International Journal of Modern Physics C

A parallel version of the invaded cluster algorithm is described. Results from large scale (up to 4096² and 512³) simulations of the Ising model are reported. No evidence of critical slowing down is found for the three-dimensional Ising model. The magnetic exponent is estimated to be 2.482±0.001(β/ν=0.518±0.001) for the three-dimensional Ising model.

We illustrate wavefunctions and half-lives of α-radioactive even-A thorium isotopes based on the simple semi-classical theory of alpha-decay process. The potential is assumed to take an attractive square-well form inside the potential barrier and to take a repulsive Coulomb one outside the barrier. Overall for the even-A thorium isotopes, only two parameters r₀=1.14 fm and V₀=16 MeV are used. Outside the region of a potential barrier, an obvious oscillating feature of wavefunction for ²¹⁸Th nucleus does not appear until the Q_α value is less than 20 MeV. Such a characteristic feature is confirmed by the three dimensional surface plot for the wave function of ²¹⁸Th nucleus. Our predicted values of half-life for even-A thorium isotopes are agreed satisfactorily with the observed results as a whole.

Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.

This paper proposes a strategy of designing routing algorithms for connectionless packet-switched networks. This strategy consists of three design elements as follows: [A] the notion of ideal routings is introduced to provide the upper performance limits attained by improving routing algorithm and it serves as a standard to measure the performance of other algorithms; [B] a method of constructing simple algorithms is presented under implementation conditions from ideal routings; [C] a method is described to enhance the performance limits of [A]. By using these elements, simple algorithms with a maximum degree of performance attainment are realized. By "degree of performance attainment", we mean that we can see how much room is left for the improvement of algorithms. We develop [A] and [B] with the performance measures of throughput and average packet delay and the M/M/1 queuing network. We decide ideal static routings and their performance limits from [A]. We obtain a new simple algorithm from [B] based on the notion of the ideal routings in implementation conditions. The designed algorithm improves the throughput and the average delay, which are comparable to those from ideal static routings. This improvement is contrasted to the adaptive and distributed OSPF (Open Shortest Path First), a standard Internet routing protocol.

We propose a way of implementing the Broad Histogram Monte Carlo method to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model with periodic boundary conditions. We have found an excellent agreement between our method and traditional Metropolis results for the energy, the magnetization, the specific heat and the magnetic susceptibility on a very large temperature range. For the calculation of these quantities in the temperature range 0.7<T<4.7 our method took less CPU time than the Metropolis simulations for 16 temperature points in that temperature range. Furthermore, it calculates the whole temperature range 1.2<T<4.7 using only 2.2 times more computer effort than the Histogram Monte Carlo method for the range 2.1<T<2.2. Our way of treatment is general; it can also be applied to other systems with continuous degrees of freedom.

We study the effect of some crystal vibrations on the electron distribution and the gap HOMO–LUMO in a linear chain of atoms where, the valence electrons move in a model potential constructed by combining atromic boxes. It is found that at the turning points, these two levels collapse together for a chain with an even number of atoms while for a chain with an odd number of atoms these two levels never touch each other.

The effect of some asymmetric crystal vibrations on the electron density distribution and the gap HOMO–LUMO is also analyzed for a low-dimensional solid whose repeating unit consists of a square arrangement of atoms where the valence electrons move in a CAB model potential.

Simulations with up to 112⁵ spins confirm the prediction of Chen and Dohm of three different finite-size exponents for the spontaneous magnetization near the Curie point.

This work presents parallel multistep methods for the solution of ordinary differential equations. The characteristic of parallel computing is that there is a "front" and the computation at points ahead of the front depends only on information behind it. This requires a resetting of serial algorithms and may also lead to numerical errors and instabilities. The analysis of positive and negative aspects of parallel computing is the subject of this paper. Some of the methods presented below are uncommon in the literature on mathematical computing. Others have been elaborated for this study on the basis of the traditional Adams-Bashforth multistep methods.

