Heisenberg model and a random walk on the permutation group

It is shown that the isotropic Heisenberg model can be analysed in terms of a random walk on the permutation group. This approach makes it intuitively clear why the Heisenberg model exhibits long range order or ferrogmagnetic behavior in three dimensions and not in two and one dimensions. This approach to the Heisenberg model lends itself to computer analysis.Work supported in part by the National Science Foundation     

The Darboux point

A theory of global optimality based upon the Darboux-point concept is developed. A definition is proposed for the Darboux point, and the Darboux point is shown to exist on nonglobally optimal trajectories under relatively general conditions. A mutually exclusive classification of Darboux points is noted, and several properties are proved for one of these classes (the Type-1 Darboux point). Numerous examples are included to illustrate the Darboux-point definition and properties.     

Resistance inequalities for KMS states of the isotropic Heisenberg model

Inequalities which show that the spin correlations between spins at two lattice sites is bounded by a constant times the inverse square root of the electrical resistance between the lattice sites is proved for KMS states of the isotropic Heisenberg model. The resistance is calculated using the inverse of the coefficients occuring in the Heisenberg Hamiltionian as the resistances between neighboring lattice sites.Work supported in part by a National Science Foundation GrantOn leave from the University of Pennsylvania, Philadelphia, Pa. 19174, USA     

Numerical predictions of oblique detonation stability boundaries

Oblique detonation stability was studied by numerically integrating the two-dimensional, one-step reactive Euler equations in a generalized, curvilinear coordinate system. The integration was accomplished using the Roe scheme combined with fractional stepping; nonlinear flux limiting was used to prevent unphysical solution oscillations near discontinuities. The method was verified on one- and two-dimensional flows with exact solutions, and its ability to correctly predict one-dimensional detonation stability boundaries was demonstrated. The behavior of straight oblique detonations attached to curved walls was then considered. Using the exact, steady oblique detonation solution as an initial condition, the numerical simulation predicted both steady and unsteady oblique detonation solutions when a detonation parameter known as the normal overdrive, , was varied. For a standard test case with a specific heat ratio of , a dimensionless activation energy of , and dimensionless heat release of , an oblique detonation with a constant dimensionless component of velocity tangent to the lead shock, , underwent transition to unstable behavior at . This is slightly higher than the threshold of predicted by one-dimensional theory; thus, the two-dimensionality renders the flow slightly more susceptible to instability. Received 4 August 1996 / Accepted 5 March 1996     

Optical parametric processes and broadly tunable femtosecond sources

The basic concepts of optical parametric processes and recent results on broadly tunable high-repetition rate femtosecond Optical Parametric Oscillators (fs OPO) are reviewed. Ti:Sapphire-Laser pumped KTP, KTA, and CTA fs OPOs and intracavity-doubled fs KTP OPO in particular are discussed.     

Induced residuated maps

The purpose of this paper is to introduce a class of mappings from a lattice L, whose elements are residuated maps, into itself. The main results of this paper identify certain injective residuated mappings of L and order automorphisms of a sublattice of L with mappings from this class.