International Journal of Modern Physics C

We investigate the role played by conservative forces in dissipative particle dynamics (DPD) simulation of single-component and binary fluids. We employ equations from kinetic theory for matching the coefficients of DPD interparticle force to the macroscopic properties of fluid such as: density, temperature, diffusion coefficient, kinematic viscosity and sound velocity. The sound velocity c is coupled with scaling factor π₁ of conservative component of the DPD collision operator. Its value sets up an upper limit on the mass S of a single particle in DPD fluid. The Kirkwood–Alder fluid–solid transition is observed for a sufficiently large S. We emphasize the role of the scaling factor π₁₂ for particles of different types in simulating phase separation in binary fluids. The temporal growth of average domain size R(t) in the phase separation process depends on the value of immiscibility coefficient Δ = π₁₂ - π₁. For small immiscibility, R (t) ∝ t^β, where β ≈ 1/2 for R (t) < R_H and β ≈ 2/3 for R (t) > R_H, R_H is the hydrodynamic length. Finally, both phases separate out completely. For larger immiscibility, R(t) increases exponentially at the beginning of simulation, while finally the domain growth process becomes marginal. We also observe the creation of emulsion-like structures. This effect results from an increase of the surface tension on the two-phase interface along with increasing immiscibility.

Jacobi elliptic functions play a central role in nonlinear evolution equations. We show how with one recursive call we can calculate the Jacobi elliptic functions sn, cn, and dn. We give an implementation using C++.

The average length and average relaxation time of attractors in sequence processing neural networks are investigated. The simulation results show that a critical point of α, the loading ratio, is found. Below the turning point, the average length is equal to the number of stored patterns; conversely, the ratio of length and numbers of stored patterns, grow with an exponential dependence exp (Aα). Moreover, we find that the logarithm of average relaxation time is only linearly associated with α and the turning point of coupling degree is located for examining robustness of networks.

In the four-dimensional Edwards–Anderson ±J spin glasses, we observe that the quenched energies distribution from T=2.5 are similar to those observed for the equilibrium states at T=1.0. We show that although these states appear close there are subtle differences which are only seen when we try to quench the system from T=2.5 for a longer number of Monte Carlo steps. The T=2.5 states do not evolve to those seen for the states quenched from T=1.0. We try to identify regions responsible for the subtle differences.

We build and investigate a nonstandard model of pattern formation in a system of discrete entities evolving in discrete space and time. We chose a sandpile paradigm to fit our ideas in the frame of current research. In our model sand is hot because a grain can topple against gradient, i.e., the grain can walk to another node even when a number of grains in its current node is less than a number of neighboring nodes. Sand is choosey because behavior of the grains is not determined by any global parameter or any threshold of a number of neighboring grains (called here a grain sensitivity) but depends on the exact number of grains in the neighboring nodes. Namely, we assume that a grain being at a node x goes to one of the eight neighboring nodes, chosen at random, if there is another grain at the node x or if the number of grains in eight neighboring nodes lies in some set of 2^{1,…,8}. These 256 rules of sensitivity are investigated. The classification of the rules if offered, based on the morphology of the patterns generated by each rule. Eight morphological classes are found. Fine structure of every class is investigated and transient phenomena are analyzed. Three kinds of description of class rules by Boolean expressions are offered. Evolution of the classes governed by several one-dimensional parameters is considered.

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding and quantum teleportation. We determine the requirements for a state in the Hilbert space C⁴ to be entangled and a solution to the corresponding "factorization" problem if this is not the case. The factorization of nonentangled states is implemented in C++.

Explicit second and fourth algebraic order methods for the numerical solution of the Schrödinger equation are developed in this paper. The new methods have free parameters defined so that the methods are fitted to spherical Bessel and Neumann functions. Based on these new methods we obtained a variable-step algorithm. The results produced based on the numerical solution of the radial Schrödinger equation and the coupled differential equations arising from the Schrödinger equation indicate that this new approach is more efficient than other well known ones.

