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.

Music, rhythm, rise time perception and developmental dyslexia: Perception of musical meter predicts reading and phonology

Introduction: Rhythm organises musical events into patterns and forms, and rhythm perception in music is usually studied by using metrical tasks. Metrical structure also plays an organisational function in the phonology of language, via speech prosody, and there is evidence for rhythmic perceptual difficulties in developmental dyslexia. Here we investigate the hypothesis that the accurate perception of musical metrical structure is related to basic auditory perception of rise time, and also to phonological and literacy development in children. Methods: A battery of behavioural tasks was devised to explore relations between musical metrical perception, auditory perception of amplitude envelope structure, phonological awareness (PA) and reading in a sample of 64 typically-developing children and children with developmental dyslexia. Results: We show that individual differences in the perception of amplitude envelope rise time are linked to musical metrical sensitivity, and that musical metrical sensitivity predicts PA and reading development, accounting for over 60% of variance in reading along with age and I.Q. Even the simplest metrical task, based on a duple metrical structure, was performed significantly more poorly by the children with dyslexia. Conclusions: The accurate perception of metrical structure may be critical for phonological development and consequently for the development of literacy. Difficulties in metrical processing are associated with basic auditory rise time processing difficulties, suggesting a primary sensory impairment in developmental dyslexia in tracking the lower-frequency modulations in the speech envelope. © 2010 Elsevier.