Related papers: Disordered systems and Burgers' turbulence
We explore a connection of the deterministically forced Burgers equation for local velocity fields with probabilistic solutions of the Schr\"{o}dinger boundary data problem. An issue of deducing the most likely interpolating dynamics from…
We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing…
In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be…
Burgers' equation is a well-studied model in applied mathematics with connections to the Navier-Stokes equations in one spatial direction and traffic flow, for example. Following on from previous work, we analyse solutions to Burgers'…
The inviscid limit of the stochastic Burgers equation is discussed in terms of the level surfaces of the minimising Hamilton-Jacobi function, the classical mechanical caustic and the Maxwell set and their algebraic pre-images under the…
The model of Brownian Percolation has been introduced as an approximation of discrete last-passage percolation models close to the axis. It allowed to compute some explicit limits and prove fluctuation theorems for these, based on the…
In this survey, we review the results on turbulence for the generalised Burgers equation on the circle: u_t+f'(u)u_x=\nu u_{xx}+\eta,\ x \in S^1=\R/\Z, obtained by A.Biryuk and the author in \cite{Bir01,BorK,BorW,BorD}. Here, f is smooth…
Throughout the history of the study of turbulence in fluid dynamics, there has yet to arise a unique definition or theoretical criterion for this important phenomenon. There have been interesting conjectures made by Ruelle [2], Muriel [3],…
A putative powerlaw range of the probability density of velocity gradient in high-Reynolds-number forced Burgers turbulence is studied. In the absence of information about shock locations, elementary conservation and stationarity relations…
We consider the 1D viscous Burgers equation with a control localised in a finite interval. It is proved that, for any $\varepsilon>0$, one can find a time $T$ of order $\log\varepsilon^{-1}$ such that any initial state can be steered to the…
The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\{y(x)\}$ is given by $H\big(\{y(x)\}\big) = \sum_{x=1}^N \exyx +…
This work is devoted to the study of the decay of multiscale deterministic solutions of the unforced Burgers' equation in the limit of vanishing viscosity. A deterministic model of turbulence-like evolution is considered. We con- struct the…
The present work is devoted to the evolution of random solutions of the unforced Burgers and KPZ equations in d-dimensions in the limit of vanishing viscosity. We consider a cellular model and as initial condition assign a value for the…
We study the stability of the glassy equilibrium state of a directed polymer in random media against weak perturbations including the intriguing problem of temperature-chaos. The statistical correlation of two real replica systems under…
The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in…
We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for…
A rigorous study is carried out for the randomly forced Burgers equation in the inviscid limit. No closure approximations are made. Instead the probability density functions of velocity and velocity gradient are related to the statistics of…
A randomly pinned elastic medium in two dimensions is modeled by a disordered fully-packed loop model. The energetics of disorder-induced dislocations is studied using exact and polynomial algorithms from combinatorial optimization.…
The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing…
We present a new approach to determine the small-scale statistical behavior of hydrodynamic turbulence by means of lattice simulations. Using the functional integral representation of the random-force-driven Burgers equation we show that…