Aagesenmunoz8401

The Bonabeau model of self-organized hierarchy formation is studied by using a piecewise linear approximation to the sigmoid function. Simulations of the piecewise-linear agent model show that there exist two-level and three-level hierarchical solutions and that each agent exhibits a transition from nonergodic to ergodic behaviors. Furthermore, by using a mean-field approximation to the agent model, it is analytically shown that there are asymmetric two-level solutions, even though the model equation is symmetric (asymmetry is introduced only through the initial conditions) and that linearly stable and unstable three-level solutions coexist. It is also shown that some of these solutions emerge through supercritical-pitchfork-like bifurcations in invariant subspaces. Existence and stability of the linear hierarchy solution in the mean-field model are also elucidated.A theoretical study is presented for the random aspect of an optical vortex inherent in the nonlinear birefringent Kerr effect, which is called the optical spin vortex. We start with the two-component nonlinear Schrödinger equation. The vortex is inherent in the spin texture caused by an anisotropy of the dielectric tensor, for which the role of spin is played by the Stokes vector (or pseudospin). The evolutional equation is derived for the vortex center coordinate using the effective Lagrangian of the pseudospin field. This is converted to the Langevin equation in the presence of the fluctuation together with the dissipation. The corresponding Fokker-Planck equation is derived and analytically solved for a particular form of the birefringence inspired from the Faraday effect. The main consequence is that the relaxation distance for the distribution function is expressed by the universal constant in the Faraday effect and the size of optical vortex. The result would provide a possible clue for future experimental study in polarization optics from a stochastic aspect.We investigate the forcing strength needed to sustain a flow using linear forcing. A critical Reynolds number R_c is determined, based on the longest wavelength allowed by the system, the forcing strength and the viscosity. A simple model is proposed for the dissipation rate, leading to a closed expression for the kinetic energy of the flow as a function of the Reynolds number. The dissipation model and the prediction for the kinetic energy are assessed using direct numerical simulations and two-point closure integrations. An analysis of the dissipation-rate equation and the triadic structure of the nonlinear transfer allows to refine the model in order to reproduce the low-Reynolds-number asymptotic behavior, where the kinetic energy is proportional to R-R_c.We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearest-neighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the model itself is intended as a simple representation of penetrable particles encountered in realistic soft-matter systems. Our specific focus is on a binary mixture, where particles of the same species repel and those of the opposite species attract each other. As a consequence of penetrability and the unlimited occupation of each site, the system exhibits thermodynamic collapse, which in simulations is manifested by an emergence of extremely dense clusters scattered throughout the system with energy of a cluster E∝-n^2, where n is the number of particles in a cluster. After transforming a particle system into a spin system, in the large density limit the Hamiltonian recovers a simple harmonic form, resulting in the discrete Gaussian model used in the past to model the roughening transition of interfaces. For finite densities, due to the presence of a nonharmonic term, the system is approximated using a variational Gaussian model.A small tagged particle immersed in a fluid exhibits Brownian motion and diffuses on a long timescale. Meanwhile, on a short timescale, the dynamics of the tagged particle cannot be simply described by the usual generalized Langevin equation with Gaussian noise, since the number of collisions between the tagged particle and fluid particles is rather small. On such a timescale, we should explicitly consider individual collision events between the tagged particle and the surrounding fluid particles. In this study we analyze the short-time dynamics of a tagged particle in an ideal gas, where we do not have static or hydrodynamic correlations between fluid particles. We perform event-driven hard-sphere simulations and show that the short-time dynamics of the tagged particle is correlated even under such an idealized situation. Namely, the velocity autocorrelation function becomes negative when the tagged particle is relatively light and the fluid density is relatively high. This result can be attributed to the dynamical correlation between collision events. https://www.selleckchem.com/products/Eloxatin.html To investigate the physical mechanism which causes the dynamical correlation, we analyze the correlation between successive collision events. We find that the tagged particle can collide with the same ideal-gas particle several times and such collisions cause a strong dynamical correlation for the velocity.A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of phase oscillators of distributed frequencies that are globally coupled through the sine of their phase differences. We study here a variation of the model by including nearest-neighbor interactions on a one-dimensional lattice. While the mean-field interaction resulting from the global coupling favors global synchrony, the nearest-neighbor interaction may have cooperative or competitive effects depending on the sign and the magnitude of the nearest-neighbor coupling. For unimodal and symmetric frequency distributions, we demonstrate that as a result, the model in the stationary state exhibits in contrast to the usual Kuramoto model both continuous and first-order transitions between synchronized and incoherent phases, with the transition lines meeting at a tricritical point. Our results are based on numerical integration of the dynamics as well as an approximate theory involving appropriate averaging of fluctuations in the stationary state.