A two-species competition model on Z^d

We consider a two-type stochastic competition model on the integer lattice Z^d. The model describes the space evolution of two ``species'' competing for territory along their boundaries. Each site of the space may contain only one representative (also referred to as a particle) of either type. The spread mechanism for both species is the same: each particle produces offspring independently of other particles and can place them only at the neighboring sites that are either unoccupied, or occupied by particles of the opposite type. In the second case, the old particle is killed by the newborn. The rate of birth for each particle is equal to the number of neighboring sites available for expansion. The main problem we address concerns the possibility of the long-term coexistence of the two species. We have shown that if we start the process with finitely many representatives of each type, then, under the assumption that the limit set in the corresponding first passage percolation model is uniformly curved, there is positive probability of coexistence.Comment: 16 pages, 2 figure

Two HSCT Mach 1.7 low sonic boom designs

The objective of this study was to provide low sonic boom concepts, geometry, and analysis to support wind tunnel model designs. Within guidelines provided by NASA, two High Speed Civil Transport (HSCT) configurations were defined with reduced sonic boom that have low drag, high payload, and good performance. To provide information for assessing the feasibility of reduced sonic boom operation, the two designs were analyzed in terms of their sonic boom characteristics, as well as aerodynamics, weight and balance, and performance characteristics. Low drag and high payload were achieved, but both of the blended arrow-wing configurations have deficiencies in high lift capability, fuel volume, wing loading, balance, and takeoff gross weight. Further refinement of the designs is needed to better determine the commercial viability of low boom operation. To help in assessing low boom design technology, the two configurations were defined as wind tunnel models with altered aft-bodies for the wind tunnel sting mounting system

The Law and Policy of Civil Rights: A Tactical Perspective for Educators

This article is presented to share with fellow professional teacher-scholars the preparation of a freshly-formulated teaching project. The aim of this project is to provide a classroom public policy study program wherein students debate policy issues in a carefully structured and professional fashion. This structure encompasses hands-on study of actually-litigated minority set-aside/affirmative action controversies before the U.S. Supreme Court, with every student always utilizing the primary documents (the litigants\u27 briefs) used by the Supreme Court Justices themselves. These briefs provide readymade resources fueling policy debate on either side of each case

Enhanced Pairing in the "Checkerboard" Hubbard Ladder

We study signatures of superconductivity in a 2--leg "checkerboard" Hubbard ladder model, defined as a one--dimensional (period 2) array of square plaquettes with an intra-plaquette hopping $t$ and inter-plaquette hopping $t'$, using the density matrix renormalization group method. The highest pairing scale (characterized by the spin gap or the pair binding energy, extrapolated to the thermodynamic limit) is found for doping levels close to half filling, $U\approx 6t$ and $t'/t \approx 0.6$. Other forms of modulated hopping parameters, with periods of either 1 or 3 lattice constants, are also found to enhance pairing relative to the uniform two--leg ladder, although to a lesser degree. A calculation of the phase stiffness of the ladder reveals that in the regime with the strongest pairing, the energy scale associated with phase ordering is comparable to the pairing scale.Comment: 9 pages, 9 figures; Journal reference adde