350 research outputs found
Geodesics in the space of measure-preserving maps and plans
We study Brenier's variational models for incompressible Euler equations.
These models give rise to a relaxation of the Arnold distance in the space of
measure-preserving maps and, more generally, measure-preserving plans. We
analyze the properties of the relaxed distance, we show a close link between
the Lagrangian and the Eulerian model, and we derive necessary and sufficient
optimality conditions for minimizers. These conditions take into account a
modified Lagrangian induced by the pressure field. Moreover, adapting some
ideas of Shnirelman, we show that, even for non-deterministic final conditions,
generalized flows can be approximated in energy by flows associated to
measure-preserving maps
Young Measures Generated by Ideal Incompressible Fluid Flows
In their seminal paper "Oscillations and concentrations in weak solutions of
the incompressible fluid equations", R. DiPerna and A. Majda introduced the
notion of measure-valued solution for the incompressible Euler equations in
order to capture complex phenomena present in limits of approximate solutions,
such as persistence of oscillation and development of concentrations.
Furthermore, they gave several explicit examples exhibiting such phenomena. In
this paper we show that any measure-valued solution can be generated by a
sequence of exact weak solutions. In particular this gives rise to a very
large, arguably too large, set of weak solutions of the incompressible Euler
equations.Comment: 35 pages. Final revised version. To appear in Arch. Ration. Mech.
Ana
Contractive metrics for scalar conservation laws
We consider nondecreasing entropy solutions to 1-d scalar conservation laws
and show that the spatial derivatives of such solutions satisfy a contraction
property with respect to the Wasserstein distance of any order. This result
extends the L^1-contraction property shown by Kruzkov
Rank-(n – 1) convexity and quasiconvexity for divergence free fields
No description supplie
L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy method
We consider scalar nonviscous conservation laws with strictly convex flux in
one spatial dimension, and we investigate the behavior of bounded L^2
perturbations of shock wave solutions to the Riemann problem using the relative
entropy method. We show that up to a time-dependent translation of the shock,
the L^2 norm of a perturbed solution relative to the shock wave is bounded
above by the L^2 norm of the initial perturbation.Comment: 17 page
Ion-beam mixing induced by atomic and cluster bombardment in the electronic stopping-power regime
Single crystals of magnesium oxide containing nanoprecipitates of sodium were bombarded with swift ions (∼GeV-Pb, U) or cluster beams (∼20 MeV-C60) to study the phase change induced by electronic processes at high stopping power (≳10 keV/nm). The sodium precipitates and the defect creation were characterized by optical absorption and transmission electron microscopy. The ion or cluster bombardment leads to an evolution of the Na precipitate concentration but the size distribution remains unchanged. The decrease in Na metallic concentration is attributed to mixing effects at the interfaces between Na clusters and MgO. In addition, optical-absorption measurements show a broadening of the absorption band associated with electron plasma oscillations in Na clusters. This effect is due to a decrease of the electron mean free path, which could be induced by defect creation in the metal. All these results show an influence of high electronic stopping power in materials known to be very resistant to irradiation with weak ionizing projectiles. The dependence of these effects on electronic stopping power and on various solid-state parameters is discussed
Two limit cases of Born-Infeld equations
International audienceWe study two limit cases \l \rightarrow \infty and \l \rightarrow 0 in Born-Infeld equations. Here the parameter \l >0 is interpreted as the maximal electric field in the electromagnetic theory and the case \l = 0 corresponds to the string theory. Formal limits are governed by the classical Maxwell equations and pressureless magnetohydrodynamics system, respectively. For studying the limit \l \rightarrow \infty, a new scaling is introduced. We give the relations between these limits and Brenier high and low field limits. Finally, using compensated compactness arguments, the limits are rigorously justified for global entropy solutions in in one space dimension, based on derived uniform estimates and techniques for linear Lagrangian systems
Mass transportation with LQ cost functions
We study the optimal transport problem in the Euclidean space where the cost
function is given by the value function associated with a Linear Quadratic
minimization problem. Under appropriate assumptions, we generalize Brenier's
Theorem proving existence and uniqueness of an optimal transport map. In the
controllable case, we show that the optimal transport map has to be the
gradient of a convex function up to a linear change of coordinates. We give
regularity results and also investigate the non-controllable case
Scattering defect in large diameter titanium-doped sapphire crystals grown by the Kyropoulos technique
International audienceThe Kyropoulos technique allows growing large diameter Ti doped sapphire for Chirped pulse amplification laser. A scattering defect peculiar to Kyropoulos grown crystals is presented. This defect is characterized by different techniques: luminescence, absorption measurement, X-ray rocking curve. The impact of this defect to the potential application in chirped pulse amplification CPA laser is evaluated. The nature of this defect is discussed. Modified convexity of the interface is proposed to avoid the formation of this defect and increase the quality of the Ti sapphire crystal
- …