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 $n$-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

Mechanism of Near-Field Raman Enhancement in One-Dimensional Systems

We develop a theory of near-field Raman enhancement in one-dimensional systems, and report supporting experimental results for carbon nanotubes. The enhancement is established by a laser-irradiated nanoplasmonic structure acting as an optical antenna. The near-field Raman intensity is inversely proportional to the 10th power of the separation between the enhancing structure and the one-dimensional system. Experimental data obtained from single-wall carbon nanotubes indicate that the Raman enhancement process is not significantly influenced by the specific phonon eigenvector, and is mainly defined by the properties of the nanoplasmonic structure