Diffusion in a Granular Fluid - Simulation

The linear response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceeding paper. The formally exact Einstein and Green-Kubo expressions for the self-diffusion coefficient are evaluated there from an approximation to the velocity autocorrelation function. These results are compared here to those from molecular dynamics simulations over a wide range of density and inelasticity, for the particular case of self-diffusion. It is found that the approximate theory is in good agreement with simulation data up to moderate densities and degrees of inelasticity. At higher density, the effects of inelasticity are stronger, leading to a significant enhancement of the diffusion coefficient over its value for elastic collisions. Possible explanations associated with an unstable long wavelength shear mode are explored, including the effects of strong fluctuations and mode coupling

Accelerating Eulerian Fluid Simulation With Convolutional Networks

Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that leverages the approximation power of deep-learning with the precision of standard solvers to obtain fast and highly realistic simulations. Our method solves the incompressible Euler equations using the standard operator splitting method, in which a large sparse linear system with many free parameters must be solved. We use a Convolutional Network with a highly tailored architecture, trained using a novel unsupervised learning framework to solve the linear system. We present real-time 2D and 3D simulations that outperform recently proposed data-driven methods; the obtained results are realistic and show good generalization properties.Comment: Significant revisio

Generalized Geometric Cluster Algorithm for Fluid Simulation

We present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids. The connection with well-known cluster algorithms for lattice spin models is discussed, and an explicit full cluster decomposition is derived for a particle configuration in a fluid. We investigate a number of basic properties of the geometric cluster algorithm, including the dependence of the cluster-size distribution on density and temperature. Practical aspects of its implementation and possible extensions are discussed. The capabilities and efficiency of our approach are illustrated by means of two example studies.Comment: Accepted for publication in Phys. Rev. E. Follow-up to cond-mat/041274

Fluid Simulation

Tato bakalářská práce zpracovává tématiku simulace tekutin a plynů na osobních počítačích. Práce porovnává různé přístupy s ohledem na proveditelnost simulace v realném čase. Pozornost je také věnována metodam pro zobrazovaní tekutiny - implicitním plochám a metodě marching cubes. Navíc se práce zaměřuje na moderní grafické adaptéry s ohledem na jejich využití při výpočtech simulace. Obzvláště se bude věnovat pozornost technoligii CUDA od společnosti NVIDIA. Vše je navíc doplněno popisem mé implementace simulace tekutin a plynů.This bachelor´s thesis is focused on theme of fluid and gas simulation performed on personal computers. This branch of computer graphics and computer simulation is quite popular because it offers a lot of questions and a lot of solutions. Thesis is about to compare this solutions, focusing on those which can be real-time computed. One part of thesis is also about methods for fluid vizualization - isosurfaces and method marching cubes. The question of using modern graphics adapters to compute the simulation is also present. Especially NVIDIA CUDA technology will be analysed. And finally, there is an explanation of my implementation.

Multi-Fluid Simulation of the Magnetic Field Evolution in Neutron Stars

Using a numerical simulation, we study the effects of ambipolar diffusion and ohmic diffusion on the magnetic field evolution in the interior of an isolated neutron star. We are interested in the behavior of the magnetic field on a long time scale, over which all Alfven and sound waves have been damped. We model the stellar interior as an electrically neutral plasma composed of neutrons, protons and electrons, which can interact with each other through collisions and electromagnetic forces. Weak interactions convert neutrons and charged particles into each other, erasing chemical imbalances. As a first step, we assume that the magnetic field points in one fixed Cartesian direction but can vary along an orthogonal direction. We start with a uniform-density background threaded by a homogeneous magnetic field and study the evolution of a magnetic perturbation as well as the density fluctuations it induces in the particles. We show that the system evolves through different quasi-equilibrium states and estimate the characteristic time scales on which these quasi-equilibria occur.Comment: It will be published in AIP Proceedings of the Conference '40 Years of Pulsars: Milisecond Pulsars, Magnetars and More' held at University of McGill, Montreal, Canada, August 2007. Contributed Talk at Conference '40 Years of Pulsars: Milisecond Pulsars, Magnetars and More

Thermodynamic properties of short-range attractive Yukawa fluid: Simulation and theory

Coexistence properties of the hard-core attractive Yukawa potential with inverse-range parameter kappa=9, 10, 12 and 15 are calculated by applying canonical Monte Carlo simulation. As previously shown for longer ranges, we show that also for the ranges considered here the coexistence curves scaled by the critical density and temperature obey the law of corresponding states, and that a linear relationship between the critical density and the reciprocal of the critical temperature holds. The simulation results are compared with the predictions of the self-consistent Ornstein-Zernike approximation, and a good agreement is found for both the critical points and the coexistence curves, although some slight discrepancies are present.Comment: 19 pages, 4 figures. A few changes have been made in the text compared to the former versio