Weyl Expansion for Symmetric Potentials

We present a semiclassical expansion of the smooth part of the density of states in potentials with some form of symmetry. The density of states of each irreducible representation is separately evaluated using the Wigner transforms of the projection operators. For discrete symmetries the expansion yields a formally exact but asymptotic series in $\hbar$, while for the rotational $SO(n)$ symmetries the expansion requires averaging over angular momentum as well as energy. A numerical example is given in two dimensions, in which we calculate the leading terms of the Weyl expansion as well as the leading periodic orbit contributions to the symmetry reduced level density.Comment: Four of the five figures are appended as a postscript file. The fifth figure is available by snail mail

Engineering a Conformant Probabilistic Planner

We present a partial-order, conformant, probabilistic planner, Probapop which competed in the blind track of the Probabilistic Planning Competition in IPC-4. We explain how we adapt distance based heuristics for use with probabilistic domains. Probapop also incorporates heuristics based on probability of success. We explain the successes and difficulties encountered during the design and implementation of Probapop

Geometric and Diffractive Orbits in the Scattering from Confocal Hyperbolae

We study the scattering resonances between two confocal hyperbolae and show that the spectrum is dominated by the effect of a single periodic orbit. There are two distinct cases depending on whether the orbit is geometric or diffractive. A generalization of periodic orbit theory allows us to incorporate the second possibility. In both cases we also perform a WKB analysis. Although it is found that the semiclassical approximations work best for resonances with large energies and narrow widths, there is reasonable agreement even for resonances with large widths - unlike the two disk scatterer. We also find agreement with the next order correction to periodic orbit theory.Comment: Written in RevTeX. After \end{document} comes a uuencoded .ps file with two figure

First Direct Simulation of Brown Dwarf Formation in a Compact Cloud Core

Brown dwarf formation and star formation efficiency are studied using a nested grid simulation that covers five orders of magnitude in spatial scale (10^4 - 0.1AU). Starting with a rotating magnetized compact cloud with a mass of 0.22 M_sun, we follow the cloud evolution until the end of main accretion phase. Outflow of about 5 km/s emerges about 100 yr before the protostar formation and does not disappear until the end of the calculation. The mass accretion rate declines from 10^-6 M_sun/yr to 10^-8 - 10^-12 M_sun/yr in a short time (about 10^4 yr) after the protostar formation. This is because (1) a large fraction of mass is ejected from the host cloud by the protostellar outflow and (2) the gas escapes from the host cloud by the thermal pressure. At the end of the calculation, 74% (167 M_Jup) of the total mass (225 M_Jup) is outflowing from the protostar, in which 34% (77 M_Jup) of the total mass is ejected by the protostellar outflow with supersonic velocity and 40% (90 M_Jup) escapes with subsonic velocity. On the other hand, 20% (45 M_Jup) is converted into the protostar and 6% (13 M_Jup) remains as the circumstellar disk. Thus, the star formation efficiency is epsilon = 0.2. The resultant protostellar mass is in the mass range of brown dwarfs. Our results indicate that brown dwarfs can be formed in compact cores in the same manner as hydrogen-burning stars, and the magnetic field and protostellar outflow are essential in determining the star formation efficiency and stellar mass.Comment: 13 pages, 3 figures. Accepted for publication in ApJL. For high resolution figures, see http://www2-tap.scphys.kyoto-u.ac.jp/~machidam/astro-ph/BD.pd