6,655 research outputs found
Advanced Dynamic Algorithms for the Decay of Metastable Phases in Discrete Spin Models: Bridging Disparate Time Scales
An overview of advanced dynamical algorithms capable of spanning the widely
disparate time scales that govern the decay of metastable phases in discrete
spin models is presented. The algorithms discussed include constrained
transfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), and
projective dynamics (PD) methods. The strengths and weaknesses of each of these
algorithms are discussed, with particular emphasis on identifying the parameter
regimes (system size, temperature, and field) in which each algorithm works
best.Comment: 12 pages, 4 figures, proceedings of the US-Japan bilateral seminar on
`Understanding and Conquering Long Time Scales in Computer Simulations', July
1999, to appear in Int. J. Mod. Phys.
A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces
Advanced algorithms are necessary to obtain faster-than-real-time dynamic
simulations in a number of different physical problems that are characterized
by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms
that preserve the dynamics of the model are described. These include the
-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC)
algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use
of these algorithms, they are applied to some simplified models of dynamic
physical systems. The models studied include a model for ion motion through a
pore such as a biological ion channel and the metastable decay of the
ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic
algorithms, which are in the class of parallel discrete event simulations, are
discussed. Efforts are made to keep the article at an elementary level by
concentrating on a simple model in each case that illustrates the use of the
advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure
On the Possibility of Quasi Small-World Nanomaterials
The possibility of materials that are governed by a fixed point related to
small world networks is discussed. In particular, large-scale Monte Carlo
simulations are performed on Ising ferromagnetic models on two different
small-world networks generated from a one-dimensional spin chain. One has the
small-world bond strengths independent of the length, and exhibits a
finite-temperature phase transition. The other has small-world bonds built from
atoms, and although there is no finite-temperature phase transition the system
shows a slow power-law change of the effective critical temperature of a finite
system as a function of the system size. An outline of a possible synthesis
route for quasi small-world nanomaterials is presented.Comment: 13 pages, 9 figures, submitted to Brazilian Journal of Physics,
conference proceedings for III Brazilian Meeting on Simulational Physics
(2003
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