International Journal of Modern Physics C

An important global property of a bit string is the number of ones in it. It has been found that the parity (odd or even) of this number can be found by a sequence of deterministic, translational invariant cellular automata with parallel update in succession for a total of O(N²) time. In this paper, we discover a way to check if this number is divisible by three using the same kind of cellular automata in O(N³) time. We also speculate that the method described here could be generalized to check if it is divisible by four and other positive integers.

In this work we study, by means of numerical simulations, the out-of-equilibrium dynamics of the one-dimensional Edwards–Anderson model with long-range interactions of the form ± Jr^-α. In the limit α → 0 we recover the well known Sherrington–Kirkpatrick mean-field version of the model, which presents a very complex dynamical behavior. At the other extreme, for α → ∞ the model converges to the nearest-neighbor one-dimensional system. We focus our study on the dependence of the dynamics on the history of the sample (aging phenomena) for different values of α. The model is known to have mean-field exponents already for values of α = 2/3. Our results indicate that the crossover to the dynamic mean-field occurs at a value of α < 2/3.

A simple two-dimensional system is introduced which suggests a qualitative dynamical relationship between (1) stock market prices in the presence of nonlinear trend-followers and nonlinear value investors, (2) the world human population with a competition between a population-dependent growth rate and a nonlinear dependence on a finite carrying capacity and (3) the failure of materials subjected to a time-varying stress with a competition between positive geometrical feedback on the damage variable and nonlinear healing. Our model keeps three key ingredients (inertia, nonlinear positive and negative feedbacks) that compete to give rise to singularities in finite time decorated by accelerating oscillations.

Recently sixteen types of doubly-periodic solutions were obtained for the new (2 +1)-dimensional complex nonlinear integrable system. In this paper with the aid of computerized symbolic computation, our extended Jacobi elliptic function expansion method is extended to this system. As a result, another eight families of Jacobian elliptic functions solutions are also found.

Monte Carlo simulation techniques, like simulated annealing and parallel tempering, are often used to evaluate low-temperature properties and find ground states of disordered systems. Here we compare these methods using direct calculations of ground states for three-dimensional Ising diluted antiferromagnets in a field (DAFF) and three-dimensional Ising spin glasses (ISG). For the DAFF, we find that, with respect to obtaining ground states, parallel tempering is superior to simple Monte Carlo and to simulated annealing. However, equilibration becomes more difficult with increasing magnitude of the externally applied field. For the ISG with bimodal couplings, which exhibits a high degeneracy, we conclude that finding true ground states is easy for small systems, as is already known. But finding each of the degenerate ground states with the same probability (or frequency), as required by Boltzmann statistics, is considerably harder and becomes almost impossible for larger systems.

In this work, we study the stochastic resonance phenomenon in a bistable nonlinear dynamical system in the presence of an uncorrelated noise source whose distribution decays asymptotically as P(ξ) ∝ 1/ξ^2α. We investigate the influence of the decay exponent α on the transition rate and on the optimal noise intensity giving the maximum signal-to-noise ratio when a weak periodic signal is superposed to the external noise. We find that the transition rate achieves a maximum for a finite decay exponent α. However, the optimal noise intensity for stochastic resonance depicts a monotonic power-law correction relative to the usual behavior of nonlinear dynamical systems driven by Gaussian noises.

We study ghetto formation in a population with natives and immigrants in the framework of the two-dimensional Ising-model with Kawasaki-exchange dynamics. It is the phase structure of the Ising model, the integration speed and the immigration rate which determine whether ghetto formation between natives and immigrants can be avoided or not. Our simulations are performed in- and out-of-equilibrium.

We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA–ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.

We have translated fractional Brownian motion (FBM) signals into a text based on two "letters", as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the ζ′ exponent relating the word frequency and its rank on a log–log plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occurrence of words of length m < 8 made of such two letters: ζ′ is varying as a power law in terms of m. We have also searched how the ζ′ exponent of the Zipf law is influenced by a linear trend and the resulting effect of its slope. We can distinguish finite size effects, and results depending whether the starting FBM is persistent or not, i.e., depending on the FBM Hurst exponent H. It seems then numerically proven that the Zipf exponent of a persistent signal is more influenced by the trend than that of an antipersistent signal. It appears that the conjectured law ζ′ = |2H - 1| only holds near H = 0.5. We have also introduced considerations based on the notion of a time dependent Zipf law along the signal.

The Ramsauer–Townsend effect in hydrogen is used to force the muonic tritium in suggested heterogeneous solid hydrogen–deuterium–tritium (H/D/T) multilayer system to provide resonance muonic deuterium–tritium molecule formation. The written coupled linear point dynamical equations for the suggested system are solved by Monte-Carlo method using "Lsode" computer code. The obtained results for the optimum layer thicknesses and tritium concentration are compared with the results of solid homogeneous deuterium–tritium system in the same physical condition (temperature, density and tritium concentration). It is shown that for the same physical conditions, the muon cycling coefficient of two isotopes of deuterium–tritium (D/T) has only 3% muon cycling coefficient of suggested heterogeneous solid forced H/D/T fusion system. It is shown that with very little tritium concentration (c_t = 0.005) the obtained muon cycling rate and coefficient are ~ 120 μs^-1 and 165 respectively.

Reversible cellular automata are invertible dynamical systems characterized by discreteness, determinism and local interaction. This article studies the local behavior of reversible one-dimensional cellular automata by means of the spectral properties of their connectivity matrices. We use the transformation of every one-dimensional cellular automaton to another of neighborhood size 2 to generalize the results exposed in this paper. In particular we prove that the connectivity matrices have a single positive eigenvalue equal to 1; based on this result we also prove the idempotent behavior of these matrices. The significance of this property lies in the implementation of a matrix technique for detecting whether a one-dimensional cellular automaton is reversible or not. In particular, we present a procedure using the eigenvectors of these matrices to find the inverse rule of a given reversible one-dimensional cellular automaton. Finally illustrative examples are provided.

We present a stability and stochastic analysis of the zigzag map which describes the dynamical behavior of an electrical switching circuit. Analytical expressions are derived for the invariant density and the corresponding Lyapunov exponent for specific parameter values.