International Journal of Modern Physics C

In this paper we present a family of explicit Runge–Kutta methods of 5th algebraic order, one of which has variable coefficients, for the efficient solution of problems with oscillating solutions. Emphasis is placed on the phase-lag property in order to show its importance with regards to problems with oscillating solutions. Basic theory of Runge–Kutta methods, phase-lag analysis and construction of the new methods are described. Numerical results obtained for known problems show the efficiency of the new methods when they are compared with known methods in the literature. Furthermore we note that the method with variable coefficients appears to have much higher accuracy, which gets close to double precision, when the product of the frequency with the step-length approaches certain values. These values are constant and independent of the problem solved and depend only on the method used and more specifically on the expressions used to achieve higher algebraic order.

We have simulated (3+1)-dimensional finite temperature Z₂ gauge theory by using Metropolis algorithm. We aimed to observe the deconfinement phase transitions by using geometric methods. In order to do so we have proposed two different methods which can be applied to three-dimensional effective spin model consisting of Polyakov loop variables. The first method is based on the studies of cluster structures of each configuration. For each temperature, configurations are obtained from a set of bond probability (P) values. At a certain probability, percolating clusters start to emerge. Unless the probability value coincides with the Coniglio–Klein probability value, the fluctuations are less than the actual fluctuations at the critical point. In this method the task is to identify the probability value which yields the highest peak in the diverging quantities on finite lattices. The second method uses the scaling function based on the surface renormalization, which is of geometric origin. Since this function is a scaling function, the measurements done on different-size lattices yield the same value at the critical point, apart from the correction to scaling terms. The linearization of the scaling function around the critical point yields the critical point and the critical exponents.

In this paper, we study the effect of randomization probability p on the fundamental diagrams of the Nagel–Schreckenberg model (NS) with "slow-to-start" rule introduced by Benjamin, Johnson and Hui (BJH). It is shown that this model exhibits metastable states (which leads to the occurrence of hysteresis) only for very low values of the randomization probability (p≤0.08). Here we propose a simple generalization of the BJH model by introducing a distance-dependent randomization. With such simple generalization, the hysteresis effect and phase separation exist for all values of randomization probability. The new fundamental diagrams are analyzed within the framework of the distributions of time and distance headways.

The Sznajd model of socio-physics, with only a group of people sharing the same opinion can convince their neighbors, is applied to a scale-free random network modeled by a deterministic graph. We also study a model for elections based on the Sznajd model and the exponent obtained for the distribution of votes during the transient agrees with those obtained for real elections in Brazil and India. Our results are compared to those obtained using a Barabási–Albert scale-free network.

A field theoretical method for the treatment of the often violated charge conservation laws in computational electrodynamics is presented. This approach explores the basic symmetry features of Maxwell theory and the analogy between the gauge field anomalies of quantum field theory and the violation of charge conservation law on the lattice, in Lorentz covariant Lagrangian formalism. A mathematical construction of the counter terms to the anomalous charge conservation law is proposed, and thereby a consistent theory for the Generalized Lagrange Multiplier method is presented, which has so far lacked a concrete theoretical framework. Based on the established theoretical framework, the method has been further extended and the question regarding whether method solves "right" equations is answered. This extended method with new insight is then applied to magnetohydrodynamics and recently proposed "shallow water" . In particular, a -based Godunov-type finite-volume solver for the "shallow water" system on the Cartesian grid has been developed, and the introduced theoretical framework for model is validated. In addition, associated new analytic features of the "shallow water" system is also presented.

Periodic boundary conditions have no unique implementation in magnetic systems where all spins interact with each other through a power law decaying interaction of the form 1/r^α, r being the distance between spins. In this work we present a comparative study of the finite size effects oberved in numerical simulations by using first image and infinite image periodic boundary conditions in one- and two-dimensional spin systems with those interactions, including the ferromagnetic, anti-ferromagnetic and competitive interaction cases. Our results show no significative differences between the finite size effects produced by both boundary conditions when the low temperature phase has zero global magnetization, and it depends on the ratio α/d for systems with a low temperature ferromagnetic phase. In the last case the first image convention gives more stronger finite size effects than the other when the system enters into the classical regime α/d≤3/2.

