68,937 research outputs found
B to tensor meson form factors in the perturbative QCD approach
We calculate the form factors within the framework of the
perturbative QCD approach, where denotes a light tensor meson with
. Due to the similarities between the wave functions of a vector and a
tensor meson, the factorization formulas of form factors can be
obtained from the transition through a replacement rule. As a
consequence, we find that these two sets of form factors have the same signs
and correlated -dependence behaviors. At point, the form
factors are smaller than the ones, in accordance with the experimental
data of radiative B decays. In addition, we use our results for the form
factors to explore semilteptonic decays and the branching
fractions can reach the order .Comment: 13 pages, 3 figures, 6 tables, published versio
Existence and stability analysis of spiky solutions for the Gierer-Meinhardt system with large reaction rates
We study the Gierer-Meinhardt system in one dimension in the limit of large reaction rates. First we construct three types of solutions: (i) an interior spike; (ii) a boundary spike and (iii) two boundary spikes. Second we prove results on their stability. It is found that an interior spike is always unstable; a boundary spike is always stable. The two boundary spike configuration can be either stable or unstable, depending on the parameters. We fully classify the stability in this case. We characterise the destabilizing eigenfunctions in all cases. Numerical simulations are shown which are in full agreement with the analytical results
Diverse Temporal Properties of GRB Afterglow
The detection of delayed X-ray, optical and radio emission, "afterglow",
associated with -ray bursts (GRBs) is consistent with fireball models,
where the emission are produced by relativistic expanding blast wave, driven by
expanding fireball at cosmogical distances. The emission mechanisms of GRB
afterglow have been discussed by many authors and synchrotron radiation is
believed to be the main mechanism. The observations show that the optical light
curves of two observed gamma-ray bursts, GRB970228 and GRB GRB970508, can be
described by a simple power law, which seems to support the synchrotron
radiation explanation. However, here we shall show that under some
circumstances, the inverse Compton scattering (ICS) may play an important role
in emission spectrum and this may influence the temporal properties of GRB
afterglow. We expect that the light curves of GRB afterglow may consist of
multi-components, which depends on the fireball parameters.Comment: Latex, no figures, minor correctio
Can the jet steepen the light curves of GRB afterglow?
Beaming of relativistic ejecta in GRBs has been postulated by many authors in
order to reduce the total GRB energy, thus it is very important to look for the
observational evidence of beaming. Rhoads (1999) has pointed out that the
dynamics of the blast wave, which is formed when the beamed ejecta sweeping the
external medium, will be significantly modified by the sideways expansion due
to the increased swept up matter. He claimed that shortly after the bulk
Lorentz factor () of the blast wave drops below the inverse of the
initial opening angle () of the beamed ejecta, there will be a
sharp break in the afterglow light curves. However, some other authors have
performed numerical calculations and shown that the break of the light curve is
weaker and much smoother than the one analytically predicted. In this paper we
reanalyse the dynamical evolution of the jet blast wave, calculate the jet
emission analytically, we find that the sharp break predicted by Rhoads will
actually not exist, and for most cases the afterglow light curve will almost
not be affected by sideways expansion unless the beaming angle is extremely
small. We demonstrate that only when , the afterglow light
curves may be steepened by sideways expansion, and in fact there cannot be two
breaks as claimed before. We have also constructed a simple numerical code to
verify our conclusion.Comment: 12 pages, 2 figures, accepted by ApJ, added numerical calculation
Measures of entanglement in multipartite bound entangled states
Bound entangled states are states that are entangled but from which no
entanglement can be distilled if all parties are allowed only local operations
and classical communication. However, in creating these states one needs
nonzero entanglement resources to start with. Here, the entanglement of two
distinct multipartite bound entangled states is determined analytically in
terms of a geometric measure of entanglement and a related quantity. The
results are compared with those for the negativity and the relative entropy of
entanglement.Comment: 5 pages, no figure; title change
Existence and Stability of a Spike in the Central Component for a Consumer Chain Model
We study a three-component consumer chain model which is based on Schnakenberg type kinetics. In this model there is one consumer feeding on the producer and a second consumer feeding on the first consumer. This means that the first consumer (central component) plays a hybrid role: it acts both as consumer and producer. The model is an extension of the Schnakenberg model suggested in \cite{gm,schn1} for which there is only one producer and one consumer. It is assumed that both the producer and second consumer diffuse much faster than the central component. We construct single spike solutions on an interval for which the profile of the first consumer is that of a spike. The profiles of the producer and the second consumer only vary on a much larger spatial scale due to faster diffusion of these components. It is shown that there exist two different single spike solutions if the feed rates are small enough: a large-amplitude and a small-amplitude spike. We study the stability properties of these solutions in terms of the system parameters. We use a rigorous analysis for the linearized operator around single spike solutions based on nonlocal eigenvalue problems. The following result is established: If the time-relaxation constants for both producer and second consumer vanish, the large-amplitude spike solution is stable and the small-amplitude spike solution is unstable. We also derive results on the stability of solutions when these two time-relaxation constants are small. We show a new effect: if the time-relaxation constant of the second consumer is very small, the large-amplitude spike solution becomes unstable. To the best of our knowledge this phenomenon has not been observed before for the stability of spike patterns. It seems that this behavior is not possible for two-component reaction-diffusion systems but that at least three components are required. Our main motivation to study this system is mathematical since the novel interaction of a spike in the central component with two other components results in new types of conditions for the existence and stability of a spike. This model is realistic if several assumptions are made: (i) cooperation of consumers is prevalent in the system, (ii) the producer and the second consumer diffuse much faster than the first consumer, and (iii) there is practically an unlimited pool of producer. The first assumption has been proven to be correct in many types of consumer groups or populations, the second assumption occurs if the central component has a much smaller mobility than the other two, the third assumption is realistic if the consumers do not feel the impact of the limited amount of producer due to its large quantity. This chain model plays a role in population biology, where consumer and producer are often called predator and prey. This system can also be used as a model for a sequence of irreversible autocatalytic reactions in a container which is in contact with a well-stirred reservoir
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