680 research outputs found
Strichartz estimates for the water-wave problem with surface tension
Strichartz-type estimates for one-dimensional surface water-waves under
surface tension are studied, based on the formulation of the problem as a
nonlinear dispersive equation. We establish a family of dispersion estimates on
time scales depending on the size of the frequencies. We infer that a solution
of the dispersive equation we introduce satisfies local-in-time Strichartz
estimates with loss in derivative:
where depends on and on the norms of the
initial data in . The proof uses the frequency analysis
and semiclassical Strichartz estimates for the linealized water-wave operator.Comment: Fixed typos and mistakes. Merged with arXiv:0809.451
Corrections to the Central Limit Theorem for Heavy-Tailed Probability Densities
Classical Edgeworth expansions provide asymptotic correction terms to the
Central Limit Theorem (CLT) up to an order that depends on the number of
moments available. In this paper, we provide subsequent correction terms beyond
those given by a standard Edgeworth expansion in the general case of regularly
varying distributions with diverging moments (beyond the second). The
subsequent terms can be expressed in a simple closed form in terms of certain
special functions (Dawson's integral and parabolic cylinder functions), and
there are qualitative differences depending on whether the number of moments
available is even, odd or not an integer, and whether the distributions are
symmetric or not. If the increments have an even number of moments, then
additional logarithmic corrections must also be incorporated in the expansion
parameter. An interesting feature of our correction terms for the CLT is that
they become dominant outside the central region and blend naturally with known
large-deviation asymptotics when these are applied formally to the spatial
scales of the CLT
Stability of Circular Orbits in General Relativity: A Phase Space Analysis
Phase space method provides a novel way for deducing qualitative features of
nonlinear differential equations without actually solving them. The method is
applied here for analyzing stability of circular orbits of test particles in
various physically interesting environments. The approach is shown to work in a
revealing way in Schwarzschild spacetime. All relevant conclusions about
circular orbits in the Schwarzschild-de Sitter spacetime are shown to be
remarkably encoded in a single parameter. The analysis in the rotating Kerr
black hole readily exposes information as to how stability depends on the ratio
of source rotation to particle angular momentum. As a wider application, it is
exemplified how the analysis reveals useful information when applied to motion
in a refractive medium, for instance, that of optical black holes.Comment: 20 pages. Accepted for publication in Int. J. theor. Phy
A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions
A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for
the n-point Green functions and the amputated 1PI vertex functions at finite
temperature is derived in the framework of the Closed Time Path formalism. We
verify that this generalized FDT coincides with known results for n=2 and 3.
New explicit relations among the 4-point nonlinear response and correlation
(fluctuation) functions are presented.Comment: 34 pages, Revte
First normal stress difference and crystallization in a dense sheared granular fluid
The first normal stress difference () and the microstructure
in a dense sheared granular fluid of smooth inelastic hard-disks are probed
using event-driven simulations. While the anisotropy in the second moment of
fluctuation velocity, which is a Burnett-order effect, is known to be the
progenitor of normal stress differences in {\it dilute} granular fluids, we
show here that the collisional anisotropies are responsible for the normal
stress behaviour in the {\it dense} limit. As in the elastic hard-sphere
fluids, remains {\it positive} (if the stress is defined in
the {\it compressive} sense) for dilute and moderately dense flows, but becomes
{\it negative} above a critical density, depending on the restitution
coefficient. This sign-reversal of occurs due to the {\it
microstructural} reorganization of the particles, which can be correlated with
a preferred value of the {\it average} collision angle in the direction opposing the shear. We also report on the shear-induced
{\it crystal}-formation, signalling the onset of fluid-solid coexistence in
