1,144 research outputs found
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
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Iron-binding fragments from the N-Terminal and C-Terminal regions of human lactoferrin
Digestion of lactoferrin with pepsin at pH 3.0 gave an iron-binding half-molecule that
represents the C-terminal part of the native protein. Tryptic or chymotryptic digestion
of 30%/-iron-saturated lactoferrin yielded the N- and C-terminal half molecules, which
could be separated by DEAE-Sephadex chromatography. The N- and C-terminal fragments
did not show any immunological cross-reaction. The carbohydrate of lactoferrin
was distributed equally between the two fragments
Computing Linear Matrix Representations of Helton-Vinnikov Curves
Helton and Vinnikov showed that every rigidly convex curve in the real plane
bounds a spectrahedron. This leads to the computational problem of explicitly
producing a symmetric (positive definite) linear determinantal representation
for a given curve. We study three approaches to this problem: an algebraic
approach via solving polynomial equations, a geometric approach via contact
curves, and an analytic approach via theta functions. These are explained,
compared, and tested experimentally for low degree instances.Comment: 19 pages, 3 figures, minor revisions; Mathematical Methods in
Systems, Optimization and Control, Birkhauser, Base
Linearly Coupled Bose-Einstein Condensates: From Rabi Oscillations and Quasi-Periodic Solutions to Oscillating Domain Walls and Spiral Waves
In this paper, an exact unitary transformation is examined that allows for
the construction of solutions of coupled nonlinear Schr{\"o}dinger equations
with additional linear field coupling, from solutions of the problem where this
linear coupling is absent. The most general case where the transformation is
applicable is identified. We then focus on the most important special case,
namely the well-known Manakov system, which is known to be relevant for
applications in Bose-Einstein condensates consisting of different hyperfine
states of Rb. In essence, the transformation constitutes a distributed,
nonlinear as well as multi-component generalization of the Rabi oscillations
between two-level atomic systems. It is used here to derive a host of periodic
and quasi-periodic solutions including temporally oscillating domain walls and
spiral waves.Comment: 6 pages, 4 figures, Phys. Rev. A (in press
Generation Expansion Models including Technical Constraints and Demand Uncertainty
This article presents a Generation Expansion Model of the power system taking into account the operational constraints and the uncertainty of long-term electricity demand projections. The model is based on a discretization of the load duration curve and explicitly considers that power plant ramping capabilities must meet demand variations. A model predictive control method is used to improve the long-term planning decisions while considering the uncertainty of demand projections. The model presented in this paper allows integrating technical constraints and uncertainty in the simulations, improving the accuracy of the results, while maintaining feasible computational time. Results are tested over three scenarios based on load data of an energy retailer in Colombia
Precision Electron-Beam Polarimetry at 1 GeV Using Diamond Microstrip Detectors
We report on the highest precision yet achieved in the measurement of the polarization of a low-energy, O(1 GeV), continuous-wave (CW) electron beam, accomplished using a new polarimeter based on electron-photon scattering, in Hall C at Jefferson Lab. A number of technical innovations were necessary, including a novel method for precise control of the laser polarization in a cavity and a novel diamond microstrip detector that was able to capture most of the spectrum of scattered electrons. The data analysis technique exploited track finding, the high granularity of the detector, and its large acceptance. The polarization of the 180-mu A, 1.16-GeV electron beam was measured with a statistical precision of \u3c 1% per hour and a systematic uncertainty of 0.59%. This exceeds the level of precision required by the Qweak experiment, a measurement of the weak vector charge of the proton. Proposed future low-energy experiments require polarization uncertainty \u3c 0.4%, and this result represents an important demonstration of that possibility. This measurement is the first use of diamond detectors for particle tracking in an experiment. It demonstrates the stable operation of a diamond-based tracking detector in a high radiation environment, for two years
Nonsense mutations in alpha-II spectrin in three families with juvenile onset hereditary motor neuropathy
Distal hereditary motor neuropathies are a rare subgroup of inherited peripheral neuropathies hallmarked by a length-dependent axonal degeneration of lower motor neurons without significant involvement of sensory neurons. We identified patients with heterozygous nonsense mutations in the alpha II-spectrin gene, SPTAN1, in three separate dominant hereditary motor neuropathy families via next-generation sequencing. Variable penetrance was noted for these mutations in two of three families, and phenotype severity differs greatly between patients. The mutant mRNA containing nonsense mutations is broken down by nonsense-mediated decay and leads to reduced protein levels in patient cells. Previously, dominant-negative alpha II-spectrin gene mutations were described as causal in a spectrum of epilepsy phenotypes
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