Papers by kabbab abdelhamid
... 129 6 Introduction to Bridging Scale 131 6.1 Bridging Scale Fundamentals . . . . . ... The re... more ... 129 6 Introduction to Bridging Scale 131 6.1 Bridging Scale Fundamentals . . . . . ... The recent extension of the bridging scale to incorporate quantum mechanical information into the coupling of length scales framework is also described in this chapter. ...
IMA Volumes in …, Jan 1, 1996
Classical molecular dynamics simulation of a macromolecule requires the use of an e cient time-st... more Classical molecular dynamics simulation of a macromolecule requires the use of an e cient time-stepping scheme that can faithfully approximate the dynamics over many thousands of timesteps. Because these problems are highly nonlinear, accurate approximation of a particular solution trajectory on meaningful time intervals is neither obtainable nor desired, but some restrictions, such as symplecticness, can be imposed on the discretization which tend to imply good long term behavior. The presence of a variety of types and strengths of interatom potentials in standard molecular models places severe restrictions on the timestep for numerical integration used in explicit integration schemes, so much recent research has concentrated on the search for alternatives that possess (1) proper dynamical properties, and (2) a relative insensitivity to the fastest components of the dynamics. We survey several recent approaches.
... Computer problems at the end of each section require performing compu-v Page 7. vi tation and... more ... Computer problems at the end of each section require performing compu-v Page 7. vi tation and simulation to study the effect of various parameters determining a flow. ... 239 5.5.1 Numerical method . . . . . ... 497 9.1.5 Flow in a wavy channel . . . . . ...
Journal of …, Jan 1, 1995
In molecular dynamics simulations, the fastest components of the potential eld impose severe rest... more In molecular dynamics simulations, the fastest components of the potential eld impose severe restrictions on the stability and hence the speed of computational methods. One possibility for treating this problem is to replace the fastest components with algebraic length constraints. In this paper, the resulting systems of mixed di erential and algebraic equations are studied. Commonly used discretization schemes for constrained Hamiltonian systems are discussed. The form of the nonlinear equations is examined in detail and used to give convergence results for the traditional nonlinear solution technique SHAKE iteration and for a modi cation based on Successive OverRelaxation (SOR). A simple adaptive algorithm for nding the optimal relaxation parameter is presented. Alternative direct methods using sparse matrix techniques are discussed. Numerical results are given for the new techniques, implemented in the molecular modeling software package CHARMM, showing as much as twofold improvement over SHAKE iteration. matrix methods 1. Introduction. In molecular dynamics, the length of timestep for numerically integrating the equations of motion is dictated by the contributions to the force vector which maintain pairs of atoms near some equilibrium distance. The imposition of algebraic constraints that x these lengths removes the associated rapid vibrational modes, enabling the use of longer timesteps without substantially altering important physical characteristics of the motion 1]. Although we treat only length constraints in the present work, constrained techniques are also of interest for conformational search and conformational free energy simulations 2]. In 3] the SHAKE iteration was described for solving the nonlinear equations at each timestep of a constrained version of the Verlet discretization, and a similar scheme was proposed in 4] for use with the RATTLE discretization.
lab.univ-batna.dz
Présenté par : TAABACHE Salah Pour l'obtention du Diplôme de : Magistère en Physique option: Micr... more Présenté par : TAABACHE Salah Pour l'obtention du Diplôme de : Magistère en Physique option: Microstructure et mécanique des matériaux Soutenu le : 25 /11/2010 Devant la Commission d'examen constituée par le Jury : Président Rapporteur Examinateur Examinateur
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Papers by kabbab abdelhamid