Multi--hump soliton--like structures in interactions of lasers and Bose--Einstein condensates

An investigation is made of multi-hump and periodic solutions of the semi-classical coupled equations describing laser radiation copropagating with a Bose-Einstein condensate. Solutions reminiscent of optical vector solitons have been found and have been used to gain understanding of the dynamics observed in the numerical simulations, in particular to shed light on the phenomenon of jet emission from a condensate interacting with a laser.Comment: 6 pages, 4 figures; submitted to European Physics Letter

Residues in toric varieties

We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X.We first prove a global transformation law for toric residues. When the fan of the toric variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on an appropriate graded piece of the quotient ring. When X is simplicial, we prove that the toric residue is a sum of local residues. In the case of equal degrees, we also show how to represent X as a quotient (Y\{0})/C* such that the toric residue becomes the local residue at 0 in Y

Multi-filament structures in relativistic self-focusing

A simple model is derived to prove the multi-filament structure of relativistic self-focusing with ultra-intense lasers. Exact analytical solutions describing the transverse structure of waveguide channels with electron cavitation, for which both the relativistic and ponderomotive nonlinearities are taken into account, are presented.Comment: 21 pages, 12 figures, submitted to Physical Review

Gestures and words in naming: Evidence from cross-linguistic and cross-cultural comparison

We report on an analysis of spontaneous gesture production in 2-year-old children who come from three countries (Italy, UK and Australia) and whom speak two languages (Italian and English), in an attempt to tease apart the influence of language and culture when comparing children from different cultural and linguistic environments. Eighty-seven monolingual children aged 24-30 months completed an experimental task measuring their comprehension and production of nouns and predicates. The Italian children scored significantly higher than the other groups on all lexical measures. With regards to gestures, British children produced significantly fewer pointing and speech combinations compared to the Italian and Australian children, who did not differ from each other. In contrast, Italian children produced significantly more representational gestures than the two other groups. We conclude that spoken language development is primarily influenced by the input language over gesture production, whereas the combination of cultural and language environments affects gesture productions

Electromagnetic energy penetration in the self-induced transparency regime of relativistic laser-plasma interactions

Two scenarios for the penetration of relativistically intense laser radiation into an overdense plasma, accessible by self-induced transparency, are presented. For supercritical densities less than 1.5 times the critical one, penetration of laser energy occurs by soliton-like structures moving into the plasma. At higher background densities laser light penetrates over a finite length only, that increases with the incident intensity. In this regime plasma-field structures represent alternating electron layers separated by about half a wavelength by depleted regions.Comment: 9 pages, 4 figures, submitted for publication to PR