International Journal of Modern Physics C

The probabilistic model of epidemic in a two-dimensional lattice with an additional random, long range connections characteristic for the small world networks is presented. Relations describing the spreading process of epidemics, like epidemic curve or range of epidemic in time, were found. The influence of the borders of the lattice and the localization of the initial source of epidemic on the epidemic curve is found analytically. The application of the preventive vaccination in the population is discussed.

We propose a mechanism of opinion evolution in a closed system. The opinion evolution process can be described as the disposal of multi-information inputs with one opinion accepted as the output. We introduce the opinion neutrality in the system, observing the characteristics of the opinion evolution process; and find that the initial opinion distribution fractions play an important role in the final results. When the two opposite opinions' fraction are equal, the neutrality fraction will affect the final opinion distribution dramatically.

Equilibrium geometries, stabilities, electronic and magnetic properties of Ti_nAl (n=1–8) clusters have been studied by using density-functional theory (DFT). The ground-state structures of Ti_nAl clusters have been obtained. The resulting geometries show that the aluminum atom remains on the surface of clusters. The evolution of energy difference and gap (HOMO–LUMO) with size of cluster shows Ti₄Al cluster to be endowed with special stability. The average magnetic moments and the density of states (DOS) are also presented.

Novel procedures to determine the parallel upper critical field B_c2 (one-dimensional, 1D) have been proposed within a continuous Ginzburg–Landau model. Unlike conventional methods, where B_c2 is obtained through the determination of the smallest eigenvalue of an appropriate eigen equation, the square of the magnetic field is treated as eigenvalue problems by two procedures so that the upper critical field can be directly deduced. The two procedures proposed are extended to determine the upper critical field in the c–a crystal plane (two-dimensional, 2D) with an arbitrary angle θ tilted from the c-axis.

The calculated B_c2 from the two procedures are consistent with each other in both 1D and 2D cases. Moreover, the values of B_c2 near the direction parallel to the layers obtained in the 2D case well approximate the counterparts in the 1D case. The properties of the calculated B_c2 are in reasonably good agreement with existing theories and experiments. The profiles of the order parameters associated with B_c2 for both 1D and 2D cases are Gaussian-like, further validating the methodology proposed.

We show that, provided one focuses on properly selected episodes, one can apply to the social sciences the same observational strategy that has proved successful in natural sciences such as astrophysics or geodynamics. For instance, in order to probe the cohesion of a society, one can, in different countries, study the reactions to some huge and sudden exogenous shocks, which we call Dirac shocks. This approach naturally leads to the notion of structural (as opposed or complementary to temporal) forecast. Although structural predictions are by far the most common way to test theories in the natural sciences, they have been much less used in the social sciences. The Dirac shock approach opens the way to testing structural predictions in the social sciences. The examples reported here suggest that critical events are able to reveal pre-existing "cracks" because they probe the social cohesion which is an indicator and predictor of future evolution of the system, and in some cases they foreshadow a bifurcation. We complement our empirical work with numerical simulations of the response function ("damage spreading") to Dirac shocks in the Sznajd model of consensus build-up. We quantify the slow relaxation of the difference between perturbed and unperturbed systems, the conditions under which the consensus is modified by the shock and the large variability from one realization to another.

We investigate the coarsening dynamics of the Ising model on the honeycomb lattice by Monte Carlo simulation. Although the domain growth law and the persistence exponent at nonzero finite temperature are consistent with the known values of the two-dimensional (2D) Ising model on the square lattice, the nonequilibrium relaxation behavior of this model however shows the interesting and different relaxation properties of two-step relaxation due to the pinning effect and the slow activation process at a low temperature. Multispin heat bath dynamics is used to remove such a pinning effect, which results in the same relaxation behavior of the 2D Ising model as on the square lattice.

We study the stabilization of nonchaotic periodic and quasi-periodic solutions of both integrable (α=1) and nonintegrable (α=2/3) of CCNLS equations of the form:

In this modification of the Sznajd consensus model on the square lattice, two people of arbitrary distance who agree in their opinions convince their nearest neighbors of this opinion. Similarly to the mean field theory of Slanina and Lavicka, the times needed to reach consensus are distributed exponentially and are quite small. The width of the phase transition vanishes reciprocally to the linear lattice dimension. Advertising has effects independent of the system size. For more than two opinions, three opinions reach a consensus in roughly half of the samples, and four only rarely and only for small lattices. Up to 10⁹ agents were simulated.

This paper addresses the synchronization problem of two coupled dynamos systems in the presence of unknown system parameters. Based on Lyapunov stability theory, an active control law is derived and activated to achieve the state synchronization of two identical coupled dynamos systems. By using Gerschgorin theorem, a simple generic criterion is derived for global synchronization of two coupled dynamos systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems, where only a few algebraic inequalities are involved. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.

Lattice simulation is one important method to investigate the universal principle of protein folding. The move set is a basic element in lattice simulation. We used two move sets, dynamic move set and rigid rotation move, to run simulation and compare the thermodynamic and kinetic properties. The results indicate that the dynamic move set has advantage to simulate protein folding.

Cellular Automata (CA) are a promising architecture for computers with nanometer-scale sized components, because their regular structure potentially allows chemical manufacturing techniques based on self-organization. With the increase in integration density, however, comes a decrease in the reliability of the components from which such computers will be built. This paper employs BCH error-correcting codes to construct CA with improved reliability. We construct an asynchronous CA of which a quarter of the (ternary) bits storing a cell's state information may be corrupted without affecting the CA's operations, provided errors are evenly distributed over a cell's bits (no burst errors allowed). Under the same condition, the corruption of half of a cell's bits can be detected.

Using an empirical potential energy function parametrized for each of the Ni, Cu, Pd, Pt, and Pb systems, minimum-energy structures of Ni_n, Cu_n, Pd_n, Pt_n, and Pb_n (n=3–13) microclusters have been determined by performing molecular-dynamics simulations. The structural and energetic features of the obtained microclusters have been investigated.