9,309 research outputs found
A Shotgun Model for Gamma Ray Bursts
We propose that gamma ray bursts (GRBs) are produced by a shower of heavy
blobs running into circumstellar material at highly relativistic speeds. The
gamma ray emission is produced in the shocks these bullets drive into the
surrounding medium. The short term variability seen in GRBs is set by the
slowing-down time of the bullets while the overall duration of the burst is set
by the lifetime of the central engine. A requirement of this model is that the
ambient medium be dense, consistent with a strong stellar wind. The efficiency
of the burst can be relatively high.Comment: 4 pages, 2 figures, revised version accepted by ApJ Letter
Multiparticle correlations from momentum conservation
Using a generating-function formalism, we compute the contribution of
momentum conservation to multiparticle correlations between the emitted
particles in high-energy collisions. In particular, we derive a compact
expression of the genuine M-particle correlation, for arbitrary M.Comment: 5 pages, RevTeX. v2: typos corrected, to match journal versio
On the spectrum of the magnetohydrodynamic mean-field alpha^2-dynamo operator
The existence of magnetohydrodynamic mean-field alpha^2-dynamos with
spherically symmetric, isotropic helical turbulence function alpha is related
to a non-self-adjoint spectral problem for a coupled system of two singular
second order ordinary differential equations. We establish global estimates for
the eigenvalues of this system in terms of the turbulence function alpha and
its derivative alpha'. They allow us to formulate an anti-dynamo theorem and a
non-oscillation theorem. The conditions of these theorems, which again involve
alpha and alpha', must be violated in order to reach supercritical or
oscillatory regimes.Comment: 35 pages, 4 figures, to be published in SIAM J. Math. Anal
A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks
Approximate solutions of the chemical master equation and the chemical
Fokker-Planck equation are an important tool in the analysis of biomolecular
reaction networks. Previous studies have highlighted a number of problems with
the moment-closure approach used to obtain such approximations, calling it an
ad-hoc method. In this article, we give a new variational derivation of
moment-closure equations which provides us with an intuitive understanding of
their properties and failure modes and allows us to correct some of these
problems. We use mixtures of product-Poisson distributions to obtain a flexible
parametric family which solves the commonly observed problem of divergences at
low system sizes. We also extend the recently introduced entropic matching
approach to arbitrary ansatz distributions and Markov processes, demonstrating
that it is a special case of variational moment closure. This provides us with
a particularly principled approximation method. Finally, we extend the above
approaches to cover the approximation of multi-time joint distributions,
resulting in a viable alternative to process-level approximations which are
often intractable.Comment: Minor changes and clarifications; corrected some typo
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