Lagged Fibonacci Series Random Number Generators for the Nec Sx-3

Petersen, Wesley P.

doi:10.1142/s0129053394000202

Cited by 25 publications

(21 citation statements)

References 3 publications

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“…To check carefully the accuracy of the methods up to small time steps, we need to drastically reduce the Monte-Carlo error. We thus approximate the required moments of the numerical solutions by averages over 500 millions of trajectories computed in fortran, using the random number generator [35]. For a fair comparison, notice that we use the same set of random numbers for each numerical integrator.…”

Section: 13mentioning

confidence: 99%

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

Abdulle¹,

Cohen²,

Vilmart³

et al. 2012

SIAM J. Sci. Comput.

128

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Abstract. Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrated with the constructions of new methods of weak order two, in particular, semi-implicit integrators well suited for stiff (meansquare stable) stochastic problems, and implicit integrators that exactly conserve all quadratic first integrals of a stochastic dynamical system. Numerical examples confirm the theoretical results and show the versatility of our methodology.

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Section: 13mentioning

confidence: 99%

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

Abdulle¹,

Cohen²,

Vilmart³

et al. 2012

SIAM J. Sci. Comput.

128

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“…We integrate (6.44) numerically using the standard fourth-order Runge-Kutta method with a constant integration step t [37] and the lagged Fibonacci random number generator [43]. The delta-function is represented numerically as ı.t/ D 0 for jt j > t=2 and ı.t/ D 1=t for jt j < t=2, i.e., the numerical integration step corresponds to the correlation time of the random force.…”

Section: Topological Solitons In Crystalline Pementioning

confidence: 99%

Solitons in Polymer Systems

Lupichev

Savin

Kadantsev

2014

Synergetics of Molecular Systems

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This chapter will focus on the numerical investigation of nonlinear dynamics of localized excitations (acoustic and topological solitons and breathers) in polymer macromolecules. The characteristics of supersonic acoustic solitons in polymer macromolecules will be studied, using the examples of an isolated zigzag macromolecule of polyethylene (PE), a spiral macromolecule of polytetrafluoroethylene (PTFE), and a single-well carbon nanotube. Topological soliton dynamics will be analysed using the crystalline PE and PTFE models. We will discuss the role of topological solitons in the premelting mechanisms of crystals and their structural transitions. Nonlinear localized vibrations, or breathers, will be considered in the case of a trans zigzag PE molecule. The quasi-one-dimensional structure of isolated macromolecules, polymer crystals of PE and PTFE, and a single-well carbon nanotube will be shown to lead to the existence of all the basic types of localized nonlinear excitations (acoustic and topological solitons and breathers). The properties of such excitations will be shown to depend significantly on the structure of the polymer macromolecule.The development of contemporary nonlinear physics has led to the discovery of new fundamental mechanisms which determine, on the molecular level, the progression of many physical processes in crystals and other ordered molecular structures. It is now clear that acoustic solitons may contribute to the most efficient mechanism of energy transfer in such processes as heat conduction and breakdown of solids [1][2][3][4]. Topological solitons serve as models of structural defects in polymer crystals, and their mobility ensures the possibility of such processes as plastic deformation [5], relaxation [6], and premelting [7,8]. Crystal structure defects are described in a natural way using the concept of topological solitons [9,10], and soliton mobility defines a specific 'soliton' contribution to the thermodynamics and kinetics of polymer crystals. Breathers play a significant role in the mechanisms of energy transfer and relaxation in molecular systems [11][12][13].

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“…The advantage (on a machine with slow floatingpoint multiplication) is that multiplication of a 4-vector by A 1 requires only seven additions and one division by two (for details see [38, §2.1]). The inner loop of the implementation is similar to the inner loop for the popular "generalised Fibonacci" uniform random number generators [3,7,15,16,21,23,31,33]. Wallace's implementation of fastnorm on a RISC workstation is about as fast as a good uniform random number generator on the same workstation.…”

Section: Cost Of Transformationsmentioning

confidence: 99%

Random Number Generation

2008

Wolfram Demonstrations Project

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We outline some of Chris Wallace's contributions to pseudo-random number generation. In particular, we consider his recent idea for generating normally distributed variates without relying on a source of uniform random numbers, and compare it with more conventional methods for generating normal random numbers. Implementations of Wallace's idea can be very fast (approximately as fast as good uniform generators). We discuss the statistical quality of the output, and mention how certain pitfalls can be avoided.

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Lagged Fibonacci Series Random Number Generators for the Nec Sx-3

Cited by 25 publications

References 3 publications

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

High Weak Order Methods for Stochastic Differential Equations Based on Modified Equations

Solitons in Polymer Systems

Random Number Generation

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