36,729 research outputs found
Cross-shaped and Degenerate Singularities in an Unstable Elliptic Free Boundary Problem
We investigate singular and degenerate behavior of solutions of the unstable
free boundary problem First, we construct a
solution that is not of class and whose free boundary consists of
four arcs meeting in a {\em cross}-shaped singularity. This solution is
completely unstable/repulsive from above and below which would make it hard to
get by the usual methods, and even numerics is non-trivial. We also show
existence of a degenerate solution. This answers two of the open questions in a
recent paper by R. Monneau-G.S. Weiss
Baffling of fluid sloshing in cylindrical tanks Final report
Annular baffle for damping liquid oscillations in partially filled cylindrical tan
Identification of Coulomb blockade and macroscopic quantum tunneling by noise
The effects of Macroscopic Quantum Tunneling (MQT) and Coulomb Blockade (CB)
in Josephson junctions are of considerable significance both for the
manifestations of quantum mechanics on the macroscopic scale and potential
technological applications. These two complementary effects are shown to be
clearly distinguishable from the associated noise spectra. The current noise is
determined exactly and a rather sharp crossover between flux noise in the MQT
and charge noise in the CB regions is found as the applied voltage is changed.
Related results hold for the voltage noise in current-biased junctions.Comment: 6 pages, 3 figures, epl.cls include
Non-classical symmetries and the singular manifold method: A further two examples
This paper discusses two equations with the conditional Painleve property.
The usefulness of the singular manifold method as a tool for determining the
non-classical symmetries that reduce the equations to ordinary differential
equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics
Realizing vector meson dominance with transverse charge densities
The transverse charge density in a fast-moving nucleon is represented as a
dispersion integral of the imaginary part of the Dirac form factor in the
timelike region (spectral function). At a given transverse distance b the
integration effectively extends over energies in a range sqrt{t} ~< 1/b, with
exponential suppression of larger values. The transverse charge density at
peripheral distances thus acts as a low-pass filter for the spectral function
and allows one to select energy regions dominated by specific t-channel states,
corresponding to definite exchange mechanisms in the spacelike form factor. We
show that distances b ~ 0.5 - 1.5 fm in the isovector density are maximally
sensitive to the rho meson region, with only a ~10% contribution from
higher-mass states. Soft-pion exchange governed by chiral dynamics becomes
relevant only at larger distances. In the isoscalar density higher-mass states
beyond the omega are comparatively more important. The dispersion approach
suggests that the positive transverse charge density in the neutron at b ~ 1
fm, found previously in a Fourier analysis of spacelike form factor data, could
serve as a sensitive test of the the isoscalar strength in the ~1 GeV mass
region. In terms of partonic structure, the transverse densities in the vector
meson region b ~ 1 fm support an approximate mean-field picture of the motion
of valence quarks in the nucleon.Comment: 14 pages, 12 figure
Scaling and data collapse for the mean exit time of asset prices
We study theoretical and empirical aspects of the mean exit time of financial
time series. The theoretical modeling is done within the framework of
continuous time random walk. We empirically verify that the mean exit time
follows a quadratic scaling law and it has associated a pre-factor which is
specific to the analyzed stock. We perform a series of statistical tests to
determine which kind of correlation are responsible for this specificity. The
main contribution is associated with the autocorrelation property of stock
returns. We introduce and solve analytically both a two-state and a three-state
Markov chain models. The analytical results obtained with the two-state Markov
chain model allows us to obtain a data collapse of the 20 measured MET profiles
in a single master curve.Comment: REVTeX 4, 11 pages, 8 figures, 1 table, submitted for publicatio
Backlund transformation and special solutions for Drinfeld-Sokolov-Satsuma-Hirota system of coupled equations
Using the Weiss method of truncated singular expansions, we construct an
explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system
into itself. Then we find all the special solutions generated by this
transformation from the trivial zero solution of this system.Comment: LaTeX, 5 page
Stability of Phases in the Si-C-N-O System
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65891/1/j.1151-2916.1988.tb07532.x.pd
Deformation of grain boundaries in polar ice
The ice microstructure (grain boundaries) is a key feature used to study ice
evolution and to investigate past climatic changes. We studied a deep ice core,
in Dome Concordia, Antarctica, which records past mechanical deformations. We
measured a "texture tensor" which characterizes the pattern geometry and
reveals local heterogeneities of deformation along the core. These results
question key assumptions of the current models used for dating
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