In this empirical paper we show that in the months following a crash there is a distinct connection between the fall of stock prices and the increase in the range of interest rates for a sample of bonds. This variable, which is often referred to as the interest rate spread variable, can be considered as a statistical measure for the disparity in lenders' opinions about the future; in other words, it provides an operational definition of the uncertainty faced by economic agents. The observation that there is a strong negative correlation between stock prices and the spread variable relies on the examination of eight major crashes in the United States between 1857 and 1987. That relationship which has remained valid for one and a half century in spite of important changes in the organization of financial markets can be of interest in the perspective of Monte Carlo simulations of stock markets.

One-dimensional cellular automata are known to be able to present complex behaviors. In some cases, their evolution may be understood as movings, collisions, or creations of particles. In the case of the special Wolfram's rule 54, Boccara has previously pointed out basic particles. In this paper, we introduce a group which allows the formal study of interactions between these particles. Coming back to the complexity of rule 54 and using the new algebraic classification of Rapaport, we prove that rule 54 is not simple.

In recent years, several methods of noise cleaning have been devised, of which projective methods have been particularly effective. In our paper, we explain in detail why orthogonal projections are nonoptimal and how the nonorthogonal projections suggested by Grassberger et al., naturally emerge from the SVD method. We show that this approach when combined with a dynamic neighborhood selection yields optimal results of noise cleaning.

A modification of the Bak–Sneppen model to include simple elements of Darwinian evolution is used to check the survival of prey and predators in long food chains. Mutations, selection, and starvation resulting from depleted prey are incorporated in this model.

Using molecular-scale computer simulation, we show that structural changes may take place in phospholipid bilayers in an aqueous solution as we vary the relative concentration of water to phospholipids, the bilayer thickness, the inclination angle of the choline, dipole molecular fragment with respect to the bilayer surface, and the conformation of hydrocarbon chains of phospholipid in the hydrophobic volume of the bilayer. It is shown that in the hydrophobic volume of the bilayer, an interpenetration of the hydrocarbon chains located on opposite sides of the phospholipid bilayer takes place.

Multivariate models in the framework of artificial neural network have been constructed for systems where time series data of several variables is known. The models have been tested using computer generated data for the Lorenz and Henon systems. They are found to be robust and give accurate short term predictions. Analysis of the models is able to throw some light on theoretical questions related to multivariate "embedding" and removal of redundancy in the embedding.

The structural and electronic properties of optimized open-ended single-wall carbon nanotubes with zigzag geometry have been investigated. The calculations were performed using molecular mechanics, extended Hückel, and AM1–RHF semiempirical molecular orbital methods. It has been found that the density of states of the zigzag model is sensitive to the tube size and changes as the tube length increases. On the other hand the energetics of the tube shows an almost linear dependence to the tube length, and a converging characteristics with respect to the number of hexagons forming the tube.

It is very difficult to calculate the accurate ground-state energies of the double-electron atom like helium in a uniform magnetic field. By using the modified configuration interaction (MCI) method and the evolutionary algorithm (EA), we obtained highly accurate results. We discuss the role of magnetic field in the ground state of the double-electron system and the possibility of variational ground-state energy calculation by using evolutionary algorithm directly. Results show that compared with other algorithms, such as the simplex method, EA is more efficient in calculating atomic energies, and can be used in other fields of physics.

This work analyzes explicit and implicit methods for the solution of differential stochastic equations for crystal growth. The usefulness of these methods is analyzed by practical computations.

Monte Carlo simulations alone could not clarify the corrections to scaling for the size-dependent p_c(L) above the upper critical dimension. Including the previous series estimate for the bulk threshold p_c (∞) gives preference for the complicated corrections predicted by renormalization group and against the simple 1/L extrapolation. Additional Monte-Carlo simulations using the Leath method corroborate the series result for p_c.