834 research outputs found
Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems
Explicit Runge-Kutta schemes with large stable step sizes are developed for
integration of high order spectral difference spatial discretization on
quadrilateral grids. The new schemes permit an effective time step that is
substantially larger than the maximum admissible time step of standard explicit
Runge-Kutta schemes available in literature. Furthermore, they have a small
principal error norm and admit a low-storage implementation. The advantages of
the new schemes are demonstrated through application to the Euler equations and
the linearized Euler equations.Comment: 37 pages, 3 pages of appendi
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
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
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
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
EM Calorimeters for SoLID at Jefferson Lab
Several approved experiments at Jefferson Lab for the 12 GeV era will use the proposed Solenoid Large Intensity Device (SoLID) spectrometer. Two EM calorimeters with a total area of 15 square meters are required for electron identification and electron-pion separation. The challenge is to build calorimeters that can withstand high radiation doses in high magnetic field region and bring photon signals to low field region for readout. Several types of calorimeters were considered and we are favoring Shashlyk type as a result of balancing performance and cost. Our preliminary design and simulation of SoLID EM calorimeters are presented
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
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