16,444 research outputs found
On the fractional Fisher information with applications to a hyperbolic-parabolic system of chemotaxis
We introduce new lower bounds for the fractional Fisher information. Equipped
with these bounds we study a hyperbolic-parabolic model of chemotaxis and prove
the global existence of solutions in certain dissipation regimes
Deriving GENERIC from a generalized fluctuation symmetry
Much of the structure of macroscopic evolution equations for relaxation to
equilibrium can be derived from symmetries in the dynamical fluctuations around
the most typical trajectory. For example, detailed balance as expressed in
terms of the Lagrangian for the path-space action leads to gradient zero-cost
flow. We find a new such fluctuation symmetry that implies GENERIC, an
extension of gradient flow where a Hamiltonian part is added to the dissipative
term in such a way as to retain the free energy as Lyapunov function
A particle system with explosions: law of large numbers for the density of particles and the blow-up time
Consider a system of independent random walks in the discrete torus with
creation-annihilation of particles and possible explosion of the total number
of particles in finite time. Rescaling space and rates for
diffusion/creation/annihilation of particles, we obtain a stong law of large
numbers for the density of particles in the supremum norm. The limiting object
is a classical solution to the semilinear heat equation u_t =u_{xx} + f(u). If
f(u)=u^p, 1<p \le 3, we also obtain a law of large numbers for the explosion
time
Nonlinear Transport of Bose-Einstein Condensates Through Waveguides with Disorder
We study the coherent flow of a guided Bose-Einstein condensate incident over
a disordered region of length L. We introduce a model of disordered potential
that originates from magnetic fluctuations inherent to microfabricated guides.
This model allows for analytical and numerical studies of realistic transport
experiments. The repulsive interaction among the condensate atoms in the beam
induces different transport regimes. Below some critical interaction (or for
sufficiently small L) a stationary flow is observed. In this regime, the
transmission decreases exponentially with L. For strong interaction (or large
L), the system displays a transition towards a time dependent flow with an
algebraic decay of the time averaged transmission.Comment: 15 pages, 9 figure
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