Monte Carlo simulation is a very important class of stochastic methods for calculating thermal properties of many-particle systems—arguably these are the most important numerical techniques in statistical physics. Monte Carlo simulation methods are related to the elementary Monte Carlo integration methods that we discussed earlier, but are based on more efficient non-uniform sampling schemes. B...

Quasi-Monte Carlo integration is said to be better than Monte-Carlo integration since its error bound can be in the order of O(N (1 )) instead of the O(N 0:5) probabilistic bound of classical Monte-Carlo integration if the integrand has finite variation. However, since in computer graphics the integrand of the rendering equation is usually discontinuous and thus has infinite variation, the supe...

This paper compares quasi Monte Carlo methods, in particular so– called (t,m, s)–nets, with classical Monte Carlo approaches for simulating econometric time–series models. Quasi Monte Carlo methods have found successful application in many fields, such as physics, image processing, and the evaluation of finance derivatives. However, they are rarely used in econometrics. Here, we apply both trad...

GTNEUT is a two-dimensional code for the calculation of the transport of neutral particles in fusion plasmas. It is based on the Transmission and Escape Probabilities (TEP) method and can be considered a computationally efficient alternative to traditional Monte Carlo methods. The code has been benchmarked extensively against Monte Carlo and has been used to model the distribution of neutrals i...

Although there is now a good measure of agreement between Monte Carlo and high-temperature series expansion estimates for Ising (n = 1) models, published results for the critical temperature from series expansions up to 12th order for the three-dimensional classical Heisenberg (n = 3) and XY (n = 2) model do not agree very well with recent high-precision Monte Carlo estimates. In order to clari...

A quantum Monte Carlo method is introduced to optimize excited-state trial wave functions. The method is applied in a correlation function Monte Carlo calculation to compute ground- and excited-state energies of bosonic van der Waals clusters of up to seven particles. The calculations are performed using trial wave functions with general three-body correlations.

The charge-state evolution of highly charged ions transmitted through microcapillaries is studied theoretically by a classical trajectory Monte Carlo simulation. The interaction of highly charged ions with the internal surface of the capillary is treated within the framework of dielectric response theory. We analyze the distance of closest approach and the angular distributions of the highly ch...