arXiv subjects

Xavier Blanc

Publications and source records attributed to Xavier Blanc.

29 records · Page 2Linked to original sources

arXiv2015

Some variance reduction methods for numerical stochastic homogenization

We overview a series of recent works devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires solving a set of problems at the micro scale, the so-called corrector problems. In a random environment, these problems are stochastic and therefore need to be repeatedly solved, for several configurations of the medium considered. An empirical average over all configurations is then performed using the Monte-Carlo approach, so as to approximate the effective coefficients necessary to determine the macroscopic behavior. Variance severely affects the accuracy and the cost of such computations. Variance reduction approaches, borrowed from other contexts of the engineering sciences, can be useful. Some of these variance reduction techniques are presented, studied and tested here.

math.NA↗

arXiv2013

The Harmony Platform

According to Wikipedia, The Mining Software Repositories (MSR) field analyzes the rich data available in software repositories, such as version control repositories, mailing list archives, bug tracking systems, issue tracking systems, etc. to uncover interesting and actionable information about software systems, projects and software engineering. The MSR field has received a great deal of attention and has now its own research conference : http://www.msrconf.org/. However performing MSR studies is still a technical challenge. Indeed, data sources (such as version control system or bug tracking systems) are highly heterogeneous. Moreover performing a study on a lot of data sources is very expensive in terms of execution time. Surprisingly, there are not so many tools able to help researchers in their MSR quests. This is why we created the Harmony platform, as a mean to assist researchers in performing MSR studies.

cs.SE↗

arXiv2013

A Study of Library Migration in Java Software

Software intensively depends on external libraries whose relevance may change during its life cycle. As a consequence, software developers must periodically reconsider the libraries they depend on, and must think about \textit{library migration}. To our knowledge, no existing study has been done to understand library migration although it is known to be an expensive maintenance task. Are library migrations frequent? For which software are they performed and when? For which libraries? For what reasons? The purpose of this paper is to answer these questions with the intent to help software developers that have to replace their libraries. To that extent, we have performed a statistical analysis of a large set of open source software to mine their library migration. To perform this analysis we have defined an approach that identifies library migrations in a pseudo-automatic fashion by analyzing the source code of the software. We have implemented this approach for the Java programming language and applied it on Java Open Source Software stored in large hosting services. The main result of our study is that library migration is not a frequent practice but depends a lot on the nature of the software as well as the nature of the libraries.

cs.SE↗

arXiv2013

Homogenization of heat diffusion in a cracked medium

We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the cracks are orthogonal to the surface of the material, where an incoming heat flux is applied. The cracks are supposed to be of depth 1, of small width, and periodically arranged.

math.AP↗

arXiv2012

Existence of the thermodynamic limit for disordered quantum Coulomb systems

Following a recent method introduced by C. Hainzl, J.P. Solovej and the second author of this article, we prove the existence of the thermodynamic limit for a system made of quantum electrons, and classical nuclei whose positions and charges are randomly perturbed in an ergodic fashion. All the particles interact through Coulomb forces.

math-ph↗

arXiv2011

A numerical strategy for coarse-graining two-dimensional atomistic models at finite temperature: the membrane case

We present a numerical strategy to compute ensemble averages of coarse-grained two-dimensional membrane-like models. The approach consists in generalizing to these two-dimensional models a one-dimensional strategy exposed in [Blanc, Le Bris, Legoll, Patz, JNLS 2010], which is based on applying the ergodic theorem to Markov chains. This may be considered as a first step towards computing the constitutive law associated to such models, in the thermodynamic limit.

cond-mat.mtrl-sci↗

arXiv2008

Fast rotating condensates in an asymmetric harmonic trap

We investigate the effect of the anisotropy of a harmonic trap on the behaviour of a fast rotating Bose-Einstein condensate. Fast rotation is reached when the rotational velocity is close to the smallest trapping frequency, thereby deconfining the condensate in the corresponding direction. A striking new feature is the non-existence of visible vortices for the ground state. The condensate can be described with the lowest Landau level set of states, but using distorted complex coordinates. We find that the coarse grained atomic density behaves like an inverted parabola with large radius in the deconfined direction, and like a fixed Gaussian in the other direction. It has no visible vortices, but invisible vortices which are needed to recover the mixed Thomas-Fermi Gaussian profile. There is a regime of small anisotropy and intermediate rotational velocity where the behaviour is similar to the isotropic case: a hexagonal Abrikosov lattice of vortices, with an inverted parabola profile.

cond-mat.other↗

arXiv2008

Fast rotating Bose-Einstein condensates in an asymmetric trap

We investigate the effect of the anisotropy of a harmonic trap on the behaviour of a fast rotating Bose-Einstein condensate. This is done in the framework of the 2D Gross-Pitaevskii equation and requires a symplectic reduction of the quadratic form defining the energy. This reduction allows us to simplify the energy on a Bargmann space and study the asymptotics of large rotational velocity. We characterize two regimes of velocity and anisotropy; in the first one where the behaviour is similar to the isotropic case, we construct an upper bound: a hexagonal Abrikosov lattice of vortices, with an inverted parabola profile. The second regime deals with very large velocities, a case in which we prove that the ground state does not display vortices in the bulk, with a 1D limiting problem. In that case, we show that the coarse grained atomic density behaves like an inverted parabola with large radius in the deconfined direction but keeps a fixed profile given by a Gaussian in the other direction. The features of this second regime appear as new phenomena.

math.AP↗

arXiv2007

Nonclassical rotational inertia for a supersolid under rotation

As proposed by Leggett [4], the supersolidity of a crystal is characterized by the Non Classical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau and Rica [5], we prove that NCRI occurs. This is done by analyzing the ground state of the aforementioned model, which is related to a sphere packing problem, and then deriving a theoretical formula for the inertia momentum. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity.

cond-mat.other↗

arXiv2005

Vortex distribution in the Lowest Landau Level

We study the vortex distribution of the wave functions minimizing the Gross Pitaevskii energy for a fast rotating condensate in the Lowest Landau Level (LLL): we prove that the minimizer cannot have a finite number of zeroes thus the lattice is infinite, but not uniform. This uses the explicit expression of the projector onto the LLL. We also show that any slow varying envelope function can be approximated in the LLL by distorting the lattice. This is used in particular to approximate the inverted parabola and understand the role of ``invisible'' vortices: the distortion of the lattice is very small in the Thomas Fermi region but quite large outside, where the "invisible" vortices lie.

cond-mat.other↗

arXiv2004

Vortex patterns in a fast rotating Bose-Einstein condensate

For a fast rotating condensate in a harmonic trap, we investigate the structure of the vortex lattice using wave functions minimizing the Gross Pitaveskii energy in the Lowest Landau Level. We find that the minimizer of the energy in the rotating frame has a distorted vortex lattice for which we plot the typical distribution. We compute analytically the energy of an infinite regular lattice and of a class of distorted lattices. We find the optimal distortion and relate it to the decay of the wave function. Finally, we generalize our method to other trapping potentials.

cond-mat.other↗