Temporary Capture of Asteroids by an Eccentric Planet

We have investigated the probability of temporary capture of asteroids in eccentric orbits by a planet in a circular or an eccentric orbit through analytical and numerical calculations. We found that in the limit of the circular orbit, the capture probability is $\sim 0.1\%$ of encounters to the planet's Hill sphere, independent of planetary mass and semimajor axis. In general, the temporary capture becomes more difficult as the planet's eccentricity ($e_{\rm p}$) increases. We found that the capture probability is almost independent of $e_{\rm p}$ until a critical value ($e_{\rm p}^{\rm c}$) that is given by $\simeq$ 5 times the Hill radius scaled by the planet's semimajor axis. For $e_{\rm p} > e_{\rm p}^{\rm c}$, the probability decreases approximately in proportion to $e_{\rm p}^{-1}$. The current orbital eccentricity of Mars is several times larger than $e_{\rm p}^{\rm c}$. However, since the range of secular change in Martian eccentricity overlaps $e_{\rm p}^{\rm c}$, the capture of minor bodies by the past Mars is not ruled out.Comment: Accepted for publication in AJ, 14 pages and 6 figure

Hamiltonian model of capture into mean motion resonance

Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a protoplanetary disc. We use a Hamiltonian model to thoroughly investigate the capture behaviour for first and second order resonances. Using this method, all resonances of the same order can be described by one equation, with applications to specific resonances by appropriate scaling. We focus on the limit where one body is a massless test particle and the other a massive planet. We quantify how the the probability of capture into a resonance depends on the relative migration rate of the planet and particle, and the particle's eccentricity. Resonant capture fails for high migration rates, and has decreasing probability for higher eccentricities, although for certain migration rates, capture probability peaks at a finite eccentricity. We also calculate libration amplitudes and the offset of the libration centres for captured particles, and the change in eccentricity if capture does not occur. Libration amplitudes are higher for larger initial eccentricity. The model allows for a complete description of a particle's behaviour as it successively encounters several resonances. The model is applicable to many scenarios, including (i) Planet migration through gas discs trapping other planets or planetesimals in resonances; (ii) Planet migration through a debris disc; (iii) Dust migration through PR drag. Full details can be found in \cite{2010submitted}. (Abridged)Comment: 4 pages, Proceedings of IAUS276 "The Astrophysics of Planetary Systems: Formation, Structure, and Dynamical Evolution

Extending the relational model with uncertainty and ignorance

It has been widely recognized that in many real-life database applications there is growing demand to model uncertainty and ignorance. However the relational model does not provide this possibility. Through the years a number of efforts has been devoted to the capture of uncertainty and ignorance in databases. Most of these efforts attempted to capture uncertainty using the classic probability theory. As a consequence, the limitations of probability theory are inherited by these approaches, such as the problem of information loss. In this paper, we extend the relational model with uncertainty and ignorance without these limitations posed by the other approaches. Our approach is based on the so-called theory of belief functions, which may be considered as a generalization of probability theory. Belief functions have an attractive mathematical\ud underpinning and many intuitively appealing properties

Bogolon-mediated electron capture by impurities in hybrid Bose-Fermi systems

We investigate the processes of electron capture by a Coulomb impurity center residing in a hybrid system consisting of spatially separated two-dimensional layers of electron and Bose-condensed dipolar exciton gases coupled via the Coulomb forces. We calculate the probability of the electron capture accompanied by the emission of a single Bogoliubov excitation (bogolon), similar to regular phonon-mediated scattering in solids. Further, we study the electron capture mediated by the emission of a pair of bogolons in a single capture event and show that these processes not only should be treated in the same order of the perturbation theory, but also they give more important contribution than single bogolon-mediated capture, in contrast with regular phonon scattering.Comment: Paper: 5 pages, 4 figure

Search for Oscillation of the Electron-Capture Decay Probability of 142^{142}Pm

We have searched for time modulation of the electron capture decay probability of $^{142}$Pm in an attempt to confirm a recent claim from a group at the Gesellschaft f\"{u}r Schwerionenforschung (GSI). We produced $^{142}$Pm via the $^{124}$Sn($^{23}$Na, 5n)$^{142}$Pm reaction at the Berkeley 88-Inch Cyclotron with a bombardment time short compared to the reported modulation period. Isotope selection by the Berkeley Gas-filled Separator is followed by implantation and a long period of monitoring the $^{142}$Nd K$_{\alpha}$ x-rays from the daughter. The decay time spectrum of the x-rays is well-described by a simple exponential and the measured half-life of 40.68(53) seconds is consistent with the accepted value. We observed no oscillatory modulation at the proposed frequency at a level 31 times smaller than that reported by Litvinov {\it et al.} (Phys. Lett. B 664 (2008) 162; arXiv:0801.2079 [nucl-ex]). A literature search for previous experiments that might have been sensitive to the reported modulation uncovered another example in $^{142}$Eu electron-capture decay. A reanalysis of the published data shows no oscillatory behavior.Comment: 12 pages (double-spaced), 6 figure

Electron capture across a nuclear resonance in the strong potential Born approximation

Abstract. The strong potential Born theory for charge transfer in fast, asymmetric ion-atom collisions has been extended to allow for nuclear resonant scattering using distorted nuclear waves. In the absence of a nuclear resonance, the semiclassical result is recovered. A large variation in the capture probability is found when the projectile energy passes through the resonance. As examples, we present results for the capture from the target K shell in the collisions of protons with 22Ne and 28Si, as well as for capture from the K and L shells of 58Ni in collisions with protons, and of I6O, "Ne and 28Si by He2+ impact. 1

Fragility of the Commons under Prospect-Theoretic Risk Attitudes

We study a common-pool resource game where the resource experiences failure with a probability that grows with the aggregate investment in the resource. To capture decision making under such uncertainty, we model each player's risk preference according to the value function from prospect theory. We show the existence and uniqueness of a pure Nash equilibrium when the players have heterogeneous risk preferences and under certain assumptions on the rate of return and failure probability of the resource. Greater competition, vis-a-vis the number of players, increases the failure probability at the Nash equilibrium; we quantify this effect by obtaining bounds on the ratio of the failure probability at the Nash equilibrium to the failure probability under investment by a single user. We further show that heterogeneity in attitudes towards loss aversion leads to higher failure probability of the resource at the equilibrium.Comment: Accepted for publication in Games and Economic Behavior, 201