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In this work, we study the large-scale structure of homogeneous flows displaying high density contrasts and small turbulent Mach numbers. Following Batchelor & Proudman (PTRSA 258, 1956), we draw an analogy between this configuration and…
We show that the longitudinal position $x(t)$ of a particle in a $(d+1)$-dimensional layered random velocity field (the Matheron-de Marsily model) can be identified as a fractional Brownian motion (fBm) characterized by a variable Hurst…
It is suggested that the $\omega^{-1/2}$ high-frequency decay of the alpha loss in highly viscous liquids, which appears to be generic, is a manifestation of a negative long-time tail as typically encountered in stochastic dynamics. The…
The evolution of entropy is derived with respect to dynamical systems. For a stochastic system, its relative entropy $D$ evolves in accordance with the second law of thermodynamics; its absolute entropy $H$ may also be so, provided that the…
This study is concerned with the diffusion of a passive scalar $\Theta(\r,t)$ advected by general $n$-dimensional shear flows $\u=u(y,z,...,t)\hat{x}$ having finite mean-square velocity gradients. The unidirectionality of the incompressible…
We construct the theory of dissipative hydrodynamics of uncharged fluids living on embedded space-time surfaces to first order in a derivative expansion in the case of codimension-1 surfaces (including fluid membranes) and the theory of…
Extensive simulations are performed to study the persistence behavior of a conserved lattice gas model exhibiting an absorbing phase transition from an active phase into an inactive phase. Both the global and the local persistence exponents…
Coalescence of sessile polymeric fluid drops on a partially wettable substrate exhibits a transition from inertial to viscoelastic regime at concentration ratio $c/c^* \sim 1$. Our findings unveil that the temporal evolution of the growing…
In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain $\mathbb{T}\times \mathbb{R}$. In the inviscid case there is a generic…
This dissertation is about the study of three important issues in the theory of relativistic fluid dynamics: the stability of dissipative fluid dynamics, the shear viscosity, and fluid dynamics with triangle anomaly.(1)The second order…
We consider a passive scalar $f$ advected by a strictly monotone shear flow and with a diffusivity parameter $\nu\ll 1$. We prove an estimate on the homogeneous $\dot{H}^{-1}$ norm of $f$ that combines both the $L^2$ enhanced diffusion…
The (fractional) Brownian sheet is a simplest example of a Gaussian random field X whose covariance is the tensor product of a finite number (d) of nonnegative correlation functions of self-similar Gaussian processes. Let Y be the…
The purpose of this work is to analyze the mathematical model governing motion of $n$-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state…
We investigate the transport coefficients $\alpha$ and $\beta$ in plasma systems with varying Reynolds numbers while maintaining a unit magnetic Prandtl number. {The $\alpha$ and $\beta$ tensors parameterize the turbulent electromotive…
The spatial distribution of unvisited/persistent sites in $d=1$ $A+A\to\emptyset$ model is studied numerically. Over length scales smaller than a cut-off $\xi(t)\sim t^{z}$, the set of unvisited sites is found to be a fractal. The fractal…
In this work, the univariant two-phase coexistence line of the hydrate of tetrahydrofuran (THF) is determined from 100 to 1000 bar by molecular dynamics simulations. The study is carried out by putting in contact a THF hydrate phase with a…
We consider the time-dependence of a hierarchy of scaled $L^{2m}$-norms $D_{m,\omega}$ and $D_{m,\theta}$ of the vorticity $\boldsymbol {\omega} = \boldsymbol{\nabla} \times {\mathbf u}$ and the density gradient $\boldsymbol{\nabla}…
We analyse the process of convective mixing in two-dimensional, homogeneous and isotropic porous media with dispersion. We considered a Rayleigh-Taylor instability in which the presence of a solute produces density differences driving the…
In our previous work [J. Chem. Phys. \textbf{136}, 024502 (2012)], we reported a demixing phase transition of a two-dimensional, binary Heisenberg fluid mixture driven by the ferromagnetic interactions of the magnetic species. Here, we…
The total energy E(t) in a fluid of inelastic particles is dissipated through inelastic collisions. When such systems are prepared in a homogeneous initial state and evolve undriven, E(t) decays initially as t^{-2} \aprox exp[ - 2\epsilon…