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Many physical systems can be modeled as scattering problems. For example, the motions of stars escaping from a galaxy can be described using a potential with two or more escape routes. Each escape route is crossed by an unstable Lyapunov orbit. The region between the two Lyapunov orbits is where the particle interacts with the system. We study a simple dynamical system with escapes using a suitably selected surface of section. The surface of section is partitioned in different escape regions which are defined by the intersections of the asymptotic manifolds of the Lyapunov orbits with the surface of section. The asymptotic curves of the other unstable periodic orbits form spirals around various escape regions. These manifolds, together with the manifolds of the Lyapunov orbits, govern the transport between different parts of the phase space. We study in detail the form of the asymptotic manifolds of a central unstable periodic orbit, the form of the escape regions and the infinite spirals of the asymptotic manifolds around the escape regions. We compute the escape rate for different values of the energy. In particular, we give the percentage of orbits that escape after a finite number of iterations. In a system with escapes one cannot define a Poincaré recurrence time, because the available phase space is infinite. However, for certain domains inside the lobes of the asymptotic manifolds there is a finite minimum recurrence time. We find the minimum recurrence time as a function of the energy.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   
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We explore whether our models for starbursts, quiescent star-forming galaxies and for active galactic nuclei (AGN) dust tori are able to model the full range of Spitzer Infrared Spectrograph (IRS) spectra measured with Spitzer . The diagnostic plot of 9.7 μm silicate optical depth versus 6.2 μm polycyclic aromatic hydrocarbon (PAH) equivalent width, introduced by Spoon and coworkers in 2007, gives a good indication of the age and optical depth of a starburst, and of the contribution of an AGN dust torus. However, there is aliasing between age and optical depth at later times in the evolution of a starburst, and between age and the presence of an AGN dust torus. Modelling the full IRS spectra and using broad-band 25–850 μm fluxes can help to resolve these aliases. The observed spectral energy distributions require starbursts of a range of ages with initial dust optical depth ranging from 50–200, optically thin dust emission ('cirrus') illuminated by a range of surface brightnesses of the interstellar radiation field, and AGN dust tori with a range of viewing angles.  相似文献   
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There has been increasing interest by cosmologists in applying Bayesian techniques, such as Bayesian Evidence, for model selection. A typical example is in assessing whether observational data favour a cosmological constant over evolving dark energy. In this paper, the example of dark energy is used to illustrate limitations in the application of Bayesian Evidence associated with subjective judgements concerning the choice of model and priors. An analysis of recent cosmological data shows a statistically insignificant preference for a cosmological constant over simple dynamical models of dark energy. It is argued that for nested problems, as considered here, Bayesian parameter estimation can be more informative than computing Bayesian Evidence for poorly motivated physical models.  相似文献   
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