相关论文: Homogenization effects on non-local functionals
It is well-known that nonlinearity may lead to localization effects and coupling of internally resonant modes. However, research focused primarily on conservative systems commonly assumes that the near-resonant forced response closely…
We consider periodic homogenization of boundary value problems for second-order semilinear elliptic systems in 2D of the type $$ \partial_{x_i}\left(a_{ij}^{\alpha…
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…
We perform a simultaneous homogenization and linearization analysis for a magnetoelastic energy functional featuring a mixed Eulerian-Lagrangian structure. Neglecting Zeeman and anisotropic contributions, we characterize the asymptotic…
In this paper, we study the homogenization of elliptic equations that combine a local part, given by the Laplacian with Neumann boundary conditions, and its nonlocal version, defined through an integral operator with a smooth kernel. These…
The end compactification |\Gamma| of the locally finite graph \Gamma is the union of the graph and its ends, endowed with a suitable topology. We show that \pi_1(|\Gamma|) embeds into a nonstandard free group with hyperfinitely many…
In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $\Gamma$-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the…
In conventional finite element simulations, foil windings with a thin foil and many turns require many mesh elements. This renders models quickly computationally infeasible. With the use of homogenization approaches, the finite element mesh…
We give a necessary and sufficient condition for non-local functionals on vector-valued Lebesgue spaces to be weakly sequentially lower semi-continuous. Here a non-local functional shall have the form of a double integral of a density which…
Recent years have seen considerable research success in the field of dynamic homogenization which seeks to define frequency dependent effective properties for heterogeneous composites for the purpose of studying wave propagation. There is…
Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…
The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierachical lattices is investigated. The geometric fluctuations are introduced by generalized…
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…
A variational model for the interaction between homogenization and phase separation is considered. The focus is on the regime where the latter happens at a smaller scale than the former, and when the wells of the double well potential are…
We study non-convex elastic energy functionals associated to (spatially) periodic, frame indifferent energy densities with a single non-degenerate energy well at SO(n). Under the assumption that the energy density admits a quadratic Taylor…
We study the local scaling properties associated with straight line periodic orbits in homogeneous Hamiltonian systems, whose stability undergoes repeated oscillations as a function of one parameter. We give strong evidence of local scaling…
In this paper we homogenise monotone parabolic problems with two spatial scales and finitely many temporal scales. Under a certain well-separatedness assumption on the spatial and temporal scales as explained in the paper, we show that…
We show that artificial magnetism of periodic dielectric or metal/dielectric structures has limitations and is subject to at least two "uncertainty principles". First, the stronger the magnetic response (the deviation of the effective…
We introduce two new concepts, local homogeneity and local L^q-spectrum, both of which are tools that can be used in studying the local structure of measures. The main emphasis is given to the examination of local dimensions of measures in…
We prove that certain non-local functionals defined on measurable sets Gamma-converge to the perimeter in the sense of De Giorgi.