Interior error estimate for periodic homogenization

In a previous article about the homogenization of the classical problem of diff usion in a bounded domain with su ciently smooth boundary we proved that the error is of order $\epsilon^{1/2}$. Now, for an open set with su ciently smooth boundary $C^{1,1}$ and homogeneous Dirichlet or Neuman limits conditions we show that in any open set strongly included in the error is of order $\epsilon$. If the open set $\Omega\subset R^n$ is of polygonal (n=2) or polyhedral (n=3) boundary we also give the global and interrior error estimates

Asymptotic behavior of Structures made of Plates

The aim of this work is to study the asymptotic behavior of a structure made of plates of thickness $2\delta$ when $\delta\to 0$. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on several decompositions of the structure displacements and on the passing to the limit in fixed domains. We begin with studying the displacements of a plate. We show that any displacement is the sum of an elementary displacement concerning the normal lines on the middle surface of the plate and a residual displacement linked to these normal lines deformations. An elementary displacement is linear with respect to the variable $x$3. It is written $U(^x)+R(^x)\land x3e3$ where U is a displacement of the mid-surface of the plate. We show a priori estimates and convergence results when $\delta \to 0$. We characterize the limits of the unfolded displacements of a plate as well as the limits of the unfolded of the strained tensor. Then we extend these results to the structures made of plates. We show that any displacement of a structure is the sum of an elementary displacement of each plate and of a residual displacement. The elementary displacements of the structure (e.d.p.s.) coincide with elementary rods displacements in the junctions. Any e.d.p.s. is given by two functions belonging to $H1(S;R3)$ where S is the skeleton of the structure (the plates mid-surfaces set). One of these functions : U is the skeleton displacement. We show that U is the sum of an extensional displacement and of an inextensional one. The first one characterizes the membrane displacements and the second one is a rigid displacement in the direction of the plates and it characterizes the plates flexion. Eventually we pass to the limit as $\delta \to 0$ in the linearized elasticity system, on the one hand we obtain a variational problem that is satisfied by the limit extensional displacement, and on the other hand, a variational problem satisfied by the limit of inextensional displacements

Homogenization of contact problem with Coulomb's friction on periodic cracks

We consider the elasticity problem in a %heterogeneous domain with contact on multiple periodic open cracks. The contact is described by the Signorini and Coulomb-friction conditions. Problem is non-linear, the dissipative functional depends on the un-known solution and the existence of the solution for fixed period of the structure is usually proven by the fix-point argument in the Sobolev spaces with a little higher regularity, $H^{1+\alpha}$. We rescaled norms, trace, jump and Korn inequalities in fractional Sobolev spaces with positive and negative exponent, using the unfolding technique, introduced by Griso, Cioranescu and Damlamian. Then we proved the existence and uniqieness of the solution for friction and period fixed. Then we proved the continuous dependency of the solution to the problem with Coulomb's friction on the given friction and then estimated the solution using fixed point theorem. However, we were not able to pass to the strong limit in the frictional dissipative term. For this reason, we regularized the problem by adding a fourth-order term, which increased the regularity of the solution and allowed the passing to the limit. This can be interpreted as micro-polar elasticity

Locally periodic unfolding method and two-scale convergence on surfaces of locally periodic microstructures

In this paper we generalize the periodic unfolding method and the notion of two-scale convergence on surfaces of periodic microstructures to locally periodic situations. The methods that we introduce allow us to consider a wide range of non-periodic microstructures, especially to derive macroscopic equations for problems posed in domains with perforations distributed non-periodically. Using the methods of locally periodic two-scale convergence (l-t-s) on oscillating surfaces and the locally periodic (l-p) boundary unfolding operator, we are able to analyze differential equations defined on boundaries of non-periodic microstructures and consider non-homogeneous Neumann conditions on the boundaries of perforations, distributed non-periodically

Homogenization of an elasticity problem for a catalyst support by using the unfolding method

The goal of this work is to study the asymptotic behaviour of catalyst supports in a linear elasticity problem. The catalyst support is a structure made of beams, placed periodically and with inner holes. We introduce a decomposition of the displacements in such a structure and we prove some convergence results. Finally, we obtain the limit problem when the elasticity parameter e and the periodicity parameter ε go to zero.This research was supported by Xunta de Galicia (projects PGIDT00PXI20701PR, PGIDT02PXIC20701PN) and CICYT-FEDER (project DPI2004-01993).S

