An asymptotic analysis of supersonic reacting mixing layers

The purpose of this paper is to present an asymptotic analysis of the laminar mixing of the simultaneous chemical reaction between parallel supersonic streams of two reacting species. The study is based on a one-step irreversible Arrhenius reaction and on large activation energy asymptotics. Essentially it extends the work of Linan and Crespo to include the effect of free shear and Mach number on the ignition regime, the deflagration regime and the diffusion flame regime. It is found that the effective parameter is the product of the characteristic Mach number and a shear parameter

Automatic rendezvous and capture system development in a manned environment

This paper presents the development of a 'Phase One' AR&C system capability as a logical outgrowth of Rendezvous and Proximity Operations (R&PO) system development for manned space programs. The continuity of the approach to R&PO across the Apollo, Skylab, Apollo-Soyuz, and Shuttle programs is traced and lessons learned which are applicable to AR&C discussed. Use of the Shuttle as a test bed for Automatic Rendezvous and Capture capabilities and technology demonstrations is discussed. A status of the current Phase One System design and brief overview of its capabilities is presented

Resolving the structure of TiBe12_{12}

There has been considerable controversy regarding the structure of TiBe$_{12}$, which is variously reported as hexagonal and tetragonal. Lattice dynamics simulations based on density functional theory show the tetragonal phase space group $I4/mmm$ to be more stable over all temperatures, while the hexagonal phase exhibits an imaginary phonon mode, which, if followed, would lead to the cell adopting the tetragonal structure. We then report the predicted ground state elastic constants and temperature dependence of the bulk modulus and thermal expansion for the tetragonal phase.Comment: In press at Acta Crystallographica B. Supplementary material appende

Oscillations of a Bose-Einstein condensate rotating in a harmonic plus quartic trap

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities, $\Omega$, where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency $\sqrt{6} \Omega$ in the rotating frame, irrespective of the mode multipolarity $m$, as well as a class of low energy modes with frequency proportional to $|m|/\Omega$. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.Comment: 4 pages, 2 figure

Evaluation of directionally solidified eutectic superalloys for turbine blade applications

Alloys from the following systems were selected for property evaluation: (1) gamma/gamma-Mo (Ni-base, rods of Mo); (2) gamma-beta (Ni-base, lamellae or rods of (Ni, Fe/Co Al); and (3) gamma-gamma (Ni-base rods of Ni3Al gamma). The three alloys were subjected to longitudinal and transverse tensile and rupture tests from 750 C to 1100 C, longitudinal shear strength was measured at several temperatures, resistance to thermal cycling to 1150 C was determined, cyclic oxidation resistance was evaluated at 750 C and 1100 C, and each system was directionally solidified in an alumina shell mold turbine shape to evaluate mold/metal reactivity. The gamma/gamma Mo system has good rupture resistance, transverse properties and processability, and is a high potential system for turbine blades. The gamma-beta system has good physical properties and oxidation resistance, and is a potential system for turbine vanes. The gamma-gamma system has good high temperature rupture resistance and requires further exploratory research

The temporal changes in the emission spectrum of Comet 9P/Tempel 1 after Deep Impact

The time dependence of the changes in the emission spectra of Comet 9P/Tempel 1 after Deep Impact are derived and discussed. This was a unique event because for the first time it gave astronomers the opportunity to follow the time history of the formation and decay of O(1S), OH, CN, C2, C3, NH, and NH2. Least squares fits of a modified Haser model with constraints using known rate constants were fit to the observed data. In the case of OH a simple two-step Haser model provides a reasonable fit to the observations. Fitting the emissions from O(1S), CN, C2, C3, NH, and NH2 requires the addition of a delayed component to a regular two or three step Haser model. From this information a picture of the Deep Impact encounter emerges where there is an initial formation of gas and dust, which is responsible for the prompt emission that occurs right after impact. A secondary source of gas starts later after impact when the initial dust has dissipated enough so that solar radiation can reach the surface of freshly exposed material. The implications of this and other results are discussed in terms of the implications on the structure and composition of the comet's nucleus.Comment: Accepted for publication in The Astrophysical Journal; 26 pages including 8 figures and 1 tabl

Lax matrices for Yang-Baxter maps

It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations on quad-graphs has been recently discovered by A. Bobenko and one of the authors, and by F. Nijhoff

Assortative Mixing Equilibria in Social Network Games

It is known that individuals in social networks tend to exhibit homophily (a.k.a. assortative mixing) in their social ties, which implies that they prefer bonding with others of their own kind. But what are the reasons for this phenomenon? Is it that such relations are more convenient and easier to maintain? Or are there also some more tangible benefits to be gained from this collective behaviour? The current work takes a game-theoretic perspective on this phenomenon, and studies the conditions under which different assortative mixing strategies lead to equilibrium in an evolving social network. We focus on a biased preferential attachment model where the strategy of each group (e.g., political or social minority) determines the level of bias of its members toward other group members and non-members. Our first result is that if the utility function that the group attempts to maximize is the degree centrality of the group, interpreted as the sum of degrees of the group members in the network, then the only strategy achieving Nash equilibrium is a perfect homophily, which implies that cooperation with other groups is harmful to this utility function. A second, and perhaps more surprising, result is that if a reward for inter-group cooperation is added to the utility function (e.g., externally enforced by an authority as a regulation), then there are only two possible equilibria, namely, perfect homophily or perfect heterophily, and it is possible to characterize their feasibility spaces. Interestingly, these results hold regardless of the minority-majority ratio in the population. We believe that these results, as well as the game-theoretic perspective presented herein, may contribute to a better understanding of the forces that shape the groups and communities of our society

Operational modules for space station construction

Identification of an effective space construction concept is a current objective of NASA studies. One concept, described in this memorandum, consists of repetitive use of operational modules, which minimizes on-orbit stay time for the shuttle. A space station constructed of operational modules may benefit from fabrication and system checkout in ground-based facilities, and since the modules are the primary structure of the space station, a minimum of additional structure, and trips and on-orbit stay time of the shuttle are required