Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schrodinger equation

The two-dimensional cubic nonlinear Schrodinger equation admits a large family of one-dimensional bounded traveling-wave solutions. All such solutions may be written in terms of an amplitude and a phase. Solutions with piecewise constant phase have been well studied previously. Some of these solutions were found to be stable with respect to one-dimensional perturbations. No such solutions are stable with respect to two-dimensional perturbations. Here we consider stability of the larger class of solutions whose phase is dependent on the spatial dimension of the one-dimensional wave form. We study the spectral stability of such nontrivial-phase solutions numerically, using Hill's method. We present evidence which suggests that all such nontrivial-phase solutions are unstable with respect to both one- and two-dimensional perturbations. Instability occurs in all cases: for both the elliptic and hyperbolic nonlinear Schrodinger equations, and in the focusing and defocusing case.Comment: Submitted: 13 pages, 3 figure

Relative age, biological maturation and anaerobic characteristics in elite youth soccer players

Being relatively older and having an advanced biological maturation status have been associated with increased likelihood of selection in young elite soccer players. The aims of the study were to investigate the presence of a relative age effect (RAE) and the influence of birth quarter on anthropometry, biological maturity and anaerobic parameters in 374 elite Belgian youth soccer players. The sample was divided into 3 age groups, each subdivided into 4 birth quarters (BQ). Players had their APHV estimated and height, weight, SBJ, CMJ, sprint 5 and 30 m were assessed. Overall, more players were born in BQ1 (42.3%) compared with players born in BQ4 (13.7%). Further, MANCOVA revealed no differences in all parameters between the 4 BQ's, controlled for age and APHV. These results suggest that relatively youngest players can offset the RAE if they enter puberty earlier. Furthermore, the results demonstrated possible differences between BQ1 and BQ4, suggesting that caution is necessary when estimating differences between players because of large discrepancies between statistical and practical significance. These findings also show that coaches should develop realistic expectations of the physical abilities of younger players and these expectations should be made in the context of biological characteristics rather than chronological age-based standards. © Georg Thieme Verlag KG Stuttgart. New York

Pole dynamics for the Flierl-Petviashvili equation and zonal flow

We use a systematic method which allows us to identify a class of exact solutions of the Flierl-Petvishvili equation. The solutions are periodic and have one dimensional geometry. We examine the physical properties and find that these structures can have a significant effect on the zonal flow generation.Comment: Latex 40 pages, seven figures eps included. Effect of variation of g_3 is studied. New references adde

Vortices in Bose-Einstein Condensates: Some Recent Developments

In this brief review we summarize a number of recent developments in the study of vortices in Bose-Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices we also consider the existence of stable dipole clusters for two-component condensates. Last but not least, we discuss mesoscopic patterns formed by vortices, the so-called vortex lattices and analyze some of their intriguing dynamical features. A number of interesting future directions are highlighted.Comment: 24 pages, 8 figs, ws-mplb.cls, to appear in Modern Physics Letters B (2005

Climatic and palaeoceanographic changes during the Pliensbachian (Early Jurassic) 2 inferred from clay mineralogy and stable isotope (C-O) geochemistry (NW Europe)

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Available online 17 January 2017The Early Jurassic was broadly a greenhouse climate period that was punctuated by short warm and cold climatic events, positive and negative excursions of carbon isotopes, and episodes of enhanced organic matter burial. Clay minerals from Pliensbachian sediments recovered from two boreholes in the Paris Basin, are used here as proxies of detrital supplies, runoff conditions, and palaeoceanographic changes. The combined use of these minerals with ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT stable isotope data (C-O) from bulk carbonates and organic matter allows palaeoclimatic reconstructions to be refined for the Pliensbachian. Kaolinite/illite ratio is discussed as a reliable proxy of the hydrological cycle and runoff from landmasses. Three periods of enhanced runoff are recognised within the Pliensbachian. The first one at the SinemurianPliensbachian transition shows a significant increase of kaolinite concomitant with the negative carbon isotope excursion at the so-called Sinemurian Pliensbachian Boundary Event (SPBE). The Early/Late Pliensbachian transition was also characterised by more humid conditions. This warm interval is associated with a major change in oceanic circulation during the Davoei Zone, likely triggered by sea-level rise; the newly created palaeogeography, notably the flooding of the London-Brabant Massif, allowed boreal detrital supplies, including kaolinite and chlorite, to be exported to the Paris Basin. The last event of enhanced runoff occurred during the late Pliensbachian (Subdonosus Subzone of the Margaritatus Zone), which occurred also during a warm period, favouring organic matter production and preservation. Our study highlights the major role of the London Brabant Massif in influencing oceanic circulation of the NW European area, as a topographic barrier (emerged lands) during periods of lowstand sea-level and its flooding during period of high sea-level. This massif was the unique source of smectite in the Paris Basin. Two episodes of smectite-rich sedimentation (‘smectite events’), coincide with regressive intervals, indicating emersion of the London Brabant Massif and thus suggesting that an amplitude of sea-level change high enough to be linked to glacio-eustasy. This mechanism is consistent with sedimentological and geochemical evidences of continental ice growth notably during the Latest Pliensbachian (Spinatum Zone), and possibly during the Early Pliensbachian (late Jamesoni/early Ibex Zones).The study was supported by the “Agence Nationale pour la Gestion des Déchets Radioactifs” (Andra––French National Radioactive Waste Management Agency)

Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential

We present a new family of stationary solutions to the cubic nonlinear Schroedinger equation with a Jacobian elliptic function potential. In the limit of a sinusoidal potential our solutions model a dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided the ratio of the height of the variations of the condensate to its DC offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Numerical simulations suggest such stationary states are experimentally observable.Comment: 4 pages, 4 figure

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schr\"odinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.Comment: 12 pages, 17 figure