A performance comparison of the methods is made by numerical testing in molecular dynamics calculations. The increase of the number of processors m appears to seriously deteriorate the stability of the calculations and the use of m larger than 2 seems impractical.

Spatially extended systems yield complex patterns arising from the coupled dynamics of its different regions. In this paper we introduce a matrix computational operator, , for the characterization of asymmetric amplitude fragmentation in extended systems. For a given matrix of amplitudes this operation results in an asymmetric-triangulation field composed by L points and I straight lines. The parameter (I-L)/L is a new quantitative measure of the local complexity defined in terms of the asymmetry in the gradient field of the amplitudes. This asymmetric fragmentation parameter is a measure of the degree of structural complexity and characterizes the localized regions of a spatially extended system and symmetry breaking along the evolution of the system. For the case of a random field, in the real domain, which has total asymmetry, this asymmetric fragmentation parameter is expected to have the highest value and this is used to normalize the values for the other cases. Here, we present a detailed description of the operator and some of the fundamental conjectures that arises from its application in spatio-temporal asymmetric patterns.

A one-dimensional cellular automaton with a probabilistic evolution rule can generate stochastic surface growth in (1+1) dimensions. Two such discrete models of surface growth are constructed from a probabilistic cellular automaton which is known to show a transition from an active phase to an absorbing phase at a critical probability associated with two particular components of the evolution rule. In one of these models, called Model A in this paper, the surface growth is defined in terms of the evolving front of the cellular automaton on the space-time plane. In the other model, called Model B, surface growth takes place by a solid-on-solid deposition process controlled by the cellular automaton configurations that appear in successive time-steps. Both the models show a depinning transition at the critical point of the generating cellular automaton. In addition, Model B shows a kinetic roughening transition at this point. The characteristics of the surface width in these models are derived by scaling arguments from the critical properties of the generating cellular automaton and by Monte Carlo simulations.

We use the Hoshen–Kopelman algorithm with the Nakanashi method of recycling redundant labels to measure the fraction of spanning configurations, R(p_c), at and near p_c, for random site percolation in two and three dimensions with different boundary conditions. For the square and cubic lattices we find that R(p_c) is 0.50 and 0.28 for free edges and 0.64 (2-d) and 0.56 (3-d) for both helical and periodic boundary conditions. The error bars are of the order of ±0.01 for these results.

We present computational aspects of Molecular Dynamics calculations of thermal properties of diamond using the Brenner potential. Parallelization was essential in order to carry out these calculations on samples of suitable sizes. Our implementation uses MPI on a multi-processor machine such as the IBM SP2. Three aspects of parallelization of the Brenner potential are discussed in depth. These are its long-range nature, the need for different parallelization algorithms for forces and neighbors, and the relative expense of force calculations compared to that of data communication. The efficiency of parallelization is presented as a function of different approaches to these issues as well as of cell size and number of processors employed in the calculation. In the calculations presented here, information from almost half of the atoms were needed by each processor even when 16 processors were used. This made it worthwhile to avoid unnecessary complications by making data from all atoms available to all processors. Superlinear speedup was achieved for four processors (by avoiding paging) with 512 atom samples, and 5ps long trajectories were calculated (for 5120 atom samples) in 53 hours using 16 processors; 514 hours would have been needed to complete this calculation using a serial program. Finally, we discuss and make available a set of routines that enable MPI-based codes such as ours to be debugged on scalar machines.

The Monte Carlo simulation method is used to study monomer-dimer bidirectional reactions on modified surfaces. The assumed model predicts that reaction leads to different products depending on the state of reacting molecules, which depends on the state of adjacent adsorbing sites. The model assumes that the catalyst surface is precovered by a certain amount of modifier, which partially deactivates the surface and changes the state of the adsorbed reactant species. It is demonstrated that the surface concentration of the modifier atoms and the topography of their distribution over the surface are both important factors which influence the behavior of systems considered in this paper. In particular, it has been found that the reaction direction, the reaction window location and its width depend strongly on the surface morphology. The results are in a good qualitative agreement with the experimentally observed changes in the direction of the methanol oxidation on the sulfur-modified Fe(100) catalyst.

