40,329 research outputs found
Neutrino-Induced Fission and r-Process Nucleosynthesis
An r-process scenario with fission but no fission cycling is considered to
account for the observed abundance patterns of neutron-capture elements in
ultra-metal-poor stars. It is proposed that neutrino reactions play a crucial
role in inducing the fission of the progenitor nuclei after the r-process
freezes out in Type II Supernovae. To facilitate neutrino-induced fission, the
proposed r-process scenario is restricted to occur in a low-density environment
such as the neutrino-driven wind from the neutron star. Further studies to
develop this scenario are emphasized.Comment: 11 pages, 2 figures, to appear in ApJ
Estimating the spectral gap of a trace-class Markov operator
The utility of a Markov chain Monte Carlo algorithm is, in large part,
determined by the size of the spectral gap of the corresponding Markov
operator. However, calculating (and even approximating) the spectral gaps of
practical Monte Carlo Markov chains in statistics has proven to be an extremely
difficult and often insurmountable task, especially when these chains move on
continuous state spaces. In this paper, a method for accurate estimation of the
spectral gap is developed for general state space Markov chains whose operators
are non-negative and trace-class. The method is based on the fact that the
second largest eigenvalue (and hence the spectral gap) of such operators can be
bounded above and below by simple functions of the power sums of the
eigenvalues. These power sums often have nice integral representations. A
classical Monte Carlo method is proposed to estimate these integrals, and a
simple sufficient condition for finite variance is provided. This leads to
asymptotically valid confidence intervals for the second largest eigenvalue
(and the spectral gap) of the Markov operator. In contrast with previously
existing techniques, our method is not based on a near-stationary version of
the Markov chain, which, paradoxically, cannot be obtained in a principled
manner without bounds on the spectral gap. On the other hand, it can be quite
expensive from a computational standpoint. The efficiency of the method is
studied both theoretically and empirically
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