A new and flexible method for constructing designs for computer experiments

We develop a new method for constructing "good" designs for computer experiments. The method derives its power from its basic structure that builds large designs using small designs. We specialize the method for the construction of orthogonal Latin hypercubes and obtain many results along the way. In terms of run sizes, the existence problem of orthogonal Latin hypercubes is completely solved. We also present an explicit result showing how large orthogonal Latin hypercubes can be constructed using small orthogonal Latin hypercubes. Another appealing feature of our method is that it can easily be adapted to construct other designs; we examine how to make use of the method to construct nearly orthogonal and cascading Latin hypercubes.Comment: Published in at http://dx.doi.org/10.1214/09-AOS757 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The magnetic properties of the planet host star Kepler-78

Kepler-78 is host to a transiting 8.5-hour orbit super-Earth. In this paper, the rotation and magnetic properties of the planet host star are studied. We first revisit the Kepler photometric data for a detailed description of the rotation properties of Kepler-78, showing that the star seems to undergo a cycle in the spot pattern of ~1,300 day duration. We then use spectropolarimetric observations with CFHT/ESPaDOnS to measure the circular polarization in the line profile of the star during its rotation cycle, as well as spectroscopic proxies of the chromospheric activity. The average field has an amplitude of 16 G. The magnetic topology is characterized by a poloidal and a toroidal component, encompassing 60% and 40% of the magnetic energy, respectively. Differential rotation is detected with an estimated rate of 0.105+-0.039 rad/d. Activity tracers vary with the rotation cycle of the star; there is no hint that a residual activity level is related to the planetary orbit at the precision of our data. The description of the star magnetic field's characteristics then may serve as input for models of interactions between the star and its close-by planet, e.g., Ohmic dissipation and unipolar induction

Interaction of Close-in Planets with the Magnetosphere of their Host Stars I: Diffusion, Ohmic Dissipation of Time Dependent Field, Planetary Inflation, and Mass Loss

The unanticipated discovery of the first close-in planet around 51 Peg has rekindled the notion that shortly after their formation outside the snow line, some planets may have migrated to the proximity of their host stars because of their tidal interaction with their nascent disks. If these planets indeed migrated to their present-day location, their survival would require a halting mechanism in the proximity of their host stars. Most T Tauri stars have strong magnetic fields which can clear out a cavity in the innermost regions of their circumstellar disks and impose magnetic induction on the nearby young planets. Here we consider the possibility that a magnetic coupling between young stars and planets could quench the planet's orbital evolution. After a brief discussion of the complexity of the full problem, we focus our discussion on evaluating the permeation and ohmic dissipation of the time dependent component of the stellar magnetic field in the planet's interior. Adopting a model first introduced by C. G. Campbell for interacting binary stars, we determine the modulation of the planetary response to the tilted magnetic field of a non-synchronously spinning star. We first compute the conductivity in the young planets, which indicates that the stellar field can penetrate well into the planet's envelope in a synodic period. For various orbital configurations, we show that the energy dissipation rate inside the planet is sufficient to induce short-period planets to inflate. This process results in mass loss via Roche lobe overflow and in the halting of the planet's orbital migration.Comment: 47 pages, 12 figure

Finite volume effects using lattice chiral perturbation theory

Lattice regularization is used to perform chiral perturbation theory calculations in finite volume. The lattice spacing is chosen small enough to be irrelevant, and numerical results are obtained from simple summations.Comment: Lattice2004(spectrum), 3 page