Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

A STRUCTURE-FROM-MOTION SCHEME THAT LOOKS FOR PARALLELS, AND ITS IMPLICATIONS FOR APPARENT REVERSALS IN ROTATING TRAPEZIA

Apparent reversals in rotating trapezia have been regarded as evidence that human vision favours methods which are heuristic or form dependent. However, the argument is based on the assumption that general algorithmic methods would avoid the illusion, and that has never been clear. A general algorithm for interpreting moving parallels has been developed to address the issue. It handles a considerable range of stimuli successfully, but finds multiple interpretations in situations which correspond closely to those where apparent reversals occur. This strengthens the hypothesis that apparent reversals may occur when general algorithmic methods fail and heuristics are invoked as a stopgap.