Related papers: Phase and precession evolution in the Burgers equa…
We construct a discrete shell-model for two-dimensional turbulence that takes into account local and nonlocal interactions between velocity modes in Fourier space. In real space, its continuous limit is described by the one-dimensional…
We prove that the stochastic Burgers equation, which is related to the Kardar-Parisi-Zhang/KPZ equation via weak derivative, is a "critical" scaling limit for density fluctuations for a family of non-integrable and non-stationary…
We develop a model in two dimensions to characterise the growth rate of a tracer gradient mixed by a statistically homogeneous flow with rapid temporal variations. % % The model is based on the orientation dynamics of the passive-tracer…
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…
Statistical properties of the noisy Burgers and KdV-Burgers equations are numerically studied. It is found that shock-like structures appear in the time-averaged patterns for the case of stepwise fixed boundary conditions. Our results show…
We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities <v(x,0)v(x',0)>\sim|x-x'|^{-2}.…
We undertake a systematic, direct numerical simulation (DNS) of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of…
We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D>1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D=1. The prediction is based on a field-theory…
We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and…
There is increased interest in time-dependent (non-autonomous) Hamiltonians, stemming in part from the active field of Floquet quantum materials. Despite this, dispersive time-decay bounds, which reflect energy transport in such systems,…
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…
We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in…
Protein folding is a universal process, very fast and accurate, which works consistently (as it should be) in a wide range of physiological conditions. The present work is based on three premises, namely: ($i$) folding reaction is a process…
We use the mapping between Burgers' equation and the problem of a directed polymer in a random medium in order to study the fully developped turbulence in the $N$ dimensional forced Burgers' equation. The stirring force corresponds to a…
In this Letter we show how the nonlinear evolution of a resonant triad depends on the special combination of the modes' phases chosen according to the resonance conditions. This phase combination is called dynamical phase. Its evolution is…
This paper examines the properties of a regularization of Burgers equation in one and multiple dimensions using a filtered convective velocity, which we have dubbed as convectively filtered Burgers (CFB) equation. A physical motivation…
Gathering together some existing results, we show that the solutions to the one-dimensional Burgers equation converge for long times towards the stationary solutions to the steady Burgers equation, whose Fourier spectrum is not integrable.…
We investigate the dynamics of triaxial collapse in terms of eigenvalues of the deformation tensor, the velocity derivative tensor and the gravity Hessian. Using the Bond-Myers model of ellipsoidal collapse, we derive a new set of equations…
Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions. In the present work, we consider the well-known Burgers equation with random…
This study investigates the relationship between low-frequency shock-wave oscillations and buffet cells on the main wing of the NASA common research model. The flow conditions were set at a Mach number of 0.85, Reynolds number of 2.27…