Index theorems for quantum graphs

In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order differential operators as an intermediary. In this paper, the case of quantum graphs is addressed. A quantum graph is a graph considered as a (singular) one-dimensional variety and equipped with a second-order differential Hamiltonian H (a "Laplacian") with suitable conditions at vertices. For the case of scale-invariant vertex conditions (i.e., conditions that do not mix the values of functions and of their derivatives), the constant term of the heat-kernel expansion is shown to be proportional to the trace of the internal scattering matrix of the graph. This observation is placed into the index-theory context by factoring the Laplacian into two first-order operators, H =A*A, and relating the constant term to the index of A. An independent consideration provides an index formula for any differential operator on a finite quantum graph in terms of the vertex conditions. It is found also that the algebraic multiplicity of 0 as a root of the secular determinant of H is the sum of the nullities of A and A*.Comment: 19 pages, Institute of Physics LaTe

Analysis of the physical atomic forces between noble gas atoms, alkali ions and halogen ions

The physical forces between atoms and molecules are important in a number of processes of practical importance, including line broadening in radiative processes, gas and crystal properties, adhesion, and thin films. The components of the physical forces between noble gas atoms, alkali ions, and halogen ions are analyzed and a data base for the dispersion forces is developed from the literature based on evaluations with the harmonic oscillator dispersion model for higher order coefficients. The Zener model of the repulsive core is used in the context of the recent asymptotic wave functions of Handler and Smith; and an effective ionization potential within the Handler and Smith wave functions is defined to analyze the two body potential data of Waldman and Gordon, the alkali-halide molecular data, and the noble gas crystal and salt crystal data. A satisfactory global fit to this molecular and crystal data is then reproduced by the model to within several percent. Surface potentials are evaluated for noble gas atoms on noble gas and salt crystal surfaces with surface tension neglected. Within this context, the noble gas surface potentials on noble gas and salt crystals are considered to be accurate to within several percent

Repulsive Casimir Pistons

Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive. We present three scenarios in which that is not true. Two of these depend on mixing two types of boundary conditions. The other, however, is a simple type of quantum graph in which the sign of the force depends upon the number of edges.Comment: 4 pages, 2 figures; RevTeX. Minor additions and correction

Helicopter Anti-Torque System Using Strakes

A helicopter is disclosed with a system for controlling main-rotor torque which reduces the power and size requirements of conventional anti-torque means. The torque countering forces are generated by disrupting the main rotor downwash flowing around the fuselage. The downwash flow is separated from the fuselage surface by a strake positioned at a specified location on the fuselage. This location is determined by the particular helicopter wash pattern and fuselage configuration, generally being located between 20 deg before top dead center (TDC) and 80 deg from TDC on the fuselage side to which the main rotor blade approaches during rotation. The strake extends along the fuselage from the cabin section to the aft end and can be continuous or separated for aerodynamic surfaces such as a horizontal stabilizer

Patterns of gene expression in schistosomes: localization by whole mount in situ hybridization

rom the identification of genes to the characterization of their functions and interactions. Developmental biologists have long used whole mount in situ hybridization (WISH) to determine gene expression patterns, as a vital tool for formulating and testing hypotheses about function. This paper describes the application of WISH to the study of gene expression in larval and adult schistosomes. Fixed worms were permeablized by proteinase K treatment for hybridization with digoxygenin-labelled RNA probes, with binding being detected by alkaline phosphatase-coupled anti-digoxygenin antibodies, and BM Purple substrate. Discrete staining patterns for the transcripts of the molecules Sm29, cathepsin L, antigen 10.3 and chorion were observed in the tegument cell bodies, gut epithelium, oesophageal gland and vitelline lobules, respectively, of adult worms. Transcripts of the molecules SGTP4, GP18-22 and cathepsin L were localized to tegument cell bodies and embryonic gut, respectively, of lung schistosomula. We also showed that Fast Red TR fluorescent substrate can refine the pattern of localization permitting use of confocal microscopy. We believe that method of WISH will find broad application, in synergy with other emerging post-genomic techniques, such as RNA interference, to studies focused at increasing our molecular understanding of schistosomes

The Nuclear Outflow in NGC 2110

We present a HST/STIS spectroscopic and optical/radio imaging study of the Seyfert NGC 2110 aiming to measure the dynamics and understand the nature of the nuclear outflow in the galaxy. Previous HST studies have revealed the presence of a linear structure in the Narrow-Line Region (NLR) aligned with the radio jet. We show that this structure is strongly accelerated, probably by the jet, but is unlikely to be entrained in the jet flow. The ionisation properties of this structure are consistent with photoionisation of dusty, dense gas by the active nucleus. We present a plausible geometrical model for the NLR, bringing together various components of the nuclear environment of the galaxy. We highlight the importance of the circum-nuclear disc in determining the appearance of the emission line gas and the morphology of the jet. From the dynamics of the emission line gas, we place constraints on the accelerating mechanism of the outflow and discuss the relative importance of radio source synchrotron pressure, radio jet ram pressure and nuclear radiation pressure in accelerating the gas. While all three mechanisms can account for the energetics of the emission line gas, gravitational arguments support radio jet ram pressure as the most likely source of the outflow.Comment: 15 pages, 7 figures; accepted to MNRA

Chemical kinetic modeling of benzene and toluene oxidation behind shock waves

The oxidation of stoichiometric mixtures of benzene and toluene behind incident shock waves was studied for a temperature range from 1700 to 2800 K and a pressure range from 1.1 to 1.7 atm. The concentration of CO and CO2 produced were measured as well as the product of the oxygen atom and carbon monoxide concentrations. Comparisons between the benzene experimental data and results calculated by use of a reaction mechanism published in the open literature were carried out. With some additional reactions and changes in rate constants to reflect the pressure-temperature range of the experimental data, a good agreement was achieved between computed and experimental results. A reaction mechanism was developed for toluene oxidation based on analogous rate steps from the benzene mechanism. Measurements of NOx levels in an actual flame device, a jet-stirred combustor, were reproduced successfully by use of the reaction mechanism developed from the shock-tube experiments on toluene. These experimental measurements of NOx levels were reproduced from a computer simulation of a jet-stirred combustor

A simple model of proton damage in GaAs solar cells

A simple proton damage model for GaAs solar cells is derived and compared to experimental values of change in short circuit currents. The recombination cross section associated with the defects was determined from the experimental comparison to be approximately 1.2 x 10 to the -13th power sq cm in fair agreement with values determined from the deep level transient spectroscopy technique