dense granular fluids. Different approaches to take into account the normal
stress differences are discussed in the framework of the relaxation-type
rheological models.Comment: 21 pages, 13 figure
Anomalous Pseudoscalar-Photon Vertex In and Out of Equilibrium
The anomalous pseudoscalar-photon vertex is studied in real time in and out
of equilibrium in a constituent quark model. The goal is to understand the
in-medium modifications of this vertex, exploring the possibility of enhanced
isospin breaking by electromagnetic effects as well as the formation of neutral
pion condensates in a rapid chiral phase transition in peripheral,
ultrarelativistic heavy-ion collisions. In equilibrium the effective vertex is
afflicted by infrared and collinear singularities that require hard thermal
loop (HTL) and width corrections of the quark propagator. The resummed
effective equilibrium vertex vanishes near the chiral transition in the chiral
limit. In a strongly out of equilibrium chiral phase transition we find that
the chiral condensate drastically modifies the quark propagators and the
effective vertex. The ensuing dynamics for the neutral pion results in a
potential enhancement of isospin breaking and the formation of
condensates. While the anomaly equation and the axial Ward identity are not
modified by the medium in or out of equilibrium, the effective real-time
pseudoscalar-photon vertex is sensitive to low energy physics.Comment: Revised version to appear in Phys. Rev. D. 42 pages, 4 figures, uses
Revte
Evidence of prokineticin dysregulation in fallopian tube from women with ectopic pregnancy
OBJECTIVE: To demonstrate expression and regulation of prokineticins (PROKs) and their receptors (PROKRs) in Fallopian tube (FT) from non-pregnant women and women with ectopic pregnancy (EP). DESIGN: Tissue analysis. SETTING: Large UK teaching hospital PATIENTS: Women undergoing hysterectomy for benign gynecological conditions (n=15) and surgery for EP (n=16). INTERVENTIONS: Quantitative RT-PCR and immunohistochemistry were used to determine FT PROK/PROKR mRNA expression and protein localization, respectively. PROK/PROKR levels were measured in tubal explant cultures stimulated with estrogen and progestogen. MAIN OUTCOME MEASURES: Differential expression of PROK and PROKR. RESULTS: FT PROK2 and PROKR1 mRNA levels were upregulated during the progesterone-dominant mid-luteal phase of the menstrual cycle. Increased PROKR1 expression was observed in tubal explant cultures treated with medroxyprogesterone acetate. PROK and PROKR proteins were localized to the epithelium and smooth muscle layers of the FT. PROKR1 and PROKR2 mRNA levels were lower in FT from women with EP compared to non-pregnant FT from the mid-luteal phase. CONCLUSION: These data suggest a potential role for PROKs in FT function. PROKs are known to affect smooth muscle contraction in the gut. Dysregulated PROK expression in FT could affect FT smooth muscle contractility and embryo-tubal transport, providing a potential cause for EP
Evidence of Color Coherence Effects in W+jets Events from ppbar Collisions at sqrt(s) = 1.8 TeV
We report the results of a study of color coherence effects in ppbar
collisions based on data collected by the D0 detector during the 1994-1995 run
of the Fermilab Tevatron Collider, at a center of mass energy sqrt(s) = 1.8
TeV. Initial-to-final state color interference effects are studied by examining
particle distribution patterns in events with a W boson and at least one jet.
The data are compared to Monte Carlo simulations with different color coherence
implementations and to an analytic modified-leading-logarithm perturbative
calculation based on the local parton-hadron duality hypothesis.Comment: 13 pages, 6 figures. Submitted to Physics Letters
Search for Higgs bosons decaying to tautau pairs in ppbar collisions at sqrt(s) = 1.96 TeV
We present a search for the production of neutral Higgs bosons decaying into
tautau pairs in ppbar collisions at a center-of-mass energy of 1.96 TeV. The
data, corresponding to an integrated luminosity of 5.4 fb-1, were collected by
the D0 experiment at the Fermilab Tevatron Collider. We set upper limits at the
95% C.L. on the product of production cross section and branching ratio for a
scalar resonance decaying into tautau pairs, and we then interpret these limits
as limits on the production of Higgs bosons in the minimal supersymmetric
standard model (MSSM) and as constraints in the MSSM parameter space.Comment: 7 pages, 5 figures, submitted to PL
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