1,720,974 research outputs found
Hausdorff dimension for level sets of upper and lower limits of generalized averages of binary digits
No full textThe problem of averaging of binary digits of numbers in [0,1] is considered. A class M of Toeplitz matrices regular with respect to usual (Cesaro) averages is characterized. The Hausdorff dimension of the level sets of the upper and lower limits of some generalized averages is explicitly computed and it is proved to be equal for every T in M. A description of sets on which finite measures on [0, 1] are concentrated is given using Toeplitz matrices in X. Copyright (C) 2006 John Wiley & Sons, Ltd
Homogenization of the wave equation in composites with imperfect interface: A memory effect
No full textIn this paper we study the asymptotic behaviour of the
wave equation with
rapidly oscillating coefficients in a two-component composite with
ε-periodic imperfect inclusions.
We prescribe on the interface between the two components a jump of
the solution proportional to the conormal derivatives through a
function of order ε^γ. For the different values of
γ, we obtain different limit problems. In particular, for
γ=1 we have a linear memory effect in the homogenized
problem
Correctors for the homogenization of a classof hyperbolic equations with imperfect interfaces
No full textWe present here some corrector results for the homogenization of the wave equation in a two-component composite with ε-periodic connected inclusions which complete the homogenization results proved in [P. Donato, L. Faella, and S. Monsurr`o, J. Math. Pures Apple., 87 (2007), pp. 119– 143] by the authors. On the interface separating the two components we prescribe a jump of the solution proportional to the conormal derivatives via a function of order ε^γ , with −1 < γ ≤ 1. Due to different expressions of the energies of the limit problems, the cases −1 < γ < 1 and γ = 1 need to be treated separately. The second one, where a memory effect appears in the homogenized problem, is the most interesting. For this critical case, displaying lack of compactness, we in particulur establish the central upper semicontinuity type inequalities by splitting a related energy term into a compact part and a part vanishing in appropriate norms
Memory Effects Arising in the Homogenization of Composites with Inclusions
No full textWe want to describe the asymptotic behavior, as ε-> 0,of the solution of a first order evolution problem set in a domain of Rn with periodic inclusions of size ε and prescribing a jump on the interface proportional to the conormal derivatives by means of a function of order ε^γ.
The limit behaviors obtained are different according to the values of the parameter y. In particular, for y = 1, a linear memory term appears in the homogenized problem
Uniform resolvent convergence for strip with fast oscillating boundary
No full textIn a planar infinite strip with a fast oscillating boundary we consider an elliptic operator assuming that both the period and the amplitude of the oscillations are small. On the oscillating boundary we impose Dirichlet, Neumann or Robin boundary condition. In all cases we describe the homogenized operator, establish the uniform resolvent convergence of the perturbed resolvent to the homogenized one, and prove the estimates for the rate of convergence. These results are obtained as the order of the amplitude of the oscillations is less, equal or greater than that of the period. It is shown that under the homogenization the type of the boundary condition can change. (C) 2013 Elsevier Inc. All rights reserved
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