The melting transition of hard disks in two dimensions is still an unsolved problem and improved simulation algorithms may be helpful for its investigation. We suggest the application of simulating tempering for grand canonical hard-disk systems as an efficient alternative to the commonly-used Monte Carlo algorithms for canonical systems. This approach allows the direct study of the packing fraction as a function of the chemical potential even in the vicinity of the melting transition. Furthermore, estimates of several spatial characteristics including pair correlation function are studied in order to test the accuracy of the method and to analyze the melting transition in hard-disk systems. Our results seem to show that there is a weak first-order phase transition.

Using cellular automata model, we simulate the British Government Policy (BGP) in the 2001 foot and mouth epidemic in Great Britain. When clinical symptoms of the disease appeared in a farm, there is mandatory slaughter (culling) of all livestock in an infected premise (IP). Those farms in the neighboring of an IP (contiguous premise, CP), are also culled, aka nearest neighbor interaction. Farms where the disease may be prevalent from animal, human, vehicle or airborne transmission (dangerous contact, DC), are additionally culled, aka next-to-nearest neighbor interactions and lightning factor. The resulting mathematical model possesses a phase transition, whereupon if the physical disease transmission kernel exceeds a critical value, catastrophic loss of animals ensues. The nonlocal disease transport probability can be as low as 0.01% per day and the disease can still be in the high mortality phase. We show that the fundamental equation for sustainable disease transport is the criticality equation for neutron fission cascade. Finally, we calculate that the percentage of culled animals that are actually healthy is ≈30%.

In this research, we have presented the phase space of the so-called spin glass or glassy systems with a one-dimensional randomly-oriented diode network (RODN) in which the bonds between the lattice points are represented with diodes and these diodes are assumed to be fully conducting in the forward biased direction, whereas they are assumed to have some constraints, in the reverse direction, depending on the temperature and/or some other external effects. Thus, a particle's conduction (or transition) probability in the reverse direction through a diode like bond, p_r, can be assumed to have values between zero and one. By employing the Monte Carlo simulation technique to the diffusion of particles through this network we have explored the relaxation mechanism, and their functional forms. Our simulation data indicates that for reverse transition probability values of p_r=1.0 and 0.9, the time dependence of the relaxation data is exponential, on the other hand for p_r<0.2 it may be represented by either power or logarithmic time dependence. However, in general, our data can be represented by a stretched exponential time dependence, exp(-(t/τ)^α), especially in the limit of long t. Here the exponent α has values in the range of 0.3≤α≤1. For α≈1, obviously, exponential time dependence is regained. The value of α≈0.3, obtained for p_r→0, is very interesting, since it is almost the same as the critical exponent, 1/3, reported in the literature for the lowest occupation probability of site points spanning percolation clusters.

Real world networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a natural means for relating such networks with metric spaces, but also a natural means for obtaining fractal complex networks. A series of comprehensive measurements closely related to spatial aspects of these networks is proposed, which includes the effective length, adjacency, as well as the fractal dimension of the network in terms of the spatial scales defined by successive shortest paths starting from a specific node. The potential of such features is illustrated with respect to the random, small-world, scale-free and fractal network models.

A new system of library code is proposed and initiated. It is emphasized that the same terminologies as we find in our textbooks should be used for class names in the library code. This proposal is inspired by .NET of Microsoft. Several rules of thumb are suggested in order to obtain easy-readable coherent codes. As a first step, we present the library code for exact diagonalization in physics. When we build codes, we distinguish between model independent and dependent parts. For the model independent parts, we use the familiar terminologies like , etc as class names. As an explicit example, we calculate ground state energy of a quantum dot, showing the triplet–singlet transition.

We have performed parallel large-scale molecular-dynamics simulations on the QSC-machine at Los Alamos. The good scalability of the SPaSM code is demonstrated together with its capability of efficient data analysis for enormous system sizes up to 19 000 416 964 particles. Furthermore, we introduce a newly-developed graphics package that renders in a very efficient parallel way a huge number of spheres necessary for the visualization of atomistic simulations. These abilities pave the way for future atomistic large-scale simulations of physical problems with system sizes on the μ-scale.