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A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…
A homogenization result for a family of oscillating integral energies is presented, where the fields under consideration are subjected to first order linear differential constraints depending on the space variable x. The work is based on…
Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures,…
Recently it has been established that asymptotic incoherence can be used to facilitate subsampling, in order to optimize reconstruction quality, in a variety of continuous compressed sensing problems, and the coherence structure of certain…
The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast…
Systems under external confinement and constraints often show interesting properties. In this thesis, we study some systems under external confinement. We begin by finding out the probability distribution of end-to-end separation of a Worm…
We report the experimental realization of a correlated insulating phase in 2D GaAs/AlGaAs heterostructures at low electron densities in a limited window of background disorder. This has been achieved at mesoscopic length scales, where the…
We consider an inhomogeneous strongly correlated system where external disorder divides it into mesoscopic cells.Strong inter-particle repulsion suppresses the quantum tunneling between cells and open a wide temperature range for incoherent…
We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale $\varepsilon$. Numerical homogenization methods are popular for such problems, because they capture efficiently…
This paper presents a consistent computational framework for multiscale 1st order finite strain homogenization and stability analyses of rate-independent solids with periodic microstructures. Based on the principle of multiscale virtual…
Homogenization method is used to analyse the equivalent behavior of transient flow of a passive solute through highly heterogeneous porous media. The flow is governed by a coupled system which includes an elliptic equation and a linear…
Strongly correlated amorphous solids are a class of glass-formers whose inter-particle potential admits an approximate inverse power-law form in a relevant range of inter-particle distances. We study the steady-state plastic flow of such…
In this work, we consider the problem of multi-pitch estimation, i.e., identifying super-imposed truncated harmonic series from noisy measurements. We phrase this as recovering a harmonically-structured measure on the unit circle, where the…
Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
We establish an existence result for weak solutions to an aggregation-diffusion-reaction equation with a constraint, arising in the modelling of multiple sclerosis. The model is derived from a general chemotaxis-type framework and describes…
The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence…
We consider the mathematical analysis and homogenization of a moving boundary problem posed for a highly heterogeneous, periodically perforated domain. More specifically, we are looking at a one-phase thermo-elasticity system with phase…
We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…