Kinetic energy conserving integrators for Gaussian thermostatted SLLOD

A new integration scheme is developed for nonequilibrium molecular dynamics simulations where the temperature is constrained by a Gaussian thermostat. The utility of the scheme is demonstrated by its application to the SLLOD algorithm which is the standard nonequilibrium molecular dynamics algorithm for studying shear flow. Unlike conventional integrators, the new integrators are constructed using operator-splitting techniques to ensure stability and that little or no drift in the kinetic energy occurs. Moreover, they require minimum computer memory and are straightforward to program. Numerical experiments show that the efficiency and stability of the new integrators compare favorably with conventional integrators such as the Runge-Kutta and Gear predictor-corrector methods. (C) 1999 American Institute of Physics. [S0021-9606(99)50125-6].

Quantum dynamics with stochastic gauge simulations

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite stochastic time-evolution equations, equivalent to master equations, for many systems including quantum time evolution. The method is illustrated with a variety of simple examples ranging from astrophysical molecular hydrogen production, through to the topical problem of Bose-Einstein condensation in an optical trap and the resulting quantum dynamics.

Eigenvalues of Casimir invariants for Uq[osp(m|n)]

For each quantum superalgebra U-q[osp(m parallel to n)] with m > 2, an infinite family of Casimir invariants is constructed. This is achieved by using an explicit form for the Lax operator. The eigenvalue of each Casimir invariant on an arbitrary irreducible highest weight module is also calculated. (c) 2005 American Institute of Physics.

Analysis of trigonometric implicit Runge-Kutta methods

Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.