相关论文: The Batchelor--Howells--Townsend spectrum: three-d…
The influence of compressibility on the stability of the scaling regimes of the passive scalar advected by a Gaussian velocity field with finite correlation time is investigated by the field theoretic renormalization group within two-loop…
We show that the decay of a passive scalar $\theta$ advected by a random incompressible flow with zero correlation time in Batchelor limit can be mapped exactly to a certain quantum-mechanical system with a finite number of degrees of…
We consider turbulent advection of a scalar field $T(\B.r)$, passive or active, and focus on the statistics of gradient fields conditioned on scalar differences $\Delta T(R)$ across a scale $R$. In particular we focus on two conditional…
We characterize the early stages of the approach to equilibrium in isolated quantum systems through the evolution of the entanglement spectrum. We find that the entanglement spectrum of a subsystem evolves with at least three distinct…
We consider the quantum mechanical description of the de Sitter static patch in three-dimensional general relativity. We consider a Lorentzian path integral that conjecturally computes the Fourier transform of the spectrum of the static…
The 3D incompressible Euler equations with a passive scalar $\theta$ are considered in a smooth domain $\Omega\subset \mathbb{R}^{3}$ with no-normal-flow boundary conditions $\bu\cdot\bhn|_{\partial\Omega} = 0$. It is shown that smooth…
We show that a Hagedorn spectrum (i.e., spectrum where the number of hadrons grows exponentially with the mass) emerges automatically in large $N_c$ QCD in 2+1 and 3+1 dimensions. The approach is based on the study of Euclidean space…
We study the behavior of a tracer particle driven by a one-dimensional fluctuating potential, defined initially as a Brownian motion, and evolving in time according to the heat equation. We obtain two main results. First, in the short time…
This paper investigates the stochastic 3D Euler equations on a periodic domain $\mathbb{T}^3$, driven by a $GG^*$-Wiener process $B$ of trace class: \begin{align*} \mathrm{d} u+\mathrm{div}(u\otimes u)\,\mathrm{d} t+\nabla…
As presented in Annenkov & Shrira (2009), when a surface gravity wave field is subjected to an abrupt perturbation of external forcing, its spectrum evolves on a ``fast'' dynamic time scale of $O(\varepsilon^{-2})$, with $\varepsilon$ a…
Three-dimensional scalar electrodynamics, with a local U(1) gauge symmetry, is believed to be dual to a scalar theory with a global U(1) symmetry, near the phase transition point. The conjectured duality leads to definite predictions for…
A multi-scale model for the evolution of the velocity gradient tensor in fully developed turbulence is proposed. The model is based on a coupling between a ``Restricted Euler'' dynamics [{\it P. Vieillefosse, Physica A, {\bf 14}, 150…
One of the primitive aims of the two-dimensional BTW model had been to explain the $1/f^{\alpha}$ noise which is widely seen in the natural systems. In this paper we study some time signals, namely the activity inside an avalanche ($x(t)$),…
In the initial conditions of the $3 + 1$ formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point.…
Batchelor predicted that a passive scalar $\psi^\nu$ with diffusivity $\nu$, advected by a smooth fluid velocity, should typically have Fourier mass distributed as $|\hat \psi^\nu|^2(k) \approx |k|^{-d}$ for $|k| \ll \nu^{-1/2}$. For a…
Scaling exponents are the central quantitative prediction of theories of turbulence and in-situ satellite observations of the high Reynolds number solar wind flow have provided an extensive testbed of these. We propose a general, instrument…
We consider advection of a passive scalar theta(t,r) by an incompressible large-scale turbulent flow. In the framework of the Kraichnan model the whole PDF's (probability distribution functions) for the single-point statistics of theta and…
In 1959, Batchelor gave a prediction for the power spectral density of a passive scalar advected by an incompressible fluid exhibiting shear-straining, a mechanism for the creation of small scales in the scalar [Bat59]. Recently, a…
Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood number and at Prandtl number one is investigated by means of high resolution direct numerical simulations of the Boussinesq equations. RT turbulence is a…
We examine the effect of a threshold bias on the power spectrum and the bispectrum in an ensemble of numerical simulations (Gaussian initial perturbations with power law spectra P(k) \sim k^n, n=+1, 0, -1, -2) and compare our results with…