5,577 research outputs found
The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator
We establish the existence of the asymptotic expansion of the Bergman kernel
associated to the spin-c Dirac operators acting on high tensor powers of line
bundles with non-degenerate mixed curvature (negative and positive eigenvalues)
by extending the paper " On the asymptotic expansion of Bergman kernel "
(math.DG/0404494) of Dai-Liu-Ma. We compute the second coefficient b_1 in the
asymptotic expansion using the method of our paper "Generalized Bergman kernels
on symplectic manifolds" (math.DG/0411559).Comment: 21 pages, to appear in Internat. J. Math. Precisions added in the
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Evidence of Raleigh-Hertz surface waves and shear stiffness anomaly in granular media
Due to the non-linearity of Hertzian contacts, the speed of sound in granular
matter increases with pressure. Under gravity, the non-linear elastic
description predicts that acoustic propagation is only possible through surface
modes, called Rayleigh-Hertz modes and guided by the index gradient. Here we
directly evidence these modes in a controlled laboratory experiment and use
them to probe the elastic properties of a granular packing under vanishing
confining pressure. The shape and the dispersion relation of both transverse
and sagittal modes are compared to the prediction of non-linear elasticity that
includes finite size effects. This allows to test the existence of a shear
stiffness anomaly close to the jamming transition.Comment: 4 pages 4 figure
Rate-Control or Rhythm-Contol: Where do we stand?
Atrial fibrillation is the most common sustained rhythm disturbance and its prevalence is increasing worldwide due to the progressive aging of the population. Current guidelines clearly depict the gold standard management of acute symptomatic atrial fibrillation but the best-long term approach for first or recurrent atrial fibrillation is still debated with regard to quality of life, risk of new hospitalizations, and possible disabling complications, such as thromboembolic stroke, major bleeds and death. Some authors propose that regaining sinus rhythm in all cases, thus re-establishing a physiologic cardiac function not requiring a prolonged antithrombotic therapy, avoids the threat of intracranial or extracranial haemorrhages due to Vitamin K antagonists or aspirin. On the contrary, advocates of a rate control approach with an accurate antithrombotic prophylaxis propose that such a strategy may avoid the risk of cardiovascular and non cardiovascular side effects related to antiarrhythmic drugs. This review aims to explore the state of our knowledge in order to summarize evidences and issues that need to be furthermore clarified
Erosion waves: transverse instabilities and fingering
Two laboratory scale experiments of dry and under-water avalanches of
non-cohesive granular materials are investigated. We trigger solitary waves and
study the conditions under which the front is transversally stable. We show the
existence of a linear instability followed by a coarsening dynamics and finally
the onset of a fingering pattern. Due to the different operating conditions,
both experiments strongly differ by the spatial and time scales involved.
Nevertheless, the quantitative agreement between the stability diagram, the
wavelengths selected and the avalanche morphology reveals a common scenario for
an erosion/deposition process.Comment: 4 pages, 6 figures, submitted to PR
Contact angles on a soft solid: from Young's law to Neumann's law
The contact angle that a liquid drop makes on a soft substrate does not obey
the classical Young's relation, since the solid is deformed elastically by the
action of the capillary forces. The finite elasticity of the solid also renders
the contact angles different from that predicted by Neumann's law, which
applies when the drop is floating on another liquid. Here we derive an
elasto-capillary model for contact angles on a soft solid, by coupling a
mean-field model for the molecular interactions to elasticity. We demonstrate
that the limit of vanishing elastic modulus yields Neumann's law or a slight
variation thereof, depending on the force transmission in the solid surface
layer. The change in contact angle from the rigid limit (Young) to the soft
limit (Neumann) appears when the length scale defined by the ratio of surface
tension to elastic modulus reaches a few molecular sizes
CLEO Spectroscopy Results
Recent contributions of the CLEO experiment to hadron spectroscopy are
presented.Comment: 6 pages, 4 figures, presented at Beauty 2005, Assisi, Italy, 20--24
June 2005 References further update
Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds
We consider an abstract compact orientable Cauchy-Riemann manifold endowed
with a Cauchy-Riemann complex line bundle. We assume that the manifold
satisfies condition Y(q) everywhere. In this paper we obtain a scaling
upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high
tensor powers of the line bundle. This gives after integration weak Morse
inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a
refined spectral analysis we obtain also strong Morse inequalities which we
apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a
multiplicative constant 1/2 ; v.2 is a final updat
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