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- Institut für Physik und Astronomie (40) (remove)
We investigate localized periodic solutions (breathers) in a lattice of parametrically driven, nonlinear dissipative oscillators. These breathers are demonstrated to be exponentially localized, with two characteristic localization lengths. The crossover between the two lengths is shown to be related to the transition in the phase of the lattice oscillations.
We prove the existence of nonlinear localized time-periodic solutions in a chain of symplectic mappings with nearest neighbour coupling. This is a class of systems whose behaviour can be seen as representation of a lattice of pendula. The effect of discrete time changes the mathematical as well as the numerical procedures. Applying the discrete version of Floquet theory eases and clarifies the procedure of proving the existence of the localized time-periodic solutions. As an extension of the concept of rotobreathers one can produce solutions which rotate at every site of the lattice. To consider these we use a general definition of localization.
We study spatially localized excitations in a lattice of coupled standard maps. Time-periodic solutions (breathers) exist in a range of coupling that is shown to shrink as the period grows to infinity, thus excluding the possibility of time-quasiperiodic breathers. The evolution of initially localized chaotic and quasiperiodic states in a lattice is studied numerically. Chaos is demonstrated to spread
The Problem of front propagation in flowing media is addressed for laminar velocity fields in two dimensions. Three representative cases are discussed: stationary cellular flow, stationary shear flow, and percolating flow. Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius type are considered under the assumption of no feedback of the concentration on the velocity. Numerical simulations of advection-reaction-diffusion equations have been performed by an algorithm based on discrete-time maps. The results show a generic enhancement of the speed of front propagation by the underlying flow. For small molecular diffusivity, the front speed <i>V<sub><i>f</sub> depends on the typical flow velocity <i>U as<sup> </sup>a power law with an exponent depending on the topological properties of the flow, and on the ratio of reactive and advective time scales. For open-streamline flows we find always<sup> </sup><i>V<sub><i>f</sub>~<i>U, whereas for cellular flows we observe <i>V<sub><i>f</ sub>~<i>U<sup>1/4</sup> for fast advection and <i>V<sub><i>f</sub>~<i>U<sup>3/4</sup> for slow advection.
Vortex ripples in sand are studied experimentally in a one-dimensional setup with periodic boundary conditions. The nonlinear evolution, far from the onset of instability, is analyzed in the framework of a simple model developed for homogeneous patterns. The interaction function describing the mass transport between neighboring ripples is extracted from experimental runs using a recently proposed method for data analysis, and the predictions of the model are compared to the experiment. An analytic explanation of the wavelength selection mechanism in the model is provided, and the width of the stable band of ripples is measured.