infinite dimensional diffusion processes…
We studied the stability of linear vortex filaments in 3-dimensional (3D) excitable media, using both analytical and numerical methods. We found an intrinsic 3D instability of vortex filaments that is diffusion-induced, and is due to the…
We study the evolution of a localized perturbation in a chemical system with multiple homogeneous steady states, in the presence of stirring by a fluid flow. Two distinct regimes are found as the rate of stirring is varied relative to the…