Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (M\"obius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0 > 0$. The chromatic zeros and their accumulation set ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.Comment: 7 pages, Latex, 4 figs., J. Phys. A Lett., in pres

Mathematical wind profiles, parts 1, 2, 3, 4

Fourier holograph representation of wind velocity over Cape Kenned

Mathematical wind profiles

Augmented Fourier polynomials for mathematical representation of vertical profiles for horizontal wind velocitie

Development of a space qualified high reliability rotary actuator. Volume 1: Technical report

A space-qualified, high reliability, 150 ft-lb rated torque rotary acutator based on the Bendix Dynavector drive concept was developed. This drive is an integrated variable reluctance orbit motor-epicyclic transmission actuator. The performance goals were based on future control moment gyro torquer applications and represent a significant advancement in the torque-to-weight ratio, backlash, inertia and response characteristics of electric rotary drives. The program accomplishments have been in two areas: (1) the development of two high ratio (818:1) actuator configurations (breadboard and flightweight), and (2) the invention of a reliable proximity switch sensor system for self-commutation without use of optical or electrical brush techniques

Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, $W$, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, ${\cal B}$, of nonanalyticities in $W$. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where $S_0 > 0$.Comment: 27 pages, Latex, 17 figs. J. Phys. A, in pres

Edge excitations and Topological orders in rotating Bose gases

The edge excitations and related topological orders of correlated states of a fast rotating Bose gas are studied. Using exact diagonalization of small systems, we compute the energies and number of edge excitations, as well as the boson occupancy near the edge for various states. The chiral Luttinger-liquid theory of Wen is found to be a good description of the edges of the bosonic Laughlin and other states identified as members of the principal Jain sequence for bosons. However, we find that in a harmonic trap the edge of the state identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An experimental way of detecting these correlated states is also discussed.Comment: Results extended to larger systems. Improved presentatio

A simplified model of the Martian atmosphere - Part 1: a diagnostic analysis

In this paper we derive a reduced-order approximation to the vertical and horizontal structure of a simplified model of the baroclinically unstable Martian atmosphere. The original model uses the full hydrostatic primitive equations on a sphere, but has only highly simplified schemes to represent the detailed physics of the Martian atmosphere, e.g. forcing towards a plausible zonal mean temperature state using Newtonian cooling. Three different norms are used to monitor energy conversion processes in the model and are then compared. When four vertical modes (the barotropic and first three baroclinic modes) are retained in the reduced-order approximation, the correlation norm captures approximately 90% of the variance, while the kinetic energy and total energy norms capture approximately 83% and 78% of the kinetic and total energy respectively. We show that the leading order Proper Orthogonal Decomposition (POD) modes represent the dominant travelling waves in the baroclinically-unstable, winter hemisphere. In part 2 of our study we will develop a hierarchy of truncated POD-Galerkin expansions of the model equations using up to four vertical modes

A simplified model of the Martian atmosphere - Part 2: a POD-Galerkin analysis

In Part I of this study Whitehouse et al. (2005) performed a diagnostic analysis of a simplied model of the Martian atmosphere, in which topography was absent and in which heating was modelled as Newtonian relaxation towards a zonally symmetric equilibrium temperature field. There we derived a reduced-order approximation to the vertical and the horizonal structure of the baroclinically unstable Martian atmosphere, retaining only the barotropic mode and the leading order baroclinic modes. Our objectives in Part II of the study are to incorporate these approximations into a Proper Orthogonal Decomposition-Galerkin expansion of the spherical quasi-geostrophic model in order to derive hierarchies of nonlinear ordinary differential equations for the time-varying coefficients of the spatial structures. Two different vertical truncations are considered, as well as three different norms and 3 different Galerkin truncations. We investigate each in turn, using tools from bifurcation theory, to determine which of the systems most closely resembles the data for which the original diagnostics were performed

Magnetic phenomena at and near nu =1/2 and 1/4: theory, experiment and interpretation

I show that the hamiltonian theory of Composite Fermions (CF) is capable of yielding a unified description in fair agreement with recent experiments on polarization P and relaxation rate 1/T_1 in quantum Hall states at filling nu = p/(2ps+1), at and near nu = 1/2 and 1/4, at zero and nonzero temperatures. I show how rotational invariance and two dimensionality can make the underlying interacting theory behave like a free one in a limited context.Comment: Latex 4 pages, 2 figure

Tunneling spectroscopy studies of aluminum oxide tunnel barrier layers

We report scanning tunneling microscopy and ballistic electron emission microscopy studies of the electronic states of the uncovered and chemisorbed-oxygen covered surface of AlOx tunnel barrier layers. These states change when chemisorbed oxygen ions are moved into the oxide by either flood gun electron bombardment or by thermal annealing. The former, if sufficiently energetic, results in locally well defined conduction band onsets at ~1 V, while the latter results in a progressively higher local conduction band onset, exceeding 2.3 V for 500 and 600 C thermal anneals