相关论文: Remark on the relation between passive scalars and…

In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric…

The dissipation phenomena of relative entropy from an It\^o--Langevin dynamical system is a classic topic from stochastic analysis. Relying on the time-reversal of diffusions, a novel trajectorial approach investigates the pathwise behavior…

Two dimensional passive scalar turbulence is studied by means of a k-space diffusion model based on a third order differential approximation. This simple description of local nonlinear interactions in Fourier space is shown to present a…

Pre-asymptotic transport of a scalar quantity passively advected by a velocity field formed by a large-scale component superimposed to a small-scale fluctuation is investigated both analytically and by means of numerical simulations.…

A framework to establish response theory for a class of nonlinear stochastic partial differential equations (SPDEs) is provided. More specifically, it is shown that for a certain class of observables, the averages of those observables…

For Kraichnan's problem of passive scalar advection by a velocity field delta-correlated in time, the limit of large space dimensionality $d\gg1$ is considered. Scaling exponents of the scalar field are analytically found to be…

There does not exist a notion of time which could be transferred straightforwardly from classical to quantum gravity. For this reason, a method of time quantification which would be appropriate for gravity quantization is being sought. One…

We investigate statistical properties of the passive scalar near boundaries (walls) in random (turbulent) flows assuming weakness of its diffusion. Then at advanced stages of the passive scalar mixing its unmixed residue is concentrated in…

We provide the leading behavior at large wavenumbers of the two-point correlation function of a scalar field passively advected by a turbulent flow. We first consider the Kraichnan model, in which the turbulent carrier flow is modeled by a…

This paper is concerned with a stochastic dissipativity theory using quadratic-exponential storage functions for open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential equations. The…

We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…

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…

We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are…

We propose a novel mechanism for the origin of non-Gaussian tails in the probability distribution functions (PDFs) of local variables in nonlinear, diffusive, dynamical systems including passive scalars advected by chaotic velocity fields.…

Gaussian random fields with Mat\'ern covariance functions are popular models in spatial statistics and machine learning. In this work, we develop a spatio-temporal extension of the Gaussian Mat\'ern fields formulated as solutions to a…

We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the…

The use of proper time as a tool for causality implementation in field theory is clarified and extended to allow a manifestly covariant definition of discrete fields proper to be applied in field theory and quantum mechanics. It implies on…

We propose a stochastic interpretation of spacetime non-commutativity starting from the path integral formulation of quantum mechanical commutation relations. We discuss how the (non-)commutativity of spacetime is inherently related to the…

We investigate the ghostfree scalar-tensor theory with a timelike scalar field, with derivatives of the scalar field up to the third order and with the Riemann tensor up to the quadratic order. We build two types of linear spaces. One is…

A recently proposed stochastic hidden variable model for quantum mechanics has been claimed to involve "retrocausality" due to the appearance of equations of motion with future-time boundary conditions. We formulate an equivalent system of…