We study the optimized version of the multiple invasion percolation model. Some topological aspects as the behavior of the acceptance profile, coordination number and vertex type abundance were investigated and compared to those of the ordinary invasion. Our results indicate that the clusters show a very high degree of connectivity, spoiling the usual nodes-links-blobs geometrical picture.

The three-dimensional diluted antiferromagnet in a magnetic field has a longe-range ordered state for sufficiently low temperatures and external fields. We study the irreversibilities at the phase transition from this state into the paramagnetic state at higher temperatures. Performing field cooling and zero field cooling simulation procedures we find a small irreversibility in the internal energy and the specific heat, although the behavior of the order parameter is irreversible and the phase transition is suppressed in the FC case. The specific heat shows a noncritical broad maximum above the transition temperature T_c. The results are compatible with recent experimental results obtained by Satooka et al., whereas our interpretation of the data is different.

Dissipative particle dynamics (DPD) originated as a tool for performing fluid dynamics simulations of complex fluids and amongst other things has been used to simulate dilute polymer solutions. The technique employed an Euler time-stepping technique up until recently, when a velocity-Verlet type algorithm was proposed. This paper presents a more accurate velocity-Verlet and analyses the equilibrium properties of this new technique for finite time-steps. An expression for the temperature in terms of the basic DPD parameters is derived for this scheme.

In this paper we show how the transposition, the basic operation of the permutation group, can be taken into account in a diffusion process of identical particles. Whereas in an earlier approach the method was applied to systems in which the potential is invariant under interchanging the Cartesian components of the particle coordinates, this condition on the potential is avoided here. In general, the potential introduces a switching of the boundary conditions of the walkers. These transitions modelled by a continuous-time Markov chain generate sample paths for the propagator as a Feynman–Kac functional. A few examples, including harmonic fermions with an anharmonic interaction, and the ground-state energy of ortho-helium are studied to elucidate the theoretical discussion and to illustrate the feasibility of a sign-problem-free implementation scheme for the recently developed many-body diffusion approach.

We explore the phase diagram of an O(n) model on the honeycomb lattice with vacancies, using finite-size scaling and transfer-matrix methods. We make use of the loop representation of the O(n) model, so that n is not restricted to positive integers. For low activities of the vacancies, we observe critical points of the known universality class. At high activities the transition becomes first order. For n=0 the model includes an exactly known theta point, used to describe a collapsing polymer in two dimensions. When we vary n from 0 to 1, we observe a tricritical point which interpolates between the universality classes of the theta point and the Ising tricritical point.

The phase diagram of the O(n) model, in particular the special case n=0, is studied by means of transfer-matrix calculations on the loop representation of the O(n) model. The model is defined on the square lattice; the loops are allowed to collide at the lattice vertices, but not to intersect. The loop model contains three variable parameters that determine the loop density or temperature, the energy of a bend in a loop, and the interaction energy of colliding loop segments. A finite-size analysis of the transfer-matrix results yields the phase diagram in a special plane of the parameter space. These results confirm the existence of a multicritical point and an Ising-like critical line in the low-temperature O(n) phase.

In this paper we revisit the glass model describing the macroscopic behavior of the High-Temperature superconductors. We link the glass model at the microscopic level to the striped phase phenomenon, recently discussed widely. The size of the striped phase domains is consistent with earlier predictions of the glass model when it was introduced for High-Temperature Superconductivity in 1987. In an additional step we use the Hubbard model to describe the microscopic mechanism for d-wave pairing within these finite size stripes.

We discuss the implications for superconducting correlations of the Hubbard model, which are much higher for stripes than for squares, for finite size scaling, and for the new view of the glass model picture.

A simple lava flow automaton is discretized, three different variants are shown to exhibit a wide range of behavior, while some geometrical and shape characteristics are analysed. We respect, on an underlying square topology, equalization of lava height between nearest neighbors (whenever possible), and update the evolution in parallel. This model is a discretized version (as regards the lava level) of a very successful continuous height automaton, but with no local loss through cooling.