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

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

The Unified Method: I Non-Linearizable Problems on the Half-Line

Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the complex $k$-plane (the Fourier plane), which has a jump matrix with explicit $(x,t)$-dependence involving four scalar functions of $k$, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved simply using algebraic manipulations. Here, we present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation, on the analysis of the equations obtained from the global relation via certain transformations leaving the dispersion relation of the associated linearized PDE invariant, and on the computation of the large $k$ asymptotics of the eigenfunctions defining the relevant spectral functions.Comment: 39 page

Pathogenic variants in the AFG3L2 proteolytic domain cause SCA28 through haploinsufficiency and proteostatic stress-driven OMA1 activation

Background: Spinocerebellar ataxia type 28 (SCA28) is a dominantly inherited neurodegenerative disease caused by pathogenic variants in AFG3L2. The AFG3L2 protein is a subunit of mitochondrial m-AAA complexes involved in protein quality control. Objective of this study was to determine the molecular mechanisms of SCA28, which has eluded characterisation to date. Methods: We derived SCA28 patient fibroblasts carrying different pathogenic variants in the AFG3L2 proteolytic domain (missense: the newly identified p.F664S and p.M666T, p.G671R, p.Y689H and a truncating frameshift p.L556fs) and analysed multiple aspects of mitochondrial physiology. As reference of residual m-AAA activity, we included SPAX5 patient fibroblasts with homozygous p.Y616C pathogenic variant, AFG3L2 +/\ue2 ' HEK293 T cells by CRISPR/Cas9-genome editing and Afg3l2 \ue2 '/\ue2 ' murine fibroblasts. Results: We found that SCA28 cells carrying missense changes have normal levels of assembled m-AAA complexes, while the cells with a truncating pathogenic variant had only half of this amount. We disclosed inefficient mitochondrial fusion in SCA28 cells caused by increased OPA1 processing operated by hyperactivated OMA1. Notably, we found altered mitochondrial proteostasis to be the trigger of OMA1 activation in SCA28 cells, with pharmacological attenuation of mitochondrial protein synthesis resulting in stabilised levels of OMA1 and OPA1 long forms, which rescued mitochondrial fusion efficiency. Secondary to altered mitochondrial morphology, mitochondrial calcium uptake resulted decreased in SCA28 cells. Conclusion: Our data identify the earliest events in SCA28 pathogenesis and open new perspectives for therapy. By identifying similar mitochondrial phenotypes between SCA28 cells and AFG3L2 +/- cells, our results support haploinsufficiency as the mechanism for the studied pathogenic variants

Orbital pacing of the Early Jurassic carbon cycle, black-shale formation and seabed methane seepage

The Early Jurassic (ca 201 to 174 Ma) was marked by a series of rapid perturbations in climate, the environment and global geochemical cycles, which have been linked to volcanic outgassing and the release of biogenic or thermogenic methane into the ocean–atmosphere system. The state of the global carbon cycle and prevailing climatic and environmental conditions that existed at this time are, however, poorly constrained. Here, mudrocks of the Lower Sinemurian Arietites bucklandi ammonite Biozone at coastal exposures at Kilve, Somerset, UK, have been studied. This succession includes laminated organic-rich black shales, which are present throughout the Bristol Channel Basin, and coincides with a 2 to 3‰ negative carbon-isotope excursion, distinct changes in inferred land vegetation and abundant marine prasinophytes (green algae). The event itself does not represent a single perturbation of the regional environment, but follows in a sequence of eccentricity-modulated, precession-paced perturbations that occur throughout the preceding Hettangian stage, with the periodic formation of organic-rich laminated black shales in the Bristol Channel Basin. However, the Early Sinemurian event studied herein is more extreme in nature, with sedimentary total organic carbon values of 5 to 11% persisting over about 2 m, representing ca 100 kyr, possibly in phase with short (ca 100 kyr) and long (ca 405 kyr) eccentricity forcing. The formation of methane-seep carbonate-cemented mounds took place relatively soon after the deposition of laminated black shales. Biogenic methane probably formed in response to microbial methanogenesis in the organic-rich black shale, which was subsequently channelled to the sediment–water interface approximately 5 m above the source bed, and ca 200 kyr after cessation of formation of the black shale

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

Precision Measurement of the Beam-Normal Single-Spin Asymmetry in Forward-Angle Elastic Electron-Proton Scattering

A beam-normal single-spin asymmetry generated in the scattering of transversely polarized electrons from unpolarized nucleons is an observable related to the imaginary part of the two-photon exchange process. We report a 2% precision measurement of the beam-normal single-spin asymmetry in elastic electron-proton scattering with a mean scattering angle of theta_lab = 7.9 degrees and a mean energy of 1.149 GeV. The asymmetry result is B_n = -5.194 +- 0.067 (stat) +- 0.082 (syst) ppm. This is the most precise measurement of this quantity available to date and therefore provides a stringent test of two-photon exchange models at far-forward scattering angles (theta_lab -\u3e 0) where they should be most reliable

Science Requirements and Conceptual Design for a Polarized Medium Energy Electron-Ion Collider at Jefferson Lab

This report presents a brief summary of the science opportunities and program of a polarized medium energy electron-ion collider at Jefferson Lab and a comprehensive description of the conceptual design of such a collider based on the CEBAF electron accelerator facility.Comment: 160 pages, ~93 figures This work was supported by the U.S. Department of Energy, Office of Nuclear Physics, under Contract No. DE-AC05-06OR23177, DE-AC02-06CH11357, DE-AC05-060R23177, and DESC0005823. The U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purpose