The supernova: A stellar spectacle

The life of a star, the supernova, related objects and their importance in astronomy and science in general are discussed. Written primarily for science teachers of secondary school chemistry, physics, and earth sciences, the booklet contains a glossary, reference sources, suggested topics for discussion, and projects for individual or group assignment

Fokker--Planck and Kolmogorov Backward Equations for Continuous Time Random Walk scaling limits

It is proved that the distributions of scaling limits of Continuous Time Random Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck Equations for diffusion processes. In contrast to previous such results, it is not assumed that the underlying process has absolutely continuous laws. Moreover, governing equations in the backward variables are derived. Three examples of anomalous diffusion processes illustrate the theory.Comment: in Proceedings of the American Mathematical Society, Published electronically July 12, 201

Comments on an association in Vela

Evidence for an association near the Vela pulsar rests on the H-R diagram. Definite bunching occurs around the mean line. However this evidence is not supported by correlation of proper motions in the region. If the Vela pulsar is a member of this association, a rather large mass is implied, about 10 solar masses

Semi-Markov approach to continuous time random walk limit processes

Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their finite-dimensional distributions is an important open problem. This paper develops a general semi-Markov theory for CTRW limit processes in $\mathbb{R}^d$ with infinitely many particle jumps (renewals) in finite time intervals. The particle jumps and waiting times can be coupled and vary with space and time. By augmenting the state space to include the scaling limits of renewal times, a CTRW limit process can be embedded in a Markov process. Explicit analytic expressions for the transition kernels of these Markov processes are then derived, which allow the computation of all finite dimensional distributions for CTRW limits. Two examples illustrate the proposed method.Comment: Published in at http://dx.doi.org/10.1214/13-AOP905 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org