Related papers: Burgers Turbulence and the Continuous Spontaneous …
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
This is an idiosyncratic survey of statistical fluid mechanics centering on the Hopf functional differential equation. Using the Burgers equation for illustration we review several functional integration approaches to theory of turbulence.…
The problem of one-dimensional randomly forced Burgers turbulence is considered in terms of (1+1) directed polymers. In the limit of strong turbulence (which corresponds to the zero temperature limit for the directed polymer system) using…
We study the decaying Burgers dynamics in $d$ dimensions for random Gaussian initial conditions. We focus on power-law initial energy spectra, such that the system shows a self-similar evolution. This is the case of interest for the…
This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar…
We carry out a detailed study of dynamic multiscaling in the turbulent nonequilibrium, but statistically steady, state of the stochastically forced one-dimensional Burgers equation. We introduce the concept of $\textit{interval collapse…
It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply…
This paper continue earlier investigations on the decay of Burgers turbulence in one dimension from Gaussian random initial conditions of the power-law spectral type $E_0(k)\sim|k|^n$. Depending on the power $n$, different characteristic…
The status of locality in quantum mechanics is analyzed from a nonstandard point of view. It is assumed that quantum states are relative, they depend on and are defined with respect to some bigger physical system which contains the former…
Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality…
It is shown that the shock wave solutions of the Burgers equation can be generated from localized sources. The evolution equation obeyed by the sources has a novel characteristic: It has a single-soliton solution as well as an infinite…
Is wave function collapse a prediction of the Schr\"odinger equation? This unusual problem is explored in an enlarged framework of interpretation, where quantum dynamics is considered exact and its interpretation is extended to include…
We study a spatially inhomogeneous coagulation model that contains a transport term in the spatial variable. The transport term models the vertical motion of particles due to gravity, thereby incorporating their fall into the dynamics.…
This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The…
The appearance of linear spaces, describing physical quantities by vectors and tensors, is ubiquitous in all of physics, from classical mechanics to the modern notion of local Lorentz invariance. However, as natural as this seems to the…
An ensemble of inelastically colliding grains driven by a vibrating wall in 2D exhibits density clustering. Working in the limit of nearly elastic collisions and employing granular hydrodynamics, we predict, by a marginal stability…
We discuss a connection (and a proper place in this framework) of the unforced and deterministically forced Burgers equation for local velocity fields of certain flows, with probabilistic solutions of the so-called Schr\"{o}dinger…
Many features of large N_c transition that occurs in the spectral density of Wilson loops as a function of loop area (observed recently in numerical simulations of Yang-Mills theory by Narayanan and Neuberger) can be captured by a simple…
The problem of randomly forced Burgers turbulence ("Burgulence") is considered in terms of the toy Gaussian Larkin model of directed polymers. In terms of the replica technique the explicit expressions for the two-time four-point free…
Self-similar models are important in general relativity and other fundamental theories. In this paper we shall discuss the ``similarity hypothesis'', which asserts that under a variety of physical circumstances solutions of these theories…