24,427 research outputs found
Initial-boundary value problems for conservation laws with source terms and the Degasperis-Procesi equation
We consider conservation laws with source terms in a bounded domain with
Dirichlet boundary conditions. We first prove the existence of a strong trace
at the boundary in order to provide a simple formulation of the entropy
boundary condition. Equipped with this formulation, we go on to establish the
well-posedness of entropy solutions to the initial-boundary value problem. The
proof utilizes the kinetic formulation and the compensated compactness method.
Finally, we make use of these results to demonstrate the well-posedness in a
class of discontinuous solutions to the initial-boundary value problem for the
Degasperis-Procesi shallow water equation, which is a third order nonlinear
dispersive equation that can be rewritten in the form of a nonlinear
conservation law with a nonlocal source term.Comment: 24 page
Extending Romanovski polynomials in quantum mechanics
Some extensions of the (third-class) Romanovski polynomials (also called
Romanovski/pseudo-Jacobi polynomials), which appear in bound-state
wavefunctions of rationally-extended Scarf II and Rosen-Morse I potentials, are
considered. For the former potentials, the generalized polynomials satisfy a
finite orthogonality relation, while for the latter an infinite set of
relations among polynomials with degree-dependent parameters is obtained. Both
types of relations are counterparts of those known for conventional
polynomials. In the absence of any direct information on the zeros of the
Romanovski polynomials present in denominators, the regularity of the
constructed potentials is checked by taking advantage of the disconjugacy
properties of second-order differential equations of Schr\"odinger type. It is
also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to
Rosen-Morse I potentials, the variety of rational extensions is narrowed down
from types I, II, and III to type III only.Comment: 25 pages, no figure, small changes, 3 additional references,
published versio
Work distribution for the driven harmonic oscillator with time-dependent strength: Exact solution and slow driving
We study the work distribution of a single particle moving in a harmonic
oscillator with time-dependent strength. This simple system has a non-Gaussian
work distribution with exponential tails. The time evolution of the
corresponding moment generating function is given by two coupled ordinary
differential equations that are solved numerically. Based on this result we
study the behavior of the work distribution in the limit of slow but finite
driving and show that it approaches a Gaussian distribution arbitrarily well
Daytime lidar measurements of tidal winds in the mesospheric sodium layer at Urbana, Illinois
For more than 15 years lidar systems have been used to study the chemistry and dynamics of the mesospheric sodium layer. Because the layer is an excellent tracer of atmospheric wave motions, sodium lidar has proven to be particularly useful for studying the influence of gravity waves and tides on mesospheric dynamics. These waves, which originate in the troposphere and stratosphere, propagate through the mesosphere and dissipate their energy near the mesopause making important contributions to the momentum and turbulence budget in this region of the atmosphere. Recently, the sodium lidar was modified for daytime operation so that wave phenomena and chemical effects could be monitored throughout the complete diurnal cycle. The results of continuous 24 hour lidar observations of the sodium layer structure are presented alond with measurement of the semidiurnal tidal winds
Synaptotagmin 1 Negatively Controls the Two Distinct Immune Secretory Pathways to Powdery Mildew Fungi in Arabidopsis.
Non-Classical Response from Quench-Cooled Solid Helium Confined in Porous Gold
We have investigated the non-classical response of solid 4He confined in
porous gold set to torsional oscillation. When solid helium is grown rapidly,
nearly 7% of the solid helium appears to be decoupled from the oscillation
below about 200 mK. Dissipation appears at temperatures where the decoupling
shows maximum variation. In contrast, the decoupling is substantially reduced
in slowly grown solid helium. The dynamic response of solid helium was also
studied by imposing a sudden increase in the amplitude of oscillation. Extended
relaxation in the resonant period shift, suggesting the emergence of the
pinning of low energy excitations, was observed below the onset temperature of
the non-classical response. The motion of a dislocation or a glassy solid is
restricted in the entangled narrow pores and is not likely responsible for the
period shift and long relaxation
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