Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDiffusion equations from kinetic models with non-conserved momentum
110
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We derive diffusive macroscopic equations for the particle and energy density of a system whose time evolution is described by a kinetic equation for the one particle position and velocity function f(r,v,t) that consists of a part that conserves energy and momentum such as the Boltzmann equation and an external randomization of the particle velocity directions that breaks the momentum conservation. Rescaling space and time by epsilon and epsilon square respectively and carrying out a Hilbert expansion in epsilon around a local equilibrium Maxwellian yields coupled diffusion equations with specified Onsager coefficients for the particle and energy density. Our analysis includes a system of hard disks at intermediate densities by using the Enskog equation for the collision kernel.
rate research
Read More
We describe results of computer simulations of steady state heat transport in a fluid of hard discs undergoing both elastic interparticle collisions and velocity randomizing collisions which do not conserve momentum. The system consists of N discs of radius r in a unit square, periodic in the y-direction and having thermal walls at x = 0 with temperature T0 taking values from 1 to 20 and at x = 1 with T1 = 1. We consider different values of the ratio between randomizing and interparticle collision rates and extrapolate results from different N, to N->infinity, r->0 such that rho=1/2. We find that in the (extrapolated) limit N->infinity, the systems local density and temperature profiles are those of local thermodynamic equilibrium (LTE) and obey Fouriers law. The variance of global quantities, such as the total energy, deviates from its local equilibrium value in a form consistent with macroscopic fluctuation theory.
We propose a modified voter model with locally conserved magnetization and investigate its phase ordering dynamics in two dimensions in numerical simulations. Imposing a local constraint on the dynamics has the surprising effect of speeding up the phase ordering process. The system is shown to exhibit a scaling regime characterized by algebraic domain growth, at odds with the logarithmic coarsening of the standard voter model. A phenomenological approach based on cluster diffusion and similar to Smoluchowski ripening correctly predicts the observed scaling regime. Our analysis exposes unexpected complexity in the phase ordering dynamics without thermodynamic potential.
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.
Conserved lattice gas (CLG) models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents $beta=1= u=eta$ whereas the same on a ladder belong to directed percolation (DP)universality. We conjecture that additional stochasticity in particle transfer is a relevant perturbation and its presence on a ladder force the APT to be in DP class. To substantiate this we introduce a class of restricted conserved lattice gas models on a multi-chain system ($Mtimes L$ square lattice with periodic boundary condition in both directions), where particles which have exactly one vacant neighbor are active and they move deterministically to the neighboring vacant site. We show that for odd number of chains , in the thermodynamic limit $L to infty,$ these models exhibit APT at $rho_c= frac{1}{2}(1+frac1M)$ with $beta =1.$ On the other hand, for even-chain systems transition occurs at $rho_c=frac12$ with $beta=1,2$ for $M=2,4$ respectively, and $beta= 3$ for $Mge6.$ We illustrate this unusual critical behavior analytically using a transfer matrix method.
We make a brief historical review to the moment model reduction to the kinetic equations, particularly the Grads moment method for Boltzmann equation. The focus is on the hyperbolicity of the reduced model, which is essential to the existence of its classical solution as a Cauchy problem. The theory of the framework we developed in last years is then introduced, which may preserve the hyperbolic nature of the kinetic equations with high universality. Some lastest progress on the comparison between models with/without hyperbolicity is presented to validate the hyperbolic moment models for rarefied gases.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
