7,959 research outputs found
Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System
We are concerned with rigorous mathematical analysis of shock diffraction by
two-dimensional convex cornered wedges in compressible fluid flow governed by
the nonlinear wave system. This shock diffraction problem can be formulated as
a boundary value problem for second-order nonlinear partial differential
equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be
further reformulated as a free boundary problem for nonlinear degenerate
elliptic equations of second order. We establish a first global theory of
existence and regularity for this shock diffraction problem. In particular, we
establish that the optimal regularity for the solution is across the
degenerate sonic boundary. To achieve this, we develop several mathematical
ideas and techniques, which are also useful for other related problems
involving similar analytical difficulties.Comment: 50 pages;7 figure
Unlimited simultaneous discrimination intervals in regression Technical report no. 90
Unlimited simultaneous discrimination intervals in linear regression
The Big Paper Network Supporting Doctoral Students to Degree Completion
Doctoral completion rates are a concern across disciplines. This paper describes the way in which Curriculum Leadership faculty redesigned their doctoral program from coursework through completion to include a strong support system, intellectually and emotionally. This culminated in the creation of the “Big Paper Network,” designed to support candidates from proposal writing through defense
Oseledets' Splitting of Standard-like Maps
For the class of differentiable maps of the plane and, in particular, for
standard-like maps (McMillan form), a simple relation is shown between the
directions of the local invariant manifolds of a generic point and its
contribution to the finite-time Lyapunov exponents (FTLE) of the associated
orbit. By computing also the point-wise curvature of the manifolds, we produce
a comparative study between local Lyapunov exponent, manifold's curvature and
splitting angle between stable/unstable manifolds. Interestingly, the analysis
of the Chirikov-Taylor standard map suggests that the positive contributions to
the FTLE average mostly come from points of the orbit where the structure of
the manifolds is locally hyperbolic: where the manifolds are flat and
transversal, the one-step exponent is predominantly positive and large; this
behaviour is intended in a purely statistical sense, since it exhibits large
deviations. Such phenomenon can be understood by analytic arguments which, as a
by-product, also suggest an explicit way to point-wise approximate the
splitting.Comment: 17 pages, 11 figure
Non-adiabatic pumping in an oscillating-piston model
We consider the prototypical "piston pump" operating on a ring, where a
circulating current is induced by means of an AC driving. This can be regarded
as a generalized Fermi-Ulam model, incorporating a finite-height moving wall
(piston) and non trivial topology (ring). The amount of particles transported
per cycle is determined by a layered structure of phase-space. Each layer is
characterized by a different drift velocity. We discuss the differences
compared with the adiabatic and Boltzmann pictures, and highlight the
significance of the "diabatic" contribution that might lead to a
counter-stirring effect.Comment: 6 pages, 4 figures, improved versio
Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II
Consider axisymmetric strong solutions of the incompressible Navier-Stokes
equations in with non-trivial swirl. Let denote the axis of symmetry
and measure the distance to the z-axis. Suppose the solution satisfies
either or, for some \e > 0, for and
allowed to be large. We prove that is regular at time zero.Comment: More explanations and a new appendi
Jet fuel property changes and their effect on producibility and cost in the U.S., Canada, and Europe
The effects of changes in properties and blending stocks on the refinery output and cost of jet fuel in the U.S., Canada, and Europe were determined. Computerized refinery models that minimize production costs and incorporated a 1981 cost structure and supply/demand projections to the year 2010 were used. Except in the West U.S., no changes in jet fuel properties were required to meet all projected demands, even allowing for deteriorating crude qualities and changes in competing product demand. In the West U.S., property changes or the use of cracked blendstocks were projected to be required after 1990 to meet expected demand. Generally, relaxation of aromatics and freezing point, or the use of cracked stocks produced similar results, i.e., jet fuel output could be increased by up to a factor of three or its production cost lowered by up to $10/cu m. High quality hydrocracked stocks are now used on a limited basis to produce jet fuel. The conversion of U.S. and NATO military forces from wide-cut to kerosene-based jet fuel is addressed. This conversion resulted in increased costs of several hundred million dollars annually. These costs can be reduced by relaxing kerosene jet fuel properties, using cracked stocks and/or considering the greater volumetric energy content of kerosene jet fuel
Auger de-excitation of metastable molecules at metallic surfaces
We study secondary electron emission from metallic surfaces due to Auger
de-excitation of diatomic metastable molecules. Our approach is based on an
effective model for the two active electrons involved in the process -- a
molecular electron described by a linear combination of atomic orbitals when it
is bound and a two-center Coulomb wave when it is not and a metal electron
described by the eigenfunctions of a step potential -- and employs Keldysh
Green's functions. Solving the Dyson equation for the retarded Green's function
by exponential resummation we are able to treat time-nonlocal self-energies and
to avoid the wide-band approximation.Results are presented for the
de-excitation of \NitrogenDominantMetastableState\ on aluminum and tungsten and
discussed in view of previous experimental and theoretical investigations. We
find quantitative agreement with experimental data for tungsten indicating that
the effective model captures the physics of the process quite well. For
aluminum we predict secondary electron emission due to Auger de-excitation to
be one to two orders of magnitude smaller than the one found for resonant
charge-transfer and subsequent auto-detachment.Comment: 15 pages, 9 figures, revised version using an improved
single-electron basi
Electron heating by sheaths in radio frequency discharges
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Preliminary Evidence That CD38 Moderates the Association of Neuroticism on Amygdala-Subgenual Cingulate Connectivity.
CD38 genetic variation has been associated with autism spectrum disorders and social anxiety disorder, which may result from CD38's regulation of oxytocin secretion. Converging evidence has found that the rs3796863 A-allele contributes to increased social sensitivity compared to the CC genotype. The current study examined the moderating role of CD38 genetic variants (rs3796863 and rs6449182) that have been associated with enhanced (or reduced) social sensitivity on neural activation related to neuroticism, which is commonly elevated in individuals with social anxiety and depression. Adults (n = 72) with varying levels of social anxiety and depression provided biological samples for DNA extraction, completed a measure of neuroticism, and participated in a standardized emotion processing task (affect matching) while undergoing fMRI. A significant interaction effect was found for rs3796863 x neuroticism that predicted right amygdala-subgenual anterior cingulate cortex (sgACC) functional connectivity. Simple slopes analyses showed a positive association between neuroticism and right amygdala-sgACC connectivity among rs3796863 A-allele carriers. Findings suggest that the more socially sensitive rs3796863 A-allele may partially explain the relationship between a known risk factor (i.e. neuroticism) and promising biomarker (i.e. amygdala-sgACC connectivity) in the development and maintenance of social anxiety and depression
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