Modeling of the ElectriCOIL system

Theoretical studies have indicated that sufficient fractions of O/sub 2/(/sup 1//spl Delta/) may be produced in an electrical discharge that will permit lasing of an electric discharge oxygen-iodine laser (ElectriCOIL) system. Results of those studies along with more recent experimental results show that electric excitation is a very complicated process that must be investigated with advanced diagnostics along with modeling to better understand this highly complex system. A kinetic package appropriate for the ElectriCOIL system is presented and implemented in the detailed electrodynamic GlobalKin model and the Blaze II chemical laser modeling code. A parametric study with the Blaze II model establishes that it may be possible to attain positive gain in the ElectriCOIL system, perhaps even with subsonic flow. The Blaze II model is in reasonable agreement with early gain data. Temperature is a critical issue, especially in the subsonic cases, and thus it appears that supersonic flow will be important for the ElectriCOIL system. Simulations of a supersonic ElectriCOIL system indicate that it may be possible to attain reasonable performance levels, even at low yield levels of 20% or less. In addition, pre-dissociation of the iodine is shown to be very important for the supersonic flow situation.     

Dobiński relations and ordering of boson operators

We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations.     

Group Theoretic Properties of the Group of Computable Automorphisms of a Countable Dense Linear Order

We compare Aut(Q), the classical automorphism group of a countable dense linear order, with Aut _c (Q), the group of all computable automorphisms of such an order. They have a number of similarities, including the facts that every element of each group is a commutator and each group has exactly three nontrivial normal subgroups. However, the standard proofs of these facts in Aut(Q) do not work for Aut _c (Q). Also, Aut(Q) has three fundamental properties which fail in Aut _c (Q): it is divisible, every element is a commutator of itself with some other element, and two elements are conjugate if and only if they have isomorphic orbital structures.     

Theta function transformation formulas and the Weil representation

A short proof is given that the theta functional is invariant under the Weil representation, and the explicit determination of the eighth root of unity which arises is also shown. Namely, the action of the Weil representation on the theta functional is described as the limit of integration against a specialization of the symplectic theta function as the symplectic variable approaches a cusp. The invariance is then a consequence of the automorphic nature of this theta function, coupled with the fact that in the limit it acts as the reproducing kernel for a certain lattice. Using results of Stark and Styer, this also allows one to determine the root of unity involved.     

Reaction of t-butoxy radicals with norbornadiene

95 percent of the reaction of t-butoxy radical with norbornadiene occurs by radical addition followed by rearrangement to nortricyclyl and 7-t-butoxynorbornenyl products; the remainder includes a novel radical rearrangement involving a 1,3-H shift and some radical abstraction observed for the first time.     

Epitaxial GaP by a semi-sealed dip process for high efficiency red LED's

A semi-sealed dip process has been used to grow Zn-O doped GaP layers for high efficiency red LED's. A close fitting floating quartz plug is used to prevent volatilization of Zn, Ga₂O, and GaP during saturation. Double epitaxial layers with efficiencies as high as 8. 0% have been grown by this process.