965 research outputs found
Front speed enhancement by incompressible flows in three or higher dimensions
We study, in dimensions , the family of first integrals of an
incompressible flow: these are functions whose level surfaces are
tangent to the streamlines of the advective incompressible field. One main
motivation for this study comes from earlier results proving that the existence
of nontrivial first integrals of an incompressible flow is the main key
that leads to a "linear speed up" by a large advection of pulsating traveling
fronts solving a reaction-advection-diffusion equation in a periodic
heterogeneous framework. The family of first integrals is not well understood
in dimensions due to the randomness of the trajectories of and
this is in contrast with the case N=2. By looking at the domain of propagation
as a union of different components produced by the advective field, we provide
more information about first integrals and we give a class of incompressible
flows which exhibit `ergodic components' of positive Lebesgue measure (hence
are not shear flows) and which, under certain sharp geometric conditions, speed
up the KPP fronts linearly with respect to the large amplitude. In the proofs,
we establish a link between incompressibility, ergodicity, first integrals, and
the dimension to give a sharp condition about the asymptotic behavior of the
minimal KPP speed in terms the configuration of ergodic components.Comment: 34 pages, 3 figure
A Wasserstein Gradient Flow Approach to Poisson-Nernst-Planck Equations
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational scheme is then set up and is the starting point of the construction of global weak solutions in a unified framework for the cases of both linear and non-linear diffusion. The proof of the main results relies on the derivation of additional estimates based on the flow interchange technique developed by Matthes et al. in [D. Matthes, R.J. McCann and G. Savare, Commun. Partial Differ. Equ. 34 (2009) 1352-1397]
Winning combinations of history-dependent games
The Parrondo effect describes the seemingly paradoxical situation in which
two losing games can, when combined, become winning [Phys. Rev. Lett. 85, 24
(2000)]. Here we generalize this analysis to the case where both games are
history-dependent, i.e. there is an intrinsic memory in the dynamics of each
game. New results are presented for the cases of both random and periodic
switching between the two games.Comment: (6 pages, 7 figures) Version 2: Major cosmetic changes and some minor
correction
A gradient bound for free boundary graphs
We prove an analogue for a one-phase free boundary problem of the classical
gradient bound for solutions to the minimal surface equation. It follows, in
particular, that every energy-minimizing free boundary that is a graph is also
smooth. The method we use also leads to a new proof of the classical minimal
surface gradient bound
A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows
In this article we set up a splitting variant of the JKO scheme in order to
handle gradient flows with respect to the Kantorovich-Fisher-Rao metric,
recently introduced and defined on the space of positive Radon measure with
varying masses. We perform successively a time step for the quadratic
Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao
distance. Exploiting some inf-convolution structure of the metric we show
convergence of the whole process for the standard class of energy functionals
under suitable compactness assumptions, and investigate in details the case of
internal energies. The interest is double: On the one hand we prove existence
of weak solutions for a certain class of reaction-advection-diffusion
equations, and on the other hand this process is constructive and well adapted
to available numerical solvers.Comment: Final version, to appear in SIAM SIM
The flashing ratchet and unidirectional transport of matter
We study the flashing ratchet model of a Brownian motor, which consists in
cyclical switching between the Fokker-Planck equation with an asymmetric
ratchet-like potential and the pure diffusion equation. We show that the motor
really performs unidirectional transport of mass, for proper parameters of the
model, by analyzing the attractor of the problem and the stationary vector of a
related Markov chain.Comment: 11 page
An alternating direction method for solving convex nonlinear semidefinite programming problems
An alternating direction method is proposed for solving convex semidefinite optimization problems. This method only computes several metric projections at each iteration. Convergence analysis is presented and numerical experiments in solving matrix completion problems are reported
- …