3,825 research outputs found
Stable self-similar blow-up dynamics for slightly -supercritical generalized KdV equations
In this paper we consider the slightly -supercritical gKdV equations
, with the nonlinearity
and . We will prove the existence and
stability of a blow-up dynamic with self-similar blow-up rate in the energy
space and give a specific description of the formation of the singularity
near the blow-up time.Comment: 38 page
Regular coordinate systems for Schwarzschild and other spherical spacetimes
The continuation of the Schwarzschild metric across the event horizon is
almost always (in textbooks) carried out using the Kruskal-Szekeres
coordinates, in terms of which the areal radius r is defined only implicitly.
We argue that from a pedagogical point of view, using these coordinates comes
with several drawbacks, and we advocate the use of simpler, but equally
effective, coordinate systems. One such system, introduced by Painleve and
Gullstrand in the 1920's, is especially simple and pedagogically powerful; it
is, however, still poorly known today. One of our purposes here is therefore to
popularize these coordinates. Our other purpose is to provide generalizations
to the Painleve-Gullstrand coordinates, first within the specific context of
Schwarzschild spacetime, and then in the context of more general spherical
spacetimes.Comment: 5 pages, 2 figures, ReVTeX; minor changes were made, new references
were include
Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability
A real hyperbolic system is considered that applies near the onset of the oscillatory instability in large spatial domains. The validity of that system requires that some intermediate scales (large compared with the basic wavelength of the unstable modes but small compared with the size of the system) remain inhibited; that condition is analysed in some detail. The dynamics associated with the hyperbolic system is fully analysed to conclude that it is very simple if the coefficient of the cross-nonlinearity is such that , while the system exhibits increasing complexity (including period-doubling sequences, quasiperiodic transitions, crises) as the bifurcation parameter grows if ; if then the system behaves subcritically. Our results are seen to compare well, both qualitatively and quantitatively, with the experimentally obtained ones for the oscillatory instability of straight rolls in pure Rayleigh - BĂ©nard convection
Giacobini-Zinner comet: Polarimetric and physical observations
The results of observations of the Giacobini-Zinner comet on 25 and 31 October 1959 are presented. The magnitude of the comet was measured photoelectrically in two spectral regions. The radius is on the order of one kilometer. The photoelectric measurements of comets 1959b and 1957c were used to measure the abundances of the CN and C2 radicals and of solid particles in the heads
Gravitational perturbations of the Schwarzschild spacetime: A practical covariant and gauge-invariant formalism
We present a formalism to study the metric perturbations of the Schwarzschild
spacetime. The formalism is gauge invariant, and it is also covariant under
two-dimensional coordinate transformations that leave the angular coordinates
unchanged. The formalism is applied to the typical problem of calculating the
gravitational waves produced by material sources moving in the Schwarzschild
spacetime. We examine the radiation escaping to future null infinity as well as
the radiation crossing the event horizon. The waveforms, the energy radiated,
and the angular-momentum radiated can all be expressed in terms of two
gauge-invariant scalar functions that satisfy one-dimensional wave equations.
The first is the Zerilli-Moncrief function, which satisfies the Zerilli
equation, and which represents the even-parity sector of the perturbation. The
second is the Cunningham-Price-Moncrief function, which satisfies the
Regge-Wheeler equation, and which represents the odd-parity sector of the
perturbation. The covariant forms of these wave equations are presented here,
complete with covariant source terms that are derived from the stress-energy
tensor of the matter responsible for the perturbation. Our presentation of the
formalism is concluded with a separate examination of the monopole and dipole
components of the metric perturbation.Comment: 21 page
GePEToS : A Geant4 Monte Carlo simulation package for Positron Emission Tomography
GePEToS is a simulation framework developed over the last few years for
assessing the instrumental performance of future PET scanners. It is based on
Geant4, written in Object-Oriented C++ and runs on Linux platforms. The
validity of GePEToS has been tested on the well-known Siemens ECAT EXACT HR+
camera. The results of two application examples are presented : the design
optimization of a liquid Xe micro-PET camera dedicated to small animal imaging
as well as the evaluation of the effect of a strong axial magnetic field on the
image resolution of a Concorde P4 micro-PET camera.Comment: 5 pages, 12 figures, submitted to IEEE Transactions on Nuclear
Scienc
Experimental study of a liquid Xenon PET prototype module
A detector using liquid Xenon in the scintillation mode is studied for
Positron Emission Tomography (PET). The specific design aims at taking full
advantage of the liquid Xenon properties. It does feature a promising
insensitive to any parallax effect. This work reports on the performances of
the first LXe prototype module, equipped with a position sensitive PMT
operating in the VUV range (178 nm).Comment: Proc. of the 7th International Workshops on Radiation Imaging
Detectors (IWORID-7), Grenoble, France 4-7 July 200
Non-volatile molecular memory elements based on ambipolar nanotube field effect transistors
We have fabricated air-stable n-type, ambipolar carbon nanotube field effect
transistors (CNFETs), and used them in nanoscale memory cells. N-type
transistors are achieved by annealing of nanotubes in hydrogen gas and
contacting them by cobalt electrodes. Scanning gate microscopy reveals that the
bulk response of these devices is similar to gold-contacted p-CNFETs,
confirming that Schottky barrier formation at the contact interface determines
accessibility of electron and hole transport regimes. The transfer
characteristics and Coulomb Blockade (CB) spectroscopy in ambipolar devices
show strongly enhanced gate coupling, most likely due to reduction of defect
density at the silicon/silicon-dioxide interface during hydrogen anneal. The CB
data in the ``on''-state indicates that these CNFETs are nearly ballistic
conductors at high electrostatic doping. Due to their nanoscale capacitance,
CNFETs are extremely sensitive to presence of individual charge around the
channel. We demonstrate that this property can be harnessed to construct data
storage elements that operate at the few-electron level.Comment: 6 pages text, 3 figures and 1 table of content graphic; available as
NanoLetters ASAP article on the we
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