Past

We report on two joint works with Jeremy Quastel and Alejandro Ramirez, on an

interacting particle system which can be viewed as a combustion mechanism or a

chemical reaction.

We consider a model of the reaction $X+Y\to 2X$ on the integer lattice in

which $Y$ particles do not move while $X$ particles move as independent

continuous time, simple symmetric random walks. $Y$ particles are transformed

instantaneously to $X$ particles upon contact.

We start with a fixed number $a\ge 1$ of $Y$ particles at each site to the

right of the origin, and define a class of configurations of the $X$ particles

to the left of the origin having a finite $l^1$ norm with a specified

exponential weight. Starting from any configuration of $X$ particles to the left

of the origin within such a class, we prove a central limit theorem for the

position of the rightmost visited site of the $X$ particles.

We consider the parallel solution of sparse linear systems of equations in a limited memory environment. A preliminary out-of core version of a sparse multifrontal code called MUMPS (MUltifrontal Massively Parallel Solver) has been developed as part of a collaboration between CERFACS, ENSEEIHT and INRIA (ENS-Lyon and Bordeaux).

We first briefly describe the current status of the out-of-core factorization phase. We then assume that the factors have been written on the hard disk during the factorization phase and we discuss the design of an efficient solution phase.Two different approaches are presented to read data from the disk, with a discussion on the advantages and the drawbacks of each one.

Our work differs and extends the work of Rothberg and Schreiber (1999) and of Rotkin and Toledo (2004) because firstly we consider a parallel out-of-core context, and secondly we also study the performance of the solve phase.

This is work on collaboration with E. Agullo, I.S Duff, A. Guermouche, J.-Y. L'Excellent, T. Slavova

OWL Meeting