Trotter derivation of algorithms for Brownian and dissipative particle dynamics

Thalmann, Fabrice; Farago, Jean
September 2007
Journal of Chemical Physics;9/28/2007, Vol. 127 Issue 12, p124109
Academic Journal
This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same “weak order two” accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.


Related Articles

  • A fourth algebraic order exponentially‐fitted Runge—Kutta method for the numerical solution of the Schrödinger equation. Simos, T. E. // IMA Journal of Numerical Analysis;Oct2001, Vol. 21 Issue 4, p919 

    An exponentially‐fitted Runge–Kutta method for the numerical integration of the radial Schrödinger equation is developed. Theoretical and numerical results obtained for the well known Woods–Saxon potential show the efficiency of the new method.

  • Influence of disturbances on the angular motion of a spacecraft in the powered section of its descent. Aslanov, V.; Doroshin, A. // Cosmic Research;Mar2008, Vol. 46 Issue 2, p166 

    The motion of a variable-mass spacecraft is considered in the powered section of a descending trajectory. Approximate analytical solutions are obtained for the angles of spatial orientation of the spacecraft, which allows one to analyze the nutation motion and to develop recommendations on the...

  • Embedded Pairs of Exponentially Fitted Explicit Runge-Kutta Methods for the Numerical Integration of Oscillatory Problems. París, A.; Rández, L. // AIP Conference Proceedings;9/15/2008, Vol. 1048 Issue 1, p1008 

    Two new embedded pairs of exponentially fitted explicit Runge-Kutta methods for the numerical integration of initial value problems with oscillatory or periodic solutions are developped. These new pairs have algebraic orders 4(3) and 5(4) respectively. Several numerical tests show the...

  • Special perturbation theory methods in celestial mechanics. I. Principles for the construction and substantiation of the application. Avdyushev, V. // Russian Physics Journal;Dec2006, Vol. 49 Issue 12, p1344 

    The ideas and principles for the construction of methods in special perturbation theory are discussed, and their application to the solution of problems in classical celestial mechanics is substantiated. The problem of shortperiod perturbations and their effect on the numerical integration is...

  • Constructions of copy rules. Nuyens, Dirk; Cools, Ronald // AIP Conference Proceedings;9/6/2007, Vol. 936 Issue 1, p19 

    For some function classes it is known that using copies of a scaled down lattice rule can reduce the worst-case error for numerical integration of functions from this class. In a slight generalization we show that it is possible to construct these so-called “copy rules” by the fast...

  • On the Trivariate Polynomial Interpolation. SAFAK, SULEYMAN // WSEAS Transactions on Mathematics;Aug2012, Vol. 11 Issue 8, p722 

    This paper is concerned with the formulae for computing the coefficients of the trivariate polynomial interpolation (TPI) passing through (m +1)(n +1)(r +1) distinct points in the solid rectangular region. The TPI is formulated as a matrix equation using Kronecker product and Khatri-Rao product...

  • AN ADOMIAN DECOMPOSITION METHOD FOR SOLVING LIÉNARD EQUATIONS IN GENERAL FORM. Nili Ahmadabadi, M.; Maalek Ghaini, F. M. // ANZIAM Journal;2009, Vol. 51 Issue 2, p302 

    In this study, Liénard equations in their general form are treated using the Adomian decomposition method. The special structure of the Liénard equation is exploited to obtain a numerically efficient algorithm suitable for solution by a computer program.

  • Equidistant arrangement of agents on line: Analysis of the algorithm and its generalization. Kvinto, Ya.; Parsegov, S. // Automation & Remote Control;Nov2012, Vol. 73 Issue 11, p1784 

    Consideration was given to generalization of one of the formation control algorithms, that of equidistant arrangement of agents over a fixed interval. In distinction to the earlier approaches that are based on the equations of the first order, a second-order algorithm was proposed. It was proved...

  • Complex measures having quadrature formulae with optimal exactness. Berriochoa, E.; Cachafeiro, A.; García-Amor, J. // Acta Mathematica Hungarica;Jan2010, Vol. 126 Issue 1/2, p51 

    We characterize the supports of the measures having quadrature formulae with similar exactness as Gauss’ theorem. Indeed we obtain the supports of the measures from which an m-point quadrature formula can be obtained such that it exactly integrates functions in the space ℙ m−...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics