相关论文: Homogenization for A-quasiconvexity with variable …
We consider an evolutionary problem with rapidly oscillating coefficients. This causes the problem to change frequently between a parabolic and an hyperbolic state. We prove convergence of the homogenisation process in the unit square and…
We prove a homogenization result for Mumford-Shah-type energies associated to a brittle composite material with weak inclusions distributed periodically at a scale ${\varepsilon}>0$. The matrix and the inclusions in the material have the…
The variation of energies associated with soft matter interfaces where surface inhomogeneities are present. These energies include the total bending and splay energy, the variable surface tension energy, a coupling energy between the total…
We consider the homogenization of parabolic equations with large spatially-dependent potentials modeled as Gaussian random fields. We derive the homogenized equations in the limit of vanishing correlation length of the random potential. We…
The homogenization of periodic elastic composites is addressed through the reformulation of the local equations of the mechanical problem in a geometric functional setting. This relies on the definition of Hilbert spaces of kinematically…
The diagonalization of the metrical Hamiltonian of a scalar field with an arbitrary coupling with a curvature in N-dimensional homogeneous isotropic space is performed. The energy spectrum of the corresponding quasiparticles is obtained.…
In this paper, we consider a microscopic semilinear elliptic equation posed in periodically perforated domains and associated with the Fourier-type condition on internal micro-surfaces. The first contribution of this work is the…
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…
In this note we extend to the random, stationary ergodic setting previous results of periodic homogenization for a particular family of nonlinear nonlocal "elliptic" equations with oscillatory coefficients. Such equations include, but are…
We consider the homogenization for time-fractional diffusion equations in a periodic structure and we derive the homogenized time-fractional diffusion equation. Then we discuss the determination of the constant diffusion coefficient by…
We establish a quantitative homogenization result for an interface moving through a field of sufficiently sparse but possibly impenetrable random obstacles. From a physical viewpoint, such problems arise e.g. in the context of the motion of…
We study a concentration and homogenization problem modelling electrical conduction in a composite material. The novelty of the problem is due to the specific scaling of the physical quantities characterizing the dielectric component of the…
We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.
In this paper, we provide an analysis of a recently proposed multicontinuum homogenization technique. The analysis differs from those used in classical homogenization methods for several reasons. First, the cell problems in multicontinuum…
We consider a non-relativistic quantum particle in $\mathbb{R}^d$, $d=2$ or $d = 3$, interacting with singular zero-range potentials concentrated on a large collection of points. We analyze the homogenization regime where the intensities of…
The paper deals with homogenization of Levy-type operators with rapidly oscillating coefficients. We consider cases of periodic and random statistically homogeneous micro-structures and show that in the limit we obtain a Levy-operator. In…
This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. It has previously been shown that if the random…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
We prove homogenization for possibly degenerate viscous Hamilton-Jacobi equations with a Hamiltonian of the form $G(p)+V(x,\omega)$, where $G$ is a quasiconvex, locally Lipschitz function with superlinear growth, the potential $V(x,\omega)$…
A new averaging method linking discrete to continuum variables of granular materials is developed and used to derive average balance equations. Its novelty lies in the choice of the decomposition between mean values and fluctuations of…