Diffusive Propagation of Energy in a Non-Acoustic Chain

We consider a non acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the curvature (or bending) of the chain satisfy a system of evolution equations}. We prove that, in a diffusive space-time scaling, the curvature and momentum evolve following a linear system that corresponds to a damped Euler-Bernoulli beam equation. The macroscopic energy density evolves following a non linear diffusive equation. In particular the energy transfer is diffusive in this dynamics. This provides a first rigorous example of a normal diffusion of energy in a one dimensional dynamics that conserves the momentum

Principal eigenvalue of the fractional Laplacian with a large incompressible drift

We add a divergence-free drift with increasing magnitude to the fractional Laplacian on a bounded smooth domain, and discuss the behavior of the principal eigenvalue for the Dirichlet problem. The eigenvalue remains bounded if and only if the drift has non-trivial first integrals in the domain of the quadratic form of the fractional Laplacian.Comment: 19 page

On stationarity of Lagrangian observations of passive tracer velocity in a compressible environment

We study the transport of a passive tracer particle in a steady strongly mixing flow with a nonzero mean velocity. We show that there exists a probability measure under which the particle Lagrangian velocity process is stationary. This measure is absolutely continuous with respect to the underlying probability measure for the Eulerian flow.Comment: Published at http://dx.doi.org/10.1214/105051604000000945 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Limit Theorems for Motions in a Flow with a Nonzero Drift

We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean

Evaluation of Hashing Methods Performance on Binary Feature Descriptors

In this paper we evaluate performance of data-dependent hashing methods on binary data. The goal is to find a hashing method that can effectively produce lower dimensional binary representation of 512-bit FREAK descriptors. A representative sample of recent unsupervised, semi-supervised and supervised hashing methods was experimentally evaluated on large datasets of labelled binary FREAK feature descriptors