The effect of temperature evolution on the interior structure of H2{}_{2}O-rich planets

For most planets in the range of radii from 1 to 4 R$_{\oplus}$, water is a major component of the interior composition. At high pressure H${}_{2}$O can be solid, but for larger planets, like Neptune, the temperature can be too high for this. Mass and age play a role in determining the transition between solid and fluid (and mixed) water-rich super-Earth. We use the latest high-pressure and ultra-high-pressure phase diagrams of H${}_{2}$O, and by comparing them with the interior adiabats of various planet models, the temperature evolution of the planet interior is shown, especially for the state of H${}_{2}$O. It turns out that the bulk of H${}_{2}$O in a planet's interior may exist in various states such as plasma, superionic, ionic, Ice VII, Ice X, etc., depending on the size, age and cooling rate of the planet. Different regions of the mass-radius phase space are also identified to correspond to different planet structures. In general, super-Earth-size planets (isolated or without significant parent star irradiation effects) older than about 3 Gyr would be mostly solid.Comment: Accepted by ApJ, in print for March 2014 (14 pages, 3 colored figures, 1 table

Quantum Coins, Dice and Children: Probability and Quantum Statistics

We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized that, even in the absence of interactions, (anti)symmetrizations of multi-particle wavefunctions destroy statistical independences and often lead to dramatic departures from our intuitive expectations.Comment: 8 pages in REVTe

Lowest common ancestor interconnection networks

Lowest Common Ancestor (LCA) networks are built using switches capable of connecting u + d inputs/outputs in a permutation pattern. For n source nodes and I stages of switches, n/d switches are used in stage l - n/d - u/d in stage l - 2, and in general , n-u^l-i-l/d^l-i switches in stage i. The resulting hierarchical structure possesses interesting connectivity and permutational properties. A full characterization of LCA networks is presented together with a permutation routing algorithm for a family of LCA networks. The algorithm uses the network itself to collect and disseminate information about the permutation. A schedule of O(dp log_d/u n) passes is obtained with a switch set-up cost factor of O(log_d/u n) (p is the minimum number of passes that an algorithm with global knowledge schedules)

Propagation of the 2012 March Coronal Mass Ejections from the Sun to Heliopause

In 2012 March the Sun exhibited extraordinary activities. In particular, the active region NOAA AR 11429 emitted a series of large coronal mass ejections (CMEs) which were imaged by STEREO as it rotated with the Sun from the east to west. These sustained eruptions are expected to generate a global shell of disturbed material sweeping through the heliosphere. A cluster of shocks and interplanetary CMEs (ICMEs) were observed near the Earth, and are propagated outward from 1 AU using an MHD model. The transient streams interact with each other, which erases memory of the source and results in a large merged interaction region (MIR) with a preceding shock. The MHD model predicts that the shock and MIR would reach 120 AU around 2013 April 22, which agrees well with the period of radio emissions and the time of a transient disturbance in galactic cosmic rays detected by Voyager 1. These results are important for understanding the "fate" of CMEs in the outer heliosphere and provide confidence that the heliopause is located around 120 AU from the Sun.Comment: 13 pages, 5 figures, accepted for publication in ApJ Letter