Random Number Generation

L’Ecuyer, Pierre

doi:10.1002/9780470172445.ch4

Cited by 75 publications

(16 citation statements)

References 42 publications

(76 reference statements)

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“…The spin configurations of the films are updated using the highly efficient Wolff algorithm [13] to minimise the effect from statistical errors arising from correlation time [14,15]. The random number generator (drand48) is chosen carefully [16,17,18] and we ensure that different seed numbers have no significant effect on the results. For each simulation, roughly 3, 000 × N spins are updated before the system is deemed to have reached equilibrium.…”

Section: Methodsmentioning

confidence: 99%

Magnetic properties of Ising thin films with cubic lattices

2004

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We have used Monte Carlo simulations to observe the magnetic behaviour of Ising thin-films with cubic lattice structures as a function of temperature and thickness especially in the critical region. The fourth order Binder cumulant is used to extract critical temperatures, and an extension of finite size scaling theory for reduced geometry is derived to calculate the critical exponents. Magnetisation and magnetic susceptibility per spin in each layer are also investigated. In addition, mean-field calculations are also performed for comparison. We find that the magnetic behaviour changes from two dimensional to three dimensional character with increasing thickness of the film. The crossover of the critical temperature from a two dimensional to a bulk value is also observed with both the Monte Carlo simulations and the mean-field analysis. Nevertheless, the simulations have shown that the critical exponents only vary a little from their two dimensional values. In particular, the results for films with up to eight layers provide a strong indication of two dimensional universality.

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Section: Methodsmentioning

confidence: 99%

Magnetic properties of Ising thin films with cubic lattices

2004

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“…Stochastic simulations are based on sources of randomness. The randomness can be truly random [2,3], but is usually created using algorithms called Pseudo Random Number Generators (PRNG). These algorithms do not create true random numbers.…”

Section: Introductionmentioning

confidence: 99%

Extending OPNET Modeler with External Pseudo Random Number Generators and Statistical Evaluation by the Limited Relative Error Algorithm

Becker

Weerawardane

et al. 2007

Recent Advances in Modeling and Simulation Tools for Communication Networks and Services

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Pseudo Random Number Generators (PRNG) are the base for stochastic simulations. The usage of good generators is essential for valid simulation results. OPNET Modeler a well-known tool for simulation of communication networks provides a Pseudo Random Number Generator. The extension of OPNET Modeler with external generators and additional statistical evaluation methods that has been performed for this paper increases the flexibility and options in the simulation studies performed.

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“…4.5.4 and Sec. 4.6.1 in [20]). Both LFSR113 and MT19937 fail the test scomp_LinearComp that is a linear complexity test for the binary sequences (see [18]), because the bits of LFSR113 and MT19937 have a linear structure by construction.…”

Section: The Torus Is Divided Intomentioning

confidence: 99%

Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size

Barash

2011

EPL

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The behavior of a family of dissipative dynamical systems representing transformations of twodimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying dissipative dynamical systems to generation of pseudorandom numbers is shown to be advantageous and equidistribution of probabilities for the sequences of bits can be achieved. A new algorithm for generating uniform pseudorandom numbers is proposed. The theory of the generator, which includes proofs of periodic properties and of statistical independence of bits at distances up to logarithm of mesh size, is presented. Extensive statistical testing using available test packages demonstrates excellent results, while the speed of the generator is comparable to other modern generators.

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Random Number Generation

Cited by 75 publications

References 42 publications

Magnetic properties of Ising thin films with cubic lattices

Magnetic properties of Ising thin films with cubic lattices

Extending OPNET Modeler with External Pseudo Random Number Generators and Statistical Evaluation by the Limited Relative Error Algorithm

Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size

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