Second-order stochastic leapfrog algorithm for multiplicative noise brownian motion

Chaos and noise

Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.

Frustrated brownian motion of nonlocal solitary waves

We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.

Interaction between two inhomogeneously charged parallel surfaces in the strong coupling regime

The counterion density profile and pressure between two inhomogenously charged parallel plates are analyzed analytically and numerically in the strong-coupling regime. Point charges are used and the surface charges are immobile. It is found that when the surface charge distribution is inhomogeneous, the charge coupling effect becomes stronger, the counterion spatial distribution is more localized toward the plate surfaces, and, thus, the pressure between two plates becomes lower than in the case when the surface charge distribution is homogeneous.

Complex light: dynamic phase transitions of a light beam in a nonlinear nonlocal disordered medium

The dynamics of several light filaments (spatial optical solitons) propagating in an optically nonlinear and nonlocal random medium is investigated using the paradigms of the physics of complexity. Cluster formation is interpreted as a dynamic phase transition. A connection with the random matrices approach for explaining the vibrational spectra of an ensemble of solitons is pointed out. General arguments based on a Brownian dynamics model are validated by the numerical simulation of a stochastic partial differential equation system. The results are also relevant for Bose condensed gases and plasma physics.

Quasisymplectic integrators for stochastic differential equations

Two specialized algorithms for the numerical integration of the equations of motion of a Brownian walker obeying detailed balance are introduced. The algorithms become symplectic in the appropriate limits and reproduce the equilibrium distributions to some higher order in the integration time step. Comparisons with other existing integration schemes are carried out both for static and dynamical quantities.

Gibbs attractor: A chaotic nearly Hamiltonian system, driven by external harmonic force

A chaotic autonomous Hamiltonian system, perturbed by small damping and small external force, harmonically dependent on time, can acquire a strange attractor with properties similar to that of the canonical distribution--the Gibbs attractor. The evolution of the energy in such systems can be described as the energy diffusion. For the nonlinear Pullen-Edmonds oscillator with two degrees of freedom, the properties of the Gibbs attractor and their dependence on parameters of the perturbation are studied both analytically and numerically.