Diagonal Peg Solitaire

We study the classical game of peg solitaire when diagonal jumps are allowed. We prove that on many boards, one can begin from a full board with one peg missing, and finish with one peg anywhere on the board. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more jumps by the same peg), and find the shortest solution to the "central game", which begins and ends at the center. In some cases we can prove analytically that our solutions are the shortest possible, in other cases we apply A* or bidirectional search heuristics.Comment: 20 pages, 11 figure

Solving Triangular Peg Solitaire

We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and sufficient conditions for this game to be solvable. For all solvable problems, we give an explicit solution algorithm. On the 15-hole board, we compare three simple solution strategies. We then consider the problem of finding solutions that minimize the number of moves (where a move is one or more consecutive jumps by the same peg), and find the shortest solution to the basic game on all triangular boards with up to 55 holes (10 holes on a side).Comment: 23 pages, 14 figures; published version including comments by John Beasle

Fringe field simulations of a non-scaling FFAG accelerator

Fixed-field Alternating Gradient (FFAG) accelerators offer the potential of high-quality, moderate energy ion beams at low cost. Modeling of these structures is challenging with conventional beam tracking codes because of the large radial excursions of the beam and the significance of fringe field effects. Numerous tune resonances are crossed during the acceleration, which would lead to beam instability and loss in a storage ring. In a non-scaling FFAG, the hope is that these resonances can be crossed sufficiently rapidly to prevent beam loss. Simulations are required to see if this is indeed the case. Here we simulate a non-scaling FFAG which accelerates protons from 31 to 250 MeV. We assume only that the bending magnets have mid-plane symmetry, with specified vertical bending field in the mid-plane (y=0). The magnetic field can be obtained everywhere using a power series expansion, and we develop mathematical tools for calculating this expansion to arbitrary order when the longitudinal field profile is given by an Enge function. We compare the use of a conventional hard-edge fringe with a more accurate, soft-edge fringe field model. The tune 1/3 resonance is the strongest, and crossing it in the hard-edge fringe model results in a 21% loss of the beam. Using the soft-edge fringe model the beam loss is less than 6%.Comment: 12 pages; 12 figure

Centerscope

Centerscope, formerly Scope, was published by the Boston University Medical Center "to communicate the concern of the Medical Center for the development and maintenance of improved health care in contemporary society.

The Magellanic Group and the Seven Dwarfs

The Magellanic Clouds were the largest members of a group of dwarf galaxies that entered the Milky Way (MW) halo at late times. This group, dominated by the LMC, contained ~4% of the mass of the Milky Way prior to its accretion and tidal disruption, but ~70% of the known dwarfs orbiting the MW. Our theory addresses many outstanding problems in galaxy formation associated with dwarf galaxies. First, it can explain the planar orbital configuration populated by some dSphs in the MW. Second, it provides a mechanism for lighting up a subset of dwarf galaxies to reproduce the cumulative circular velocity distribution of the satellites in the MW. Finally, our model predicts that most dwarfs will be found in association with other dwarfs. The recent discovery of Leo V (Belokurov et al. 2008), a dwarf spheroidal companion of Leo IV, and the nearby dwarf associations supports our hypothesis.Comment: Contributed talk to IAU Symposium 256: "The Magellanic System: Stars, Gas, and Galaxies