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

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

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

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

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

Search for the standard model Higgs boson decaying to a bbˉb\bar{b} pair in events with no charged leptons and large missing transverse energy using the full CDF data set

We report on a search for the standard model Higgs boson produced in association with a vector boson in the full data set of proton-antiproton collisions at $\sqrt{s} = 1.96$ TeV recorded by the CDF II detector at the Tevatron, corresponding to an integrated luminosity of 9.45 fb$^{-1}$. We consider events having no identified charged lepton, a transverse energy imbalance, and two or three jets, of which at least one is consistent with originating from the decay of a $b$ quark. We place 95% credibility level upper limits on the production cross section times standard model branching fraction for several mass hypotheses between 90 and $150 \mathrm{GeV}/c^2$. For a Higgs boson mass of $125 \mathrm{GeV}/c^2$, the observed (expected) limit is 6.7 (3.6) times the standard model prediction.Comment: Accepted by Phys. Rev. Let

Search for the standard model Higgs boson decaying to a bb pair in events with one charged lepton and large missing transverse energy using the full CDF data set

We present a search for the standard model Higgs boson produced in association with a W boson in sqrt(s) = 1.96 TeV p-pbar collision data collected with the CDF II detector at the Tevatron corresponding to an integrated luminosity of 9.45 fb-1. In events consistent with the decay of the Higgs boson to a bottom-quark pair and the W boson to an electron or muon and a neutrino, we set 95% credibility level upper limits on the WH production cross section times the H->bb branching ratio as a function of Higgs boson mass. At a Higgs boson mass of 125 GeV/c2 we observe (expect) a limit of 4.9 (2.8) times the standard model value.Comment: Submitted to Phys. Rev. Lett (v2 contains clarifications suggested by PRL

Search for the standard model Higgs boson decaying to a bb pair in events with two oppositely-charged leptons using the full CDF data set

We present a search for the standard model Higgs boson produced in association with a Z boson in data collected with the CDF II detector at the Tevatron, corresponding to an integrated luminosity of 9.45/fb. In events consistent with the decay of the Higgs boson to a bottom-quark pair and the Z boson to electron or muon pairs, we set 95% credibility level upper limits on the ZH production cross section times the H -> bb branching ratio as a function of Higgs boson mass. At a Higgs boson mass of 125 GeV/c^2 we observe (expect) a limit of 7.1 (3.9) times the standard model value.Comment: To be submitted to Phys. Rev. Let