Related papers: Pseudorandom Number Generators and the Square Site…
We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs,…
Monte Carlo simulations are an important tool in statistical physics, complex systems science, and many other fields. An increasing number of these simulations is run on parallel systems ranging from multicore desktop computers to…
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…
The present work introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly-oriented rectangles. By conducting extensive simulations, we report high precision percolation thresholds for a variety of…
Monte Carlo simulations are performed to determine the critical percolation threshold for interpenetrating square objects in two dimensions and cubic objects in three dimensions. Simulations are performed for two cases: (i) objects whose…
Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of…
The generation of pseudo-random numbers is one of the interesting problems in Monte Carlo simulations, mostly because the common computer generators produce periodic numbers. We used simple pseudo-random numbers generated with the simplest…
We develop a pseudo-random generator to fool degree-$d$ polynomial threshold functions with respect to the Gaussian distribution. For $c>0$ any constant, we construct a pseudo-random generator that fools such functions to within $\epsilon$…
Since the work of Ferrenberg et al.[PRL 69, (1992)] some pseudo random number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed.…
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators.…
The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very…
A general method to produce uniformly distributed pseudorandom numbers with extended precision by combining two pseudorandom numbers with lower precision is proposed. In particular, this method can be used for pseudorandom number generation…
Herein, we propose a site random cluster model by introducing an additional cluster weight in the partition function of the traditional site percolation. To simulate the model on a square lattice, we combine the color-assignation and the…
Empirical tests for pseudorandom number generators based on the use of processes or physical models have been successfuly used and are considered as complementary to theoretical test of randomness. In this work a statistical methodology for…
In this paper, site percolation on random $\Phi^{3}$ planar graphs is studied by Monte-Carlo numerical techniques. The method consists in randomly removing a fraction $q=1-p$ of vertices from graphs generated by Monte-Carlo simulations,…
Parallel supercomputer-based Monte Carlo applications depend on pseudorandom number generators that produce independent pseudorandom streams across many separate processes. We propose a new scalable class of parallel pseudorandom number…
In this paper we study statistical methods of parameters estimation of the site percolation model. Advantages of the proposed method is demonstrated for the computing of the confidence interval of mass fractal dimension of a percolation…
Basic uniform pseudo-random number generators are implemented on ATI Graphics Processing Units (GPU). The performance results of the realized generators (multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR, RANLUX…