Discrete Breathers

Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices - quantum breathers. Finally we will formulate a new conceptual aproach capable of predicting whether discrete breather exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm

A boundary integral formalism for stochastic ray tracing in billiards

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain

Viability-based computation of spatially constrained minimum time trajectories for an autonomous underwater vehicle: implementation and experiments.

A viability algorithm is developed to compute the constrained minimum time function for general dynamical systems. The algorithm is instantiated for a specific dynamics(Dubin’s vehicle forced by a flow field) in order to numerically solve the minimum time problem. With the specific dynamics considered, the framework of hybrid systems enables us to solve the problem efficiently. The algorithm is implemented in C using epigraphical techniques to reduce the dimension of the problem. The feasibility of this optimal trajectory algorithm is tested in an experiment with a Light Autonomous Underwater Vehicle (LAUV) system. The hydrodynamics of the LAUV are analyzed in order to develop a low-dimension vehicle model. Deployment results from experiments performed in the Sacramento River in California are presented, which show good performance of the algorithm.trajectories; underwater vehicle; viability algorithm; hybrid systems; implementation;

A role for the developing lexicon in phonetic category acquisition

Infants segment words from fluent speech during the same period when they are learning phonetic categories, yet accounts of phonetic category acquisition typically ignore information about the words in which sounds appear. We use a Bayesian model to illustrate how feedback from segmented words might constrain phonetic category learning by providing information about which sounds occur together in words. Simulations demonstrate that word-level information can successfully disambiguate overlapping English vowel categories. Learning patterns in the model are shown to parallel human behavior from artificial language learning tasks. These findings point to a central role for the developing lexicon in phonetic category acquisition and provide a framework for incorporating top-down constraints into models of category learning

Hawking radiation of massive modes and undulations

We compute the analogue Hawking radiation for modes which posses a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This generates an extra mode mixing that occurs in the supersonic region, which cancels out the infrared divergence of the near horizon spectrum. As a result, the amplitude of the undulation (0-frequency wave with macroscopic amplitude) emitted in white hole flows now saturates at the linear level, unlike what was recently found in the massless case. In addition, we point out that the mass introduces a new type of undulation which is produced in black hole flows, and which is well described in the hydrodynamical regime.Comment: 37 pages, 8 figures, published versio