293 research outputs found
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
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
Precision constrained simulation of the Local Universe
We use the formalism of constrained Gaussian random field to compute a
precise large scale simulation of the 60 Mpc/h volume of our Local Universe. We
derive the constraints from the reconstructed peculiar velocities of the 2MASS
Redshift Survey. We obtain a correlation of 0.97 between the log-density field
of the dark matter distribution of the simulation and the log-density of
observed galaxies of the Local Universe. We achieve a good comparison of the
simulated velocity field to the observed velocity field obtained from the
galaxy distances of the NBG-3k. At the end, we compare the two-point
correlation function of both the 2MRS galaxies and of the dark matter particles
of the simulation. We conclude that this method is a very promising technique
of exploring the dynamics and the particularities the Universe in our
neighbourhood.Comment: 8 pages, 5 figures, accepted by MNRA
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
Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations
We establish a connection between Optimal Transport Theory and classical
Convection Theory for geophysical flows. Our starting point is the model
designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal
Transport problems. This model can be seen as a generalization of the
Darcy-Boussinesq equations, which is a degenerate version of the
Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate
different variants of the NSB equations (in particular what we call the
generalized Hydrostatic-Boussinesq equations) to various models involving
Optimal Transport (and the related Monge-Ampere equation. This includes the 2D
semi-geostrophic equations and some fully non-linear versions of the so-called
high-field limit of the Vlasov-Poisson system and of the Keller-Segel for
Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model
can be related to the magnetic relaxation model studied by Arnold and Moffatt
to obtain stationary solutions of the Euler equations with prescribed topology
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
Global estimates for solutions to the linearized Monge--Amp\`ere equations
In this paper, we establish global estimates for solutions to the
linearized Monge-Amp\`ere equations under natural assumptions on the domain,
Monge-Amp\`ere measures and boundary data. Our estimates are affine invariant
analogues of the global estimates of Winter for fully nonlinear,
uniformly elliptic equations, and also linearized counterparts of Savin's
global estimates for the Monge-Amp\`ere equations.Comment: v2: presentation improve
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit
This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB)
model of plasma physics. This model consists of the pressureless gas dynamics
equations coupled with the Poisson equation and where the Boltzmann relation
relates the potential to the electron density. If the quasi-neutral assumption
is made, the Poisson equation is replaced by the constraint of zero local
charge and the model reduces to the Isothermal Compressible Euler (ICE) model.
We compare a numerical strategy based on the EPB model to a strategy using a
reformulation (called REPB formulation). The REPB scheme captures the
quasi-neutral limit more accurately
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
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