Related papers: First-order expansion of homogenized coefficients …

This paper is concerned with the behavior of the homogenized coefficients associated with some random stationary ergodic medium under a Bernoulli perturbation. Introducing a new family of energy estimates that combine probability and…

We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…

This paper is concerned with the behavior of the ergodic constant associated with convex and superlinear Hamilton-Jacobi equation in a periodic environment which is perturbed either by medium with increasing period or by a random Bernoulli…

The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the…

For a family of elliptic operators with periodically oscillating coefficients, $-\text{div}( A(\cdot/\varepsilon) \nabla) $ with tiny $\varepsilon>0$, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions…

This paper deals with homogenization of second order divergence form parabolic operators with locally stationary coefficients. Roughly speaking, locally stationary coefficients have two evolution scales: both an almost constant microscopic…

The single-mode approximation of the resonant state expansion has proven to give accurate first-order approximations of resonance shifts and linewidth changes when modifying the material properties inside open optical resonators. Here, we…

We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a…

We study discrete linear divergence-form operators with random coefficients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the…

We consider consequences of local disorder in systems experiencing first order phase transitions. Such systems can be of rather different nature. For example, manganates showing gigantic magnetoelectric effect, doped antiferroelectrics or…

We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of…

We propose a first rigorous homogenisation procedure in image-segmentation models by analysing the relative impact of (possibly random) fine-scale oscillations and phase-field regularisations for a family of elliptic functionals of Ambrosio…

We provide a first-order homogenization result for quadratic functionals. In particular, we identify the scaling of the energy and the explicit form of the limiting functional in terms of the first-order correctors. The main novelty of the…

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…

We present an exact first-order perturbation theory for the eigenmodes in systems with interfaces causing material discontinuities. We show that when interfaces deform, higher-order terms of the perturbation series can contribute to the…

We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variables and random stationary ergodic in time. As was proved in [24] and [12] in this case…

We study Bloch wave homogenization of periodically heterogeneous media with fourth order singular perturbations. We recover different homogenization regimes depending on the relative strength of the singular perturbation and length scale of…

We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…

In this paper, we study high order correctors in stochastic homogenization. We consider elliptic equations in divergence form on $\mathbb{Z}^d$, with the random coefficients constructed from i.i.d. random variables. We prove moment bounds…

We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that all relative distances converge to definite positive value…