517 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
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
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
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
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
A power penalty method for a bounded nonlinear complementarity problem
We propose a novel power penalty approach to the bounded nonlinear complementarity problem (NCP) in which a reformulated NCP is approximated by a nonlinear equation containing a power penalty term. We show that the solution to the nonlinear equation converges to that of the bounded NCP at an exponential rate when the function is continuous and ξ-monotone. A higher convergence rate is also obtained when the function becomes Lipschitz continuous and strongly monotone. Numerical results on discretized ‘double obstacle’ problems are presented to confirm the theoretical results
Direct approach to the problem of strong local minima in Calculus of Variations
The paper introduces a general strategy for identifying strong local
minimizers of variational functionals. It is based on the idea that any
variation of the integral functional can be evaluated directly in terms of the
appropriate parameterized measures. We demonstrate our approach on a problem of
W^{1,infinity} weak-* local minima--a slight weakening of the classical notion
of strong local minima. We obtain the first quasiconvexity-based set of
sufficient conditions for W^{1,infinity} weak-* local minima.Comment: 26 pages, no figure
"Illusion of control" in Minority and Parrondo Games
Human beings like to believe they are in control of their destiny. This
ubiquitous trait seems to increase motivation and persistence, and is probably
evolutionarily adaptive. But how good really is our ability to control? How
successful is our track record in these areas? There is little understanding of
when and under what circumstances we may over-estimate or even lose our ability
to control and optimize outcomes, especially when they are the result of
aggregations of individual optimization processes. Here, we demonstrate
analytically using the theory of Markov Chains and by numerical simulations in
two classes of games, the Minority game and the Parrondo Games, that agents who
optimize their strategy based on past information actually perform worse than
non-optimizing agents. In other words, low-entropy (more informative)
strategies under-perform high-entropy (or random) strategies. This provides a
precise definition of the "illusion of control" in set-ups a priori defined to
emphasize the importance of optimization.Comment: 17 pages, four figures, 1 tabl
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