The subject of the present paper is computer simulation of a-solid and liquid nitrogen, using a Lennard-Jones atom-atom potential and the isothermal-isobaric Monte-Carlo method. Two sets of calculations were performed, both at the same pressure (1 atm) and temperatures (a-solid at 25 and 35.6 K, liquid at 63.15 and 77.35 K). In the first set the molecules are assumed to be rigid, whereas in the...

This paper concerns Kinetic Monte Carlo (KMC) algorithms that have a singleevent execution time independent of the system size. Two methods are presented— one that combines the use of inverted-list data structures with rejection Monte Carlo and a second that combines inverted lists with the Marsaglia-Norman-Cannon algorithm. The resulting algorithms apply to models with rates that are determine...

We show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations. In the simplest case of a Lipschitz payoff and an Euler discretisation, the computational cost to achieve an accuracy of O( ) is reduced from O( −3) to O( −2(log )2). The analysis is supported by numer...

Lattice rules are a quasi-Monte Carlo method, an alternative to the Monte Carlo method for multidimensional numerical integration. The measures of performance that we estimate by simulation can be seen as the values of integrals in large dimensions. Therefore, instead of the usual Monte Carlo method, one can use lattice rules in simulation. In this paper, we compare these rules to the Monte Car...