International Journal of Modern Physics C

In the framework of vectorial field analysis, the problem of map navigation can be reduced to the construction of the appropriate goal gradients. The solution of the Laplace equation with boundary conditions can be used to build such goal gradients. Inspired by this classical method, we present a more efficient cellular automaton algorithm for robotic map navigation.

We derive catastrophic senescence of the Pacific salmon from an aging model which was recently proposed by Stauffer. The model is based on the postulates of a minimum reproduction age and a maximal genetic lifespan. It allows for self-organization of a typical age of first reproduction and a typical age of death. Our Monte Carlo simulations of the population dynamics show that the model leads to catastrophic senescence for semelparous reproduction as it occurs in the case of salmon, to a more gradually increase of senescence for iteroparous reproduction.

The Coulomb potential is estimated for the tetragonal distortion of the PbFCl-type lattice using Ewald's formula over a large lattice ratio c/a range. The expressions describing the lattice self-potentials for distinct ion sites as functions of c/a are derived by taking into account the regular symmetric crystallization. The obtained results will be useful for elucidate the ionic behavior with high-pressure of this type of layered crystals.

Using a previously introduced model on generalized Lotka–Volterra dynamics together with some recent results for the solution of generalized Langevin equations, we derive analytically the equilibrium mean field solution for the probability distribution of wealth and show that it has two characteristic regimes. For large values of wealth, it takes the form of a Pareto style power law. For small values of wealth, w ≤ w_m, the distribution function tends sharply to zero. The origin of this law lies in the random multiplicative process built into the model. Whilst such results have been known since the time of Gibrat, the present framework allows for a stable power law in an arbitrary and irregular global dynamics, so long as the market is "fair", i.e., there is no net advantage to any particular group or individual.

We further show that the dynamics of relative wealth is independent of the specific nature of the agent interactions and exhibits a universal character even though the total wealth may follow an arbitrary and complicated dynamics.

In developing the theory, we draw parallels with conventional thermodynamics and derive for the system some new relations for the "thermodynamics" associated with the Generalized Lotka–Volterra type of stochastic dynamics. The power law that arises in the distribution function is identified with new additional logarithmic terms in the familiar Boltzmann distribution function for the system. These are a direct consequence of the multiplicative stochastic dynamics and are absent for the usual additive stochastic processes.

Monte Carlo simulations of nucleation and growth processes in an Ising-binary alloy model are presented. The evolution of the cluster size distribution function and its characteristic properties (mean radius and concentration of the clusters) has been investigated from the initial quench into the metastable region of the phase diagram until the establishment of the final equilibrium. All classical stages of nucleation and growth could be observed, the stages of steady-state nucleation, independent growth and Ostwald ripening. A quantitative analysis of the simulational results in terms of the theory of regular solutions shows the validity of classical nucleation theory in the region of the phase diagram considered and provides evidence for a size and structure dependent interfacial tension between the two newly formed phases.

In physical and engineering sciences, the studies of the Korteweg-de Vries (KdV)-typed equations are of crucial significance. Performing computerized symbolic computation, we hereby obtain an auto-Bäcklund transformation for a system of the coupled KdV equations. Sample exact analytic solutions are also presented, which are the rational solutions and solitary waves.

We present a minimal regulatory model for the dynamics of the humoral immune response of two lymphocytes populations (B and T helper) interacting with a specific antigen pool (bacterium). Stability analysis reveals that the system accounts for the occurrence of multiple steady states in the absence as well as in the presence of the antigen population. The model exhibits (i) a state of immune memory, (ii) one state with high antigen and low helper concentration (disease), and (iii) one state with low antigen and high helper concentration (tolerance). The latter state allows oscillatory behavior. Injection of high antigen doses as well as minimal changes of structural parameters provoke the system to jump from the state of disease to the state of tolerance. This is reminiscent of therapies where the patient is treated with allergen, immuno-suppressants or drugs.

The bifurcated, ordered Cayley tree with disorder and frustration as a model for relaxing granular media is examined numerically. Surprisingly, only exponential time dependencies are found despite frustration. Extensions to bidirectional models are discussed extensively and qualitatively new behavior is detected.

An elastic-collision scheme is developed to achieve slip and semi-slip boundary conditions for lattice Boltzmann methods. Like the bounce-back scheme, the proposed scheme is efficient, robust and generally suitable for flows in arbitrary complex geometries. It involves an equivalent level of computation effort to the bounce-back scheme. The new scheme is verified by predicting wind-driven circulating flows in a dish-shaped basin and a flow in a strongly bent channel, showing good agreement with analytical solutions and experimental data. The capability of the scheme for simulating flows through multiple bodies has also been demonstrated.

The scaling behaviors of the percolation cumulant and the surface renormalization are studied on q = 2 and 7 state Potts models. The results show that the scaling functions can be safely used to determine infinite lattice transition points and the thermal and magnetic exponents indicating that these functions have very small correction to scaling contributions.

Recent experiments at the level of a single cell have shown that gene expression occurs in abrupt stochastic bursts. Further, in an ensemble of cells, the levels of proteins produced have a bimodal distribution. In a large fraction of cells, the gene expression is either off or has a high value. We propose a stochastic model of gene expression, the essential features of which are stochasticity and cooperative binding of RNA polymerase. The model can reproduce the bimodal behavior seen in experiments.

Joint ground states of two directed polymers in a random medium are investigated. Using exact min-cost flow optimization, the true two-line ground-state is compared with the single line ground state plus its first excited state with "worst-possible" initial conditions, where the two lines start next to each other. It is found that these two-line configurations are (for almost all disorder configurations) distinct implying that the true two-line ground-state is nonseparable, which means that the two-line ground state cannot be obtained by adding a second line to the first line in the one-line ground state without deforming the first line. The effective interaction energy between the two lines scales with the system size with the scaling exponents 0.39 ± 0.03 and 0.21 ± 0.02 in 2D and 3D, respectively.