The periodic unfolding method for perforated domains and Neumann sieve models

AbstractThe periodic unfolding method, introduced in [D. Cioranescu, A. Damlamian, G. Griso, Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 99–104], was developed to study the limit behavior of periodic problems depending on a small parameter ε. The same philosophy applies to a range of periodic problems with small parameters and with a specific period (as well as to almost any combinations thereof). One example is the so-called Neumann sieve.In this work, we present these extensions and show how they apply to known results and allow for generalizations (some in dimension N⩾3 only). The case of the Neumann sieve is treated in details. This approach is significantly simpler than the original ones, both in spirit and in practice

Convergence Rates in L^2 for Elliptic Homogenization Problems

We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a consequence, we obtain convergence rates for Dirichlet, Neumann, and Steklov eigenvalues of {L_\epsilon}. Most of our results, which rely on the recently established uniform estimates for the L^2 Dirichlet and Neumann problems in \cite{12,13}, are new even for smooth domains.Comment: 25 page

CDF experience with monte carlo production using LCG grid

The upgrades of the Tevatron collider and CDF detector have considerably increased the demand on computing resources, in particular for Monte Carlo production. This has forced the collaboration to move beyond the usage of dedicated resources and start exploiting the Grid. The CDF Analysis Farm (CAF) model has been reimplemented into LcgCAF in order to access Grid resources by using the LCG/EGEE middleware. Many sites in Italy and in Europe are accessed through this portal by CDF users mainly to produce Monte Carlo data but also for other analysis jobs. We review here the setup used to submit jobs to Grid sites and retrieve the output, including CDF-specific configuration of some Grid components. We also describe the batch and interactive monitor tools developed to allow users to verify the jobs status during their lifetime in the Grid environment. Finally we analyze the efficiency and typical failure modes of the current Grid infrastructure reporting the performances of different parts of the system used

Online b-jets tagging at CDF

We propose a method to identify b-quark jets at trigger level which exploits recently increased CDF trigger system capabilities. b-quark jets identification is of central interest for the CDF high-P{sub T} physics program, and the possibility to select online b-jets enriched samples can extend the physics reaches especially for light Higgs boson searches where the H {yields} b{bar b} decay mode is dominant. Exploiting new trigger primitives provided by two recent trigger upgrades, the Level2 XFT stereo tracking and the improved Level2 cluster-finder, in conjunction with the existing Silicon Vertex Tracker (SVT), we design an online trigger algorithm aimed at selecting good purity b-jets samples useful for many physics measurements, the most important being inclusive H {yields} b{bar b} searches. We discuss the performances of the proposed b-tagging algorithm which must guarantee reasonable trigger rates at luminosity greater than 2 x 10{sup 32} cm{sup -2}s{sup -1} and provide high efficiency on H {yields} b{bar b} events

Strong interface-induced spin-orbit coupling in graphene on WS2

Interfacial interactions allow the electronic properties of graphene to be modified, as recently demonstrated by the appearance of satellite Dirac cones in the band structure of graphene on hexagonal boron nitride (hBN) substrates. Ongoing research strives to explore interfacial interactions in a broader class of materials in order to engineer targeted electronic properties. Here we show that at an interface with a tungsten disulfide (WS2) substrate, the strength of the spin-orbit interaction (SOI) in graphene is very strongly enhanced. The induced SOI leads to a pronounced low-temperature weak anti-localization (WAL) effect, from which we determine the spin-relaxation time. We find that spin-relaxation time in graphene is two-to-three orders of magnitude smaller on WS2 than on SiO2 or hBN, and that it is comparable to the intervalley scattering time. To interpret our findings we have performed first-principle electronic structure calculations, which both confirm that carriers in graphene-on-WS2 experience a strong SOI and allow us to extract a spin-dependent low-energy effective Hamiltonian. Our analysis further shows that the use of WS2 substrates opens a possible new route to access topological states of matter in graphene-based systems.Comment: Originally submitted version in compliance with editorial guidelines. Final version with expanded discussion of the relation between theory and experiments to be published in Nature Communication