Related papers: Instantons and Intermittency
Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain-rate with highly non-Gaussian statistics.…
At long times, a fractional Brownian particle in a confining external potential reaches a non-equilibrium (non-Boltzmann) steady state. Here we consider scale-invariant power-law potentials $V(x)\sim |x|^m$, where $m>0$, and employ the…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent developments related to the application of…
The probability density function (PDF) of flux $R$ is computed in systems with logarithmic non-linearity using a model non-linear dynamical equation. The PDF tails of the first moment flux are analytically predicted to be power law. These…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
In this paper, we investigate and develop a new approach to the numerical analysis and characterization of random fluctuations with heavy-tailed probability distribution function (PDF), such as turbulent heat flow and solar flare…
This Letter provides a theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent plasma transport events. Specifically, nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence…
We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities.…
Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…
We review the euclidean path-integral formalism in connection with the one-dimensional non-relativistic particle. The configurations which allow to construct a semiclassical approximation classify themselves into either topological…
Fundamental aspects of fluid dynamics are related to construction of statistical models for incompressible Navier-Stokes fluids. The latter can be considered either \textit{deterministic} or \textit{stochastic,} respectively for…
The goal of this paper is to better understand the structure of fission fragment distributions by investigating the competition between the static structure of the collective manifold and stochastic dynamics. In particular, we study the…
We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which…
We develop a general variational approach to study the statistical properties of the tail states of a wide class of non-Hermitian operators. The utility of the method, which is a refinement of the instanton approach introduced by Zittartz…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
A characterization of instanton contributions to gauge field theory is given. The dynamics of instantons with the gluon field is given in terms of 'classical' instanton contributions, i.e. on the same footing as tree amplitudes in field…
An open problem arising in the statistical description of turbulence is related to the \textit{theoretical prediction based on first principles} of the so-called multi-point velocity probability density functions (PDFs) characterizing a…
We examine the statistics of active scalar fluctuations in high-Rayleigh number fingering convection with high-resolution three-dimensional numerical experiments. The one-point distribution of buoyancy fluctuations is found to present…
We derive from the Navier-Stokes equation an exact equation satisfied by the dissipation rate correlation function. We exploit its mathematical similarity to the corresponding equation derived from the 1-dimensional stochastic Burgers…