Patricio Cordero

An empirical assessment of priority queues in event-driven molecular dynamics simulation

In the last decades a number of near optimal priority queues have been developed. Many of these priority queues are suitable for the efficient management of events generated during simulations of hard-particle systems. In this paper we compare the execution times of the fastest priority queues known today as well as some forms of binary search trees used as priority queues. We conclude that an unusual adaptation of a strictly balanced binary tree has the best performance for this class of simulations.

On the generalized Morse potential

The equivalence between the generalized Morse (GMP) and Eckart potentials is shown. The study of the hypergeometric Natanzon potentials using SO(2,1) techniques is applied to compute the eigenfunctions and eigenvalues of the Eckart (GMP) potential. The action of the group generators is studied, with the result that a family of Eckart potentials is obtained which is different from the one obtained in SUSYQM.

Two-dimensional gas of disks: Thermal conductivity

The phenomenon of heat conduction in a two-dimensional gas ofN hard disks is studied in the hydrostatic regime by means of nonequilibrium molecular dynamics (N ranging from 100 to 8000). For systems withN≥1500 the temperature and density profiles observed are in excellent agreement with the continuous theory, but the conductivityk differs from the one derived from Enskogs theory in a systematic way. This difference seems to slowly decrease with increasing density.

Algebraic solution for the Natanzon hypergeometric potentials

An algebraic method—based on a strategy that makes use of a realization of the algebra SO(2,1)—in terms of differential operators is used to solve the bound state problem for the most general Natanzon potentials for which the Schrodinger equation can be reduced to hypergeometric form (hence, hypergeometric potentials).

Cluster birth–death processes in a vapor at equilibrium

A method is presented to analyze and observe, in molecular dynamic simulations, the statistical properties of instantaneous cluster transitions, mainly fusions and fissions for a homogeneous vapor at equilibrium. The method yields the way to obtain mean lives, branching ratios and, to some extent, transition rates as well. To the best of our knowledge branching rations in cluster decays have not been measured before (simulationally or experimentally). An application of this method to a model system provides a critical reassessment of the standard Homogeneous Nucleation Theory (HNT). Our own simulations show that transitions different from absorbing or evaporating a monomer are quite important, representing in some cases 50% of all decay events. Our method also shows unequivocally that the decay processes involving clusters classified by size alone are not Markovian.

Algebraic methods for the Natanzon potentials

It is shown that the Schrödinger equation can be solved by means of spectrum-generating algebra techniques for the most general class of Natanzon potentials based on the SO(2, 1) algebra. This paper describes in detail thelinear spectrum generating algebra method which is then applied to solve the Natanzon confluent potentials, and it is extended to one example with spin-orbit coupling. Further, the method is used to explain in detail how to find the energy spectrum for the Dirac equation with a Coulomb potential. Afterwards thequadratic spectrum generation algebra method is presented, and it is used to solve the most general hypergeometric Natanzon potential: The bound state problem and the corresponding wave functions are given. A simple example further illustrates the use of the quadratic method.

Analysis of the spectrum generating algebra method for obtaining energy spectra

We analyze and clarify how the SGA (spectrum generating algebra) method has been applied to different potentials. We emphasize that each energy level Eν obtained originally by Morse belongs to a different so(2,1) multiplet. The corresponding wave functions Ψν are eigenfuntions of the compact generators J0ν with the same eigenvalue k0, but with different eigenvalues qν of the Casimir operators Q. We derive a general expression for all effective potentials which have Ψλν,ν+m(r)∝(J+ν)mΨλν,ν(r) as eigenfunctions, without using supersymmetry formalism. The different actions of SGA is further illustrated by two diagrams.

Cluster velocity distributions in a vapor at equilibrium

We present the microscopic description of the vapor using the concept of cluster. Taking into consideration nonideal contributions, the distribution functions of every cluster species are obtained. From these distribution functions it is possible to derive kinetic “temperatures” associated with each cluster species and it is shown that the internal kinetic temperature and the kinetic temperature associated with the center of mass of the clusters are different from the thermodynamic temperature of the system as a whole. Molecular dynamic simulations show that the internal temperatures are smaller than the thermodynamic one, which is smaller than the kinetic temperatures for all cluster sizes. For the case of monomers more precise predictions can be made and they are in excellent agreement with our simulations.

Nonlinear transport laws for low density fluids

Hydrodynamics equations derived directly from Boltzmann’s equation and specialized to sheared planar flow are shown to yield approximate nonlinear laws of heat transport and of viscous flow. The law of viscous flow predicts non-Newtonian effects including shear thinning and the law of heat transport is more general than Fourier’s law: it is not linear and it implies heat flow parallel to the isotherms. These nonlinear transport laws are faithfully corroborated by molecular dynamic simulations based on straightforward Newtonian dynamics.

Free thermal convection driven by nonlocal effects.

We report and explain a convective phenomenon observed in molecular dynamics simulations that cannot be classified either as a hydrodynamics instability nor as a macroscopically forced convection. Two complementary arguments show that the velocity field by a thermalizing wall is proportional to the ratio between the heat flux and the pressure. This prediction is quantitatively corroborated by our simulations.