Search results for " Simulation"
showing 10 items of 4034 documents
Surface-directed spinodal decomposition: Lattice model versus Ginzburg-Landau theory
2009
When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long-wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. These boundary conditions can be derived from lattice models by suitable continuum approximations. But the lattice models can also be simulated directly, and thus used to clarify the conditions under which the Ginzburg–Landau type theory is valid. This comparison shows that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations can also be neglecte…
LÉVY FLIGHT SUPERDIFFUSION: AN INTRODUCTION
2008
After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of self-similarity converts the infinitely divisible characteristic function of the L\'{e}vy process into a stable characteristic function of the L\'{e}vy motion. The L\'{e}vy motion generalizes the Brownian motion on the base of the $\alpha$-stable distributions theory and fractional order derivatives. The further development of the idea lies on the generalization of the Langevin equation with a non-Gaussian white noise source and the use of functional approach. Th…
Amorphous silica modeled with truncated and screened Coulomb interactions: A molecular dynamics simulation study
2007
We show that finite-range alternatives to the standard long-range BKS pair potential for silica might be used in molecular dynamics simulations. We study two such models that can be efficiently simulated since no Ewald summation is required. We first consider the Wolf method, where the Coulomb interactions are truncated at a cutoff distance r_c such that the requirement of charge neutrality holds. Various static and dynamic quantities are computed and compared to results from simulations using Ewald summations. We find very good agreement for r_c ~ 10 Angstroms. For lower values of r_c, the long--range structure is affected which is accompanied by a slight acceleration of dynamic properties…
Logarithmic finite-size effects on interfacial free energies: Phenomenological theory and Monte Carlo studies
2014
The computation of interfacial free energies between coexisting phases (e.g.~saturated vapor and liquid) by computer simulation methods is still a challenging problem due to the difficulty of an atomistic identification of an interface, and due to interfacial fluctuations on all length scales. The approach to estimate the interfacial tension from the free energy excess of a system with interfaces relative to corresponding single-phase systems does not suffer from the first problem but still suffers from the latter. Considering $d$-dimensional systems with interfacial area $L^{d-1}$ and linear dimension $L_z$ in the direction perpendicular to the interface, it is argued that the interfacial …
Computing absolute free energies of disordered structures by molecular simulation
2009
We present a Monte Carlo simulation technique by which the free energy of disordered systems can be computed directly. It is based on thermodynamic integration. The central idea is to construct an analytically solvable reference system from a configuration which is representative for the state of interest. The method can be applied to lattice models (e.g., the Ising model) as well as off-lattice molecular models. We focus mainly on the more challenging off-lattice case. We propose a Monte Carlo algorithm, by which the thermodynamic integration path can be sampled efficiently. At the examples of the hard sphere liquid and a hard disk solid with a defect, we discuss several properties of the …
Scaling laws in the distribution of galaxies
2004
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale distribution of galaxies in the Universe is far from random: it is highly structured over a vast range of scales. To describe cosmic structures, we need to build mathematically quantifiable descriptions of structure. Identifying where scaling laws apply and the nature of those scaling laws is an important part of understanding which physical mechanisms have been responsible for the organization of clusters, superclusters of galaxies and the voids between them. Find…
Spectral broadening by incomplete thermalization of the energy in X-ray microcalorimeters with superconducting absorber and NTD-Ge thermal sensor
2004
Abstract We present a model of the response of a cryogenic microcalorimeter with superconducting absorber and phonon sensitive thermal sensor to the absorption of X-ray photons. The model is based on the main microscopic processes responsible for the thermalization of the deposited energy. We use a system of rate equations to describe the energy downconversion in the superconductor and transport to the thermal sensor. The model is a tool to investigate the thermalization efficiency with respect to the device characteristics (i.e. absorber material, geometry), in order to optimize the performances of these detectors. As a first case study, we report results of simulations for a microcalorime…
Self‐similar problems for modeling the surface chemical reactions with the gravitation
1998
The mathematical model of a chemical reaction which takes place on the surface of the uniformly moving vertically imbedded glass fibre material is considered. The effect of gravitation is taken into account. Boussinesq's and boundary layer fittings allow to derive boundary value problems for self‐similar systems of ordinary differential equations. First Published Online: 14 Oct 2010
Innovative modeling of Tuned Liquid Column Damper motion
2015
Abstract In this paper a new model for the liquid motion within a Tuned Liquid Column Damper (TLCD) device is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it is shown that existing model does not always lead to accurate prediction of the liquid motion. A better model is then needed for accurate simulation of the behavior of TLCD systems. As regards, it has been demonstrated how correctly including the first linear liquid sloshing mode, through the equivalent mechanical analogy well established in literature, produces numerical results that highly match the corresponding experimental ones. Sin…
Memory expansion for diffusion coefficients
1998
We present a memory expansion for macroscopic transport coefficients such as the collective and tracer diffusion coefficients ${D}_{C}$ and ${D}_{T},$ respectively. The successive terms in this expansion for ${D}_{C}$ describe rapidly decaying memory effects of the center-of-mass motion, leading to fast convergence when evaluated numerically. For ${D}_{T},$ one obtains an expansion of similar form that contains terms describing memory effects in single-particle motion. As an example we evaluate ${D}_{C}$ and ${D}_{T}$ for three strongly interacting surface systems through Monte Carlo simulations, and for a simple model diffusion system via molecular dynamics calculations. We show that the n…