International Journal of Modern Physics C

A number of physical systems (e.g., N body Newtonian, Coulombian or Lennard-Jones systems) can be described by N² interaction terms. Completely connected neural networks are characterised by the same kind of connections: Each neuron sends signals to all the other neurons via synapses. The APE100/Quadricsmassive parallel architecture, with processing power in excess of 100 Gigaflops and a central memory of 8 Gigabytes seems to have processing power and memory adequate to simulate systems formed by more than 1 billion synapses or interaction terms. On the other hand the processing nodes of APE100/Quadrics are organised in a tridimensional cubic lattice; each processing node has a direct communication path only toward the first neighboring nodes. Here we describe a convenient way to map systems with global connectivity onto the first-neighbors connectivity of the APE100/Quadrics architecture. Some numeric criteria, which are useful for matching SIMD tridimensional architectures with globally connected simulations, are introduced.

We present an algorithm for matrix transposition on SIMD machines and its implementation on the APE 100/Quadrics parallel processors.

The Wolff single-cluster algorithm is the most efficient method known for Monte Carlo simulation of many spin models. Due to the irregular size, shape and position of the Wolff clusters, this method does not easily lend itself to efficient parallel implementation, so that simulations using this method have thus far been confined to workstations and vector machines. Here we present two parallel implementations of this algorithm, and show that one gives fairly good performance on a MIMD parallel computer.

In our work a comparative study is made of molecular dynamics and Monte Carlo methods applied to the growth of a thin Fe epilayer on an Ag substrate. This comparison centres on the physics of the computational approaches and of the results.

The Monte Carlo method is used to study the effect of boundary scattering on the temperature dependent part of the resistivity of thin metal films. A computational scheme is used that realistically simulates electron scattering mechanisms in the semi-classical context. As a test of the accuracy of the method, comparison is made between the present method at absolute zero (impurity and boundary scattering only) and the analytical results of Fuchs, which rely on the relaxation time approximation (RTA). The inclusion of phonon scattering provides a measure of the size induced deviations from Matthiessen’s Rule (SIDMR). At low temperatures phonon scattering cannot be adequately described using the RTA and the numerical technique presented shows good promise of overcoming this problem. Calculated SIDMR results are compared with some recent data on Al and Ga films.

A bit-string model of biological life-histories is parallelized, with hundreds of millions of individuals. It gives the desired drastic decay of survival probabilities with increasing age for 32 age intervals.

In this study we derive a semi-linear Elliptic Partial Differential Equation (PDE) problem that models the static (zero voltage) behavior of a Josephson window junction. Iterative methods for solving this problem are proposed and their computer implementation is discussed. The preliminary computational results that are given, show the modeling power of our approach and exhibit its computational efficiency.

Numerical experiments with two multivariable integrands and various quasirandom sequences are described. The integrands were introduced as models of Monte Carlo algorithms for particle tracking with or without statistical weights. Though analytically both integrands are very similar, the corresponding integration errors behave quite differently.

From these experiments together with earlier ones (that are briefly summarized in the paper) several non-standard conclusions are drawn both on quasirandom sequences and on types of integrands.

We describe a new algorithm for simulating complex Markoff processes. We have used a reaction-cell method in order to simulate arbitrary reactions. It can be used for any kind of RDS on arbitrary topologies, including fractal dimensions or configurations not being related to any spatial geometry. The events within a single cell are managed by an event handler which has been implemented independently of the system studied. The method is exact on the Markoff level including the correct treatment of finite numbers of molecules.

To demonstrate its properties, we apply it on a very simple reaction-diffusion-systems (RDS). The chemical equations and in 1 to 4 dimensions serve as models for systems whose dynamics on an intermediate time scale are governed by fluctuations. We compare our results to the analytic approach by the scaling ansatz. The simulations confirm the exponents of the A+B system within statistical errors, including the logarithmic corrections in the dimension d=2.

The method is able to simulate the crossover from the reaction to diffusion limited regime, which is defined be a crossover time depending on the system size.

Using a simple master-slave parallelization scheme given by A. Berengoltz and J. Adler, we observe superlinear speedups during the search algorithm for the ground state energy of the ±J spin glass via biologically motivated methods. With this parallel implementation we are able to improve earlier sequentially-calculated estimates for the infinite lattice ground state energy of the square and simple cubic lattice to −1.401±0.001 and −1.787±0.003, respectively.