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

Safety, tolerability and pharmacokinetics of eteplirsen in young boys aged 6-48 months with Duchenne muscular dystrophy amenable to exon 51 skipping

Eteplirsen is FDA-approved for the treatment of Duchenne muscular dystrophy (DMD) in exon 51 skip-amenable patients. Previous studies in boys > 4 years of age indicate eteplirsen is well tolerated and attenuates pulmonary and ambulatory decline compared with matched natural history cohorts. Here the safety, tolerability and pharmacokinetics of eteplirsen in boys aged 6–48 months is evaluated. In this open-label, multicenter, dose-escalation study (NCT03218995), boys with a confirmed mutation of the DMD gene amenable to exon 51 skipping (Cohort 1: aged 24–48 months, n = 9; Cohort 2: aged 6 to 4 years of age. These data support the safety and tolerability of eteplirsen at the approved 30-mg/kg dose in boys as young as 6 months old

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)

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

Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 13 pages, no 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

Poloxomer 188 Has a Deleterious Effect on Dystrophic Skeletal Muscle Function

Duchenne muscular dystrophy (DMD) is an X-linked, fatal muscle wasting disease for which there is currently no cure and limited palliative treatments. Poloxomer 188 (P188) is a tri-block copolymer that has been proposed as a potential treatment for cardiomyopathy in DMD patients. Despite the reported beneficial effects of P188 on dystrophic cardiac muscle function, the effects of P188 on dystrophic skeletal muscle function are relatively unknown. Mdx mice were injected intraperitoneally with 460 mg/kg or 30 mg/kg P188 dissolved in saline, or saline alone (control). The effect of single-dose and 2-week daily treatment was assessed using a muscle function test on the Tibialis Anterior (TA) muscle in situ in anaesthetised mice. The test comprises a warm up, measurement of the force-frequency relationship and a series of eccentric contractions with a 10% stretch that have previously been shown to cause a drop in maximum force in mdx mice. After 2 weeks of P188 treatment at either 30 or 460 mg/kg/day the drop in maximum force produced following eccentric contractions was significantly greater than that seen in saline treated control mice (P = 0.0001). Two week P188 treatment at either dose did not significantly change the force-frequency relationship or maximum isometric specific force produced by the TA muscle. In conclusion P188 treatment increases susceptibility to contraction-induced injury following eccentric contractions in dystrophic skeletal muscle and hence its suitability as a potential therapeutic for DMD should be reconsidered