International Journal of Modern Physics C

In this paper we discuss the general problem of implementing the multidimensional Fast Fourier Transform algorithm on parallel computers. We show that, on a machine with P processors and fully parallel node communications, the optimal asymptotic scaling behavior of the total computational time with the number of data points, N, given in d dimensions by the formula aN/Plog(N/P)+bN/P^(d-1)/d, can actually be achieved on realistic platforms. As a concrete realization of our strategy, we have produced codes efficiently running on machines of the APE family and on Cray T3E. On the former for asymptotic values of N our codes attain the above optimal result.

Monte Carlo simulations with up to 176⁵ spins show no significant deviations between four different random number generators in multispin coding, as opposed to multiplication with 16807 for one-word-per-spin coding for 32⁵. Also world record sizes 1000192², 9984³, 880⁴ and 48⁶ spins were simulated.

Simulations at T/Tc = 1/4 agree with classical nucleation theory if the droplets are assumed as small cubes instead of spheres.

A discrete model of a neural network of excitatory and inhibitory neurons is presented which yields oscillations of its global activity. Different types of dynamics occur depending on the selection of parameters: oscillating population activity as well as randomly fluctuating but mainly constant activity. For certain sets of parameters the model also shows temporary transitions from apparently random to periodic behavior in one run, similar to an epileptic seizure.

New algorithms with O(N) complexity have been developed for fast particle-pair detections in particle simulations like the discrete element method (DEM) and molecular dynamic (MD). They exhibit robustness against broad particle size distributions when compared with conventional boxing methods. Almost similar calculation speeds are achieved at particle size distributions from is mono-size to 1:10 while the linked-cell method results in calculations more than 20 times. The basic algorithm, level-boxing, uses the variable search range according to each particle. The advanced method, multi-level boxing, employs multiple cell layers to reduce the particle size discrepancy. Another method, indexed-level boxing, reduces the size of cell arrays by introducing the hash procedure to access the cell array, and is effective for sparse particle systems with a large number of particles.

Exponentially and trigonometrically fitted third algebraic order Runge–Kutta methods for the numerical integration of the Schrödinger equation are developed in this paper. Numerical results obtained for several well known problems show the efficiency of the new methods.

We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumping along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual Kawasaki dynamics. Our goal is to determine which of the several existing theories for critical behavior is valid. We analyze finite-size scaling properties using a range of system shapes and sizes far exceeding previous studies. Four different analytic predictions are tested against the numerical data. Binder and Wang's prediction does not fit the data well. Among the two slightly different versions of Leung, the one including the effects of a dangerous irrelevant variable appears to be better. Recently proposed isotropic finite-size scaling is inconsistent with our data from cubic systems, where systematic deviations are found, especially in scaling at the critical temperature.

The four-dimensional Ising model is simulated on the Creutz cellular automaton with increased precision. The data are analyzed according to the finite-size scaling relations available. The precision of the critical values related to magnetic susceptibility is improved by one digit, but in order to reach to the same precision for those related to the specific heat more simulation runs at the critical temperatures of the finite-size lattices are required.

Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states 0,1,…,n-1; can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the above density classification task cannot be resolved by a single cellular automaton, this task can be performed efficiently by applying two cellular automaton rules in succession.

We study the capillary condensation of a lattice gas with nearest neighbor attraction confined to a slit-like pore filled with frozen obstacles (matrix). First, the lattice Monte Carlo simulations were performed for a slit-like pore without obstacles. Next, the pore filled with obstacles, i.e., confined microporous medium, is prepared by adsorbing and then by quenching a hard sphere fluid in the pore of the width H. The model includes fluid-wall attraction; however, the fluid-matrix interaction is entirely repulsive. We have investigated how concentration of obstacles and the pore width H influence the capillary phase diagrams. Our numerical experiments reveal essential changes in the critical temperature and in the shape of the coexistence line with the amount of quenched obstacles.

Numerical methods for solutions of differential equations with deviating arguments describing one-dimensional ultra-relativistic scattering of two identical charged particles in Wheeler-Feynman electrodynamics with half-retarded/half-advanced interaction are developed. Utilization of the methods for the physical problem analysis leads to the discovery of a bifurcation of solutions and breaking of their reflectional symmetry for particles asymptotic velocity v>0.937c in their center-of-mass frame.

We study the m = 3 bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability p or 1-p, respectively. Occupied sites with less than m occupied first-neighbors are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, p_c, and both scaling powers, y_p and y_h, and, contrary to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., m=0). The critical spanning probability, R(p_c), is also numerically studied for systems with linear sizes ranging from L=32 up to L=480; the value we found, R(p_c)=0.270±0.005, is the same as for usual percolation with free boundary conditions.

The hypothesis z=2 with logarithmic corrections seems inconsistent with one way of simulation but not with a different one, for the same Ising model.

Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d=2 and d=6-∊ dimensions and with earlier simulations. We also present and explain results for bus–bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend on the aspect ratios of the samples.

We use a simple traffic micro-simulation model based on queueing dynamics as introduced by Gawron [IJMPC, 9(3):393, 1998] in order to simulate traffic in Portland/Oregon. Links have a flow capacity, that is, they do not release more vehicles per second than is possible according to their capacity. This leads to queue built-up if demand exceeds capacity. Links also have a storage capacity, which means that once a link is full, vehicles that want to enter the link need to wait. This leads to queue spill-back through the network. The model is compatible with route-plan-based approaches such as TRANSIMS, where each vehicle attempts to follow its pre-computed path. Yet, both the data requirements and the computational requirements are considerably lower than for the full TRANSIMS microsimulation. Indeed, the model uses standard emme/2 network data, and runs about eight times faster than real time with more than 100 000 vehicles simultaneously in the simulation on a single Pentium-type CPU.

We derive the model's fundamental diagrams and explain it. The simulation is used to simulate traffic on the emme/2 network of the Portland (Oregon) metropolitan region (20 000 links). Demand is generated by a simplified home-to-work destination assignment which generates about half a million trips for the morning peak. Route assignment is done by iterative feedback between micro-simulation and router. An iterative solution of the route assignment for the above problem can be achieved within about half a day of computing time on a desktop workstation. We compare results with field data and with results of traditional assignment runs by the Portland Metropolitan Planning Organization.

Thus, with a model such as this one, it is possible to use a dynamic, activities-based approach to transportation simulation (such as in TRANSIMS) with affordable data and hardware. This should enable systematic research about the coupling of demand generation, route assignment, and micro-simulation output.

We investigated the influence of the distribution of bimodal bonds on phase transition in 8-state Potts model in two dimensions. We show that there is a finite size dependent threshold value of the introduced quenched randomness in the bond distribution for rounding the first-order phase transition.

The symplectic integrator of the Gauss–Legendre type is tested on the nonlinear Schrödinger equation. Preservation of high integrals (up to 10 or more) and quasiperiodic motion have been detected for dynamics on both stable soliton and homoclinic manifolds, which indicate applicability of symplectic integrators for adequate simulation of integrable equation. The tested integrator is applied to the problem of long-time stability of the solitons in higher-derivative nonlinear Schrödinger equation. The slow logarithmic-type depletion of the soliton amplitude with time has been detected.