Search results for " statistical"
showing 10 items of 1649 documents
Effective Cahn-Hilliard Equation for the Phase Separation of Active Brownian Particles
2014
The kinetic separation of repulsive active Brownian particles into a dense and a dilute phase is analyzed using a systematic coarse-graining strategy. We derive an effective Cahn-Hilliard equation on large length and time scales, which implies that the separation process can be mapped onto that of passive particles. A lower density threshold for clustering is found, and using our approach we demonstrate that clustering first proceeds via a hysteretic nucleation scenario and above a higher threshold changes into a spinodal-like instability. Our results are in agreement with particle-resolved computer simulations and can be verified in experiments of artificial or biological microswimmers.
Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling
2018
We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersatura…
Test of mode coupling theory for a supercooled liquid of diatomic molecules.I. Translational degrees of freedom
1997
A molecular dynamics simulation is performed for a supercooled liquid of rigid diatomic molecules. The time-dependent self and collective density correlators of the molecular centers of mass are determined and compared with the predictions of the ideal mode coupling theory (MCT) for simple liquids. This is done in real as well as in momentum space. One of the main results is the existence of a unique transition temperature T_c, where the dynamics crosses over from an ergodic to a quasi-nonergodic behavior. The value for T_c agrees with that found earlier for the orientational dynamics within the error bars. In the beta- regime of MCT the factorization of space- and time dependence is satisf…
Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics
1997
Density-functional theory is applied to compute the ground-state energies of quantum hard-sphere solids. The modified weighted-density approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis and the Feynman approximation, connecting the static structure factor and the linear response function. The Fermi liquid is treated by the Wu-Feenberg cluster expansion, which approximately accounts for the effects of antisymmetry. Liquid-solid transitions for both systems are obtained with no adjustment of input data. Limited …
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?
2013
An analogy of the Fokker-Planck equation (FPE) with the Schr\"odinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schr\"odinger potential with a discrete eigenvalue spectrum. Here, we will show how this approach can be also applied to a mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x=\pm L/2 and take the limit L\rightarrow\infty, considering the examples with constant Schr\"{o}dinger potential and with P\"{o}schl-Teller potential. An oversimplified approach was proposed earlier by M.T. Araujo and E. Drigo Filho. A…
Kinetic Roughening in Slow Combustion of Paper
2001
Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal development of the interface fluctuations. The asymptotic scaling properties, on long length and time scales, are well described by the Kardar-Parisi-Zhang (KPZ) equation with short-range, uncorrelated noise. To obtain a more detailed picture of the strong-coupling fixed point, characteristic of the KPZ universality class, universal amplitude ratios, and the universal coupling constant are computed from the data and found to be in good agreement with theory. Below …
Active Brownian Motion Models and Applications to Ratchets
2008
We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircase-like and Mateos ratchet potentials, also with the additional loads modeled by…
Quantitative tests of mode-coupling theory for fragile and strong glass-formers
2001
We calculate for a binary mixture of Lennard-Jones particles the time dependence of the solution of the mode-coupling equations in which the full wave vector dependence is taken into account. In addition we also take into account the short time dynamics, which we model with a simple memory kernel. We find that the so obtained solution agrees very well with the time and wave vector dependence of the coherent and incoherent intermediate scattering functions as determined from molecular dynamics computer simulations. Furthermore we calculate the wave vector dependence of the Debye-Waller factor for a realistic model of silica and compare these results with the ones obtained from a simulation o…
On the theory of light scattering in molecular liquids
2001
The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities $\rho_{lm}(q)$ with $l=0$ and $l=2$. $l$, $m$ denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger \cite{schilling97} for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules …
Light-scattering spectra of supercooled molecular liquids
2001
The light scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave vector and scattering angle dependences are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency-dependent transport kernels, generalized thermodynamic derivatives and the background spectra.