Related papers: Stochastic identities for random isotropic fields
We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…
Selected recent contributions involving fluctuating velocity fields to the rapidly developing domain of stochastic field theory are reviewed. Functional representations for solutions of stochastic differential equations and master equations…
Invariant foliations are geometric structures for describing and understanding the qualitative behaviors of nonlinear dynamical systems. For stochastic dynamical systems, however, these geometric structures themselves are complicated random…
An experimental analysis of small-scales anisotropic turbulent fluctuations has been performed in two different flows. We analyzed anisotropic properties of an homogeneous shear flows and of a turbulent boundary layer by means of two…
The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the…
We analyze data from direct numerical simulations of homogeneous and isotropic turbulence (at Re_\lambda \approx 280) and study the statistics of curvature and torsion of Lagrangian trajectories in order to extract informations on the…
The Ruelle resonances of a dynamical system are spectral data describing the precise asymptotics of correlations. We classify them completely for a class of chaotic two-dimensional maps, the linear pseudo-Anosov maps, in terms of the action…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
Energy dissipation rate is an important parameter for nearly every experiment on turbulent flow. Mathematically precise relationships between energy dissipation rate and other measurable statistics for the case of anisotropic turbulence are…
Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…
Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess,…
We use the probabilistic method to construct examples of conjectured phenomenon about asymptotic syzygies. In particular, we use the Stanley-Reisner ideals of random flag complexes to construct new examples of Ein and Lazarsfeld's…
This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in arXiv:1304.0708 to global function fields of odd characteristics. First, we present algorithm for checking if a given…
Using explicit analytical computations, generic occurrence of inequivalence between two or more statistical ensembles is obtained for a large class of equilibrium states of two-dimensional and geophysical turbulent flows. The occurrence of…
We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim…
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher…
In spatial statistics, point processes are often assumed to be isotropic meaning that their distribution is invariant under rotations. Statistical tests for the null hypothesis of isotropy found in the literature are based either on…
The structure and the dynamics of homogeneous turbulence are modified by the presence of body forces such that the Coriolis or the buoyancy forces, which may render a wide range of turbulence scales anisotropic. The corresponding…
We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of…
On their roller coaster ride through turbulence, tracer particles sample the fluctuations of the underlying fields in space and time. Quantitatively relating particle and field statistics remains a fundamental challenge in a large variety…