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