arXiv subjects

Changho Kim

Publications and source records attributed to Changho Kim.

22 records · Page 2Linked to original sources

arXiv2017

Nature of self-diffusion in two-dimensional fluids

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the velocity autocorrelation function. An asymptotic decay law of the velocity autocorrelation function resembles the previously known self-consistent form, $1/(t\sqrt{\ln t})$, however with a rescaled time.

cond-mat.soft↗

arXiv2017

Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach

We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar to the reaction-diffusion master equation (RDME) description when those SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, the FHD description naturally extends from the regime where fluctuations are strong, i.e., each hydrodynamic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion, and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy for the linearized FHD, and gives an accurate and stable structure factor for a time step size an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two-dimensional Turing-like pattern, and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing FHD simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems, and lead to a qualitatively-different disordered pattern behind a traveling wave.

physics.flu-dyn↗

arXiv2010

Brownian motion from molecular dynamics

Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force which enter the generalized Langevin equation of the Brownian particle are determined and their dependence on mass and diameter are investigated for two different fluid densities. Deviations of the fluctuating force distribution from a Gaussian form are observed for small particle diameters. For heavy particles the deviations of the fluctuating force from the total force acting on the Brownian particle decrease linearly with the mass ratio m/M where m denotes the mass of a fluid particle.

physics.chem-ph↗

arXiv2009

Rate description of Fokker-Planck processes with time-periodic parameters

The large time dynamics of a periodically driven Fokker-Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete Markovian process characterized by time dependent rates. Apart from the occupation probabilities, so-called specific probability densities and localizing functions can be associated to each metastable state. Together, these three sets of functions uniquely characterize the large time dynamics of the conditional probability density of the original process. Exact equations of motion are formulated for these three sets of functions and strategies are discussed how to solve them. These methods are illustrated and their usefulness is demonstrated by means of the example of a bistable Brownian oscillator within a large range of driving frequencies from the slow semiadiabatic to the fast driving regime.

cond-mat.stat-mech↗