Simultaneous Projectile-Target Excitation in Heavy Ion Collisions

We calculate the lowest-order contribution to the cross section for simultaneous excitation of projectile and target nuclei in relativistic heavy ion collisions. This process is, to leading order, non-classical and adds incoherently to the well-studied semi-classical Weizs\"acker-Williams cross section. While the leading contribution to the cross section is down by only $1/Z_P$ from the semiclassical process, and consequently of potential importance for understanding data from light projectiles, we find that phase space considerations render the cross section utterly negligible.Comment: 9 pages, LA-UR-94-247

Structural Phases of Bounded Three-Dimensional Screened Coulomb Clusters (Finite Yukawa System)

The formation of three-dimensional (3D) dust clusters within a complex plasma modeled as a spatially confined Yukawa system is simulated using the box_tree code. Similar to unscreened Coulomb clusters, the occurrence of concentric shells with characteristic occupation numbers was observed. Both the occupation numbers and radii were found to depend on the Debye length. Ground and low energy meta-stable states of the shielded 3D Coulomb clusters were determined for 4<N<20. The structure and energy of the clusters in different states was analyzed for various Debye lengths. Structural phase transitions, including inter-shell structural phase transitions and intra-shell structural phase transitions, were observed for varying Debye length and the critical value for transitions calculated

Impartial avoidance and achievement games for generating symmetric and alternating groups

We study two impartial games introduced by Anderson and Harary. Both games are played by two players who alternately select previously-unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. We determine the nim-numbers, and therefore the outcomes, of these games for symmetric and alternating groups.Comment: 12 pages. 2 tables/figures. This work was conducted during the third author's visit to DIMACS partially enabled through support from the National Science Foundation under grant number #CCF-1445755. Revised in response to comments from refere

Impartial avoidance games for generating finite groups

We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making the set of jointly-selected elements into a generating set for the group loses the game. We develop criteria on the maximal subgroups that determine the nim-numbers of these games and use our criteria to study our game for several families of groups, including nilpotent, sporadic, and symmetric groups.Comment: 14 pages, 4 figures. Revised in response to comments from refere