Non-local interactions in the Homogenization Closure of Thermoelectric Functionals
نویسنده
چکیده
It is a very well known fact that the effective properties of a heterogeneous electrical medium may contain a non-local term. The same phenomenon can occur within a heterogeneous thermally conducting medium. We are interested in the set of all non-local interactions which may arise from the homogenization of a thermoelectric medium where there are couplings between the temperature and the electric field. We consider a bounded open subset Ω ⊂ R3 and we show that any non-local energy of the kind
منابع مشابه
Closure of the set of diffusion functionals with respect to the Mosco-convergence
We characterize the functionals which are Mosco-limits, in the L2(Ω) topology, of some sequence of functionals of the kind Fn(u) := ∫ Ω αn(x)|∇u(x)| dx , where Ω is a bounded domain of RN (N ≥ 3). It is known that this family of functionals is included in the closed set of Dirichlet forms. Here, we prove that the set of Dirichlet forms is actually the closure of the set of diffusion functionals...
متن کاملClosure and Commutability Results for Γ-Limits and the Geometric Linearization and Homogenization of Multiwell Energy Functionals
Abstract. We consider a family of integral functionals, doubly indexed by ε > 0 and j ∈ N∪{∞}, satisfying a uniform G̊arding-type inequality. If these functionals Γ-converge for every j ∈ N as ε → 0, then the same holds also for j = ∞ if the densities fulfill a certain equivalence condition. In that case the Γ-limit for j = ∞ is recovered as the limit of the Γ-limits for finite j as j → ∞. We th...
متن کاملHomogenization of Periodic Multi-dimensional Structures: the Linearly Elastic/perfectly Plastic Case
In this paper we study the asymptotic behaviour via Γ-convergence of some integral functionals Fε which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals Fε are defined in particular classes of functions with bounded deformation while the limit problem is set in the usual framework of Sobolev spaces or BD(Ω). We also construct an exam...
متن کاملNon-local interactions resulting from the homogenization of a linear diffusive medium
It is well known that the effective properties of a heterogeneous diffusive medium may contain a non-local part. We are interested in the set of all non-local interactions which can arise from homogenization. We consider a bounded domain Ω of IR and we show that any non-local energy of the kind ∫
متن کاملA Two Scale Γ-convergence Approach for Random Non-convex Homogenization
We propose an abstract framework for the homogenization of random functionals which may contain non-convex terms, based on a two-scale Γ-convergence approach and a definition of Young measures on micropatterns which encodes the profiles of the oscillating functions and of functionals. Our abstract result is a lower bound for such energies in terms of a cell problem (on large expanding cells) an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004