Related papers: A Laplace Transform Method for Molecular Mass Dist…
The propagation of a wave in a medium is generally affected when the medium is moving with respect to the observer. Because plasma equilibria often involve plasma flows, for instance in astrophysics or in magnetic confinement nuclear fusion…
We investigate the transformation of the distribution function in the relativistic case, a problem of interest in plasma when particles with high (relativistic) velocities come into play as for instance in radiation belt physics, in the…
Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods…
A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the $\delta$, flat…
A model for the radial distribution function $g(r)$ of a square-well fluid of variable width previously proposed [S. B. Yuste and A. Santos, J. Chem. Phys. {\bf 101}, 2355 (1994)] is revisited and simplified. The model provides an explicit…
The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform,…
The purpose of this work is to find the time dependent distributions of directions and positions of a particle that undergoes multiple elastic scattering. The angular cross section is given and the scatterers are randomly placed. The…
Because of their simplicity, axisymmetric mass distributions are often used to model gravitational lenses. Since galaxies are usually observed to have elliptical light distributions, mass distributions with elliptical density contours offer…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
We investigate the anomalous dynamics of unentangled polymer melts. The proposed equation of motion formally relates the anomalous center-of-mass diffusion, as observed in computer simulations and experiments, to the nature of the effective…
Maxwell's equations are cast in the form of the Schr\"{o}dinger equation. The Lanczos propagation method is used in combination with the fast Fourier pseudospectral method to solve the initial value problem. As a result, a time-domain,…
We have developed an alternative formulation based on ${\bf F} = M {\bf a}$ rather than ${\bf F} = d{\bf P}/dt$ for studying variable mass systems. It is shown that ${\bf F} = M {\bf a}$ can be particularly useful in this context, as…
We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination…
In relativistic kinetic theory, which underlies relativistic hydrodynamics, the molecular chaos hypothesis stands at the basis of the equilibrium Maxwell-Juttner probability distribution for the four-momentum $p^{\alpha}$. We investigate…
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…
We have extended the multilevel summation (MLS) method, originally developed to evaluate long-range Coulombic interactions in molecular dynamics (MD) simulations [Skeel et al., J. Comput. Chem., 23, 673 (2002)], to handle dispersion…
We describe the remapped particle-mesh method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In…
Machine learning (ML) methods provide advanced means for understanding inherent patterns within large and complex datasets. Here, we employ the principal component analysis (PCA) and the diffusion map (DM) techniques to evaluate the glass…
We present a general formalism able to derive the kinetic equations of polymer dynamics. It is based on the application of nonequilibrium thermodynamics to analyze the irreversible processes taking place in the conformational space of the…
The relaxation modulus of a viscoelastic fluid can be decomposed into multiple Maxwell models and characterized by the relaxation spectrum for the relaxation time. It is empirically known that the logarithmic relaxation time is useful to…