Related papers: Stochastic identities for random isotropic fields
We consider equilibrium statistics for high Reynolds number isotropic turbulence in an incompressible flow driven by steady forcing at the largest scale. Motivated by shell model observations, we develop a similarity theory for the inertial…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…
Foundations of the analysis of scaling in randomly stirred compressible fluid with the aid of stochastic differential equations are discussed in the example of perfect gas. The structure of the stress tensor with nonnegative shear and bulk…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
Results from a new series of experiments on barotropic and baroclinic turbulent flows generated in a rotating tank with topographic beta-effect are presented. The velocity fields are measured by the Altimetric Imaging Velocimetry. The…
A deterministic application $\theta\,:\,\mathbb{R}^2\rightarrow\mathbb{R}^2$ deforms bijectively and regularly the plane and allows to build a deformed random field $X\circ\theta\,:\,\mathbb{R}^2\rightarrow\mathbb{R}$ from a regular,…
We show that the statistics of an edge type variable in natural images exhibits self-similarity properties which resemble those of local energy dissipation in turbulent flows. Our results show that extended self-similarity remarkably holds…
Flow-fields are ubiquitous systems that are able to transport vital signalling molecules necessary for system function. While information regarding the location and transport of such particles is often crucial, it is not well-understood how…
For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines the isochron for each point of the orbit as the cross-section with fixed return time under the flow. Equivalently, isochrons can be…
Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
Passive scalars advected by a magnetically driven two-dimensional turbulent flow are analyzed using methods of statistical topography. The passive tracer concentration is interpreted as the height of a random surface and the scaling…
Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a non trivial dispersion relation is obtained and it is shown that the instability is of…
Random models of evolution are instrumental in extracting rates of microscopic evolutionary mechanisms from empirical observations on genetic variation in genome sequences. In this context it is necessary to know the statistical properties…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
Existence of random dynamical systems for a class of coalescing stochastic flows on $\mathbb{R}$ is proved. A new state space for coalescing flows is built. As particular cases coalescing flows of solutions to stochastic differential…
Understanding the dynamics of particles in turbulent flow is important in many environmental and industrial applications. In this paper, the statistics of particle pair orientation is numerically studied in homogeneous isotropic turbulent…
We present experiments of sandpiles on grids (square, triangular, hexagonal) and Penrose tilings. The challenging part is to program such simulator; and our javacript code is available online, ready to play! We first present some identity…
Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the…