J. San Martín

Asymptotic analysis of the exponential penalty trajectory in linear programming

We consider the linear program min{c′x: Ax⩽b} and the associated exponential penalty functionfr(x) = c′x + rΣexp[(Aix − bi)/r]. Forr close to 0, the unconstrained minimizerx(r) offr admits an asymptotic expansion of the formx(r) = x* + rd* + η(r) wherex* is a particular optimal solution of the linear program and the error termη(r) has an exponentially fast decay. Using duality theory we exhibit an associated dual trajectoryλ(r) which converges exponentially fast to a particular dual optimal solution. These results are completed by an asymptotic analysis whenr tends to ∞: the primal trajectory has an asymptotic ray and the dual trajectory converges to an interior dual feasible solution.

On Burnett coefficients in periodic media in low contrast regime

In this work, we consider low contrast periodic media and we study the dependence of the effective or homogenized tensor and the dispersion tensor in terms of the microstructure. We treat both one-dimensional structures and some laminated structures in higher dimension. Interesting properties of the sign of these coefficients are found. Surprisingly, these depend on the microstructure only through the local proportion parameter, and in some cases, they do not depend on the microstructure at all.

Collisions of rigid bodies, deformable bodies and fluids

Publisher Summary The system made of two solids is deformable because the relative position of the solids may change. This fact can be applied to a complex problem of mechanics—the collision theory. The major findings are constitutive laws, which are coherent from the thermodynamics point of view. They give robust and productive models and numerical methods, for instance—for rock avalanches and collisions of solids and fluids.

STATIONARY PROCESSES WHOSE FILTRATIONS ARE STANDARD

We study the standard property of the natural filtration associated to a 0-1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershiks criterion for standardness.

Noyaux potentiels associés à une filtration

Abstract We study from the point of view of potential theory some operators V which are “integrals of martingales” and noteworthy the formula ( I + V ) −1 = I − N where N is a submarkovian kernel. We give an explicit expression of N when the filtration is finite and get the general case with an usual approximation procedure. Some links are made with the matrix theory (ultrametric and Stieltjes matrices) and the graph theory (flows and capacities) when the space is finite.

Phase transition for absorbed Brownian motion with drift

AbstractWe study one-dimensional Brownian motion with constant drift toward the origin and initial distribution concentrated in the strictly positive real line. We say that at the first time the process hits the origin, it is absorbed. We study the asymptotic behavior, ast→∞, ofmt, the conditional distribution at time zero of the process conditioned on survival up to timet and on the process having a fixed value at timet. We find that there is a phase transition in the decay rate of the initial condition. For fast decay rate (subcritical case)mt is localized, in the critical casemt is located around

The delay of shock breakout due to circumstellar material evident in most type II supernovae

\sqrt t

On Burnett Coefficients in Periodic Media with Two Phases

, and for slow rates (supercritical case)mt is located aroundt. The critical rate is given by the decay of the minimal quasistationary distribution of this process. We also study in each case the asymptotic distribution of the process, scaled by