A quantum group version of quantum gauge theories in two dimensions

For the special case of the quantum group $SL_q (2,{\bf C})\ (q= \exp \pi i/r,\ r\ge 3)$ we present an alternative approach to quantum gauge theories in two dimensions. We exhibit the similarities to Witten's combinatorial approach which is based on ideas of Migdal. The main ingredient is the Turaev-Viro combinatorial construction of topological invariants of closed, compact 3-manifolds and its extension to arbitrary compact 3-manifolds as given by the authors in collaboration with W. Mueller.Comment: 6 pages (plain TeX

Notes on Lithology, Mineralogy, and Production for Lunar Simulants

The creation of lunar simulants requires a very broad range of specialized knowledge and information. This document covers several topic areas relevant to lithology, mineralogy, and processing of feedstock materials that are necessary components of the NASA lunar simulant effort. The naming schemes used for both terrestrial and lunar igneous rocks are discussed. The conflict between the International Union of Geological Sciences standard and lunar geology is noted. The rock types known as impactites are introduced. The discussion of lithology is followed by a brief synopsis of pyroxene, plagioclase, and olivine, which are the major mineral constituents of the lunar crust. The remainder of the text addresses processing of materials, particularly the need for separation of feedstock minerals. To illustrate this need, the text includes descriptions of two norite feedstocks for lunar simulants: the Stillwater Complex in Montana, United States, and the Bushveld Complex in South Africa. Magnetic mineral separations, completed by Hazen Research, Inc. and Eriez Manufacturing Co. for the simulant task, are discussed

Global Bounds for the Lyapunov Exponent and the Integrated Density of States of Random Schr\"odinger Operators in One Dimension

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These Schr\"odinger operators are given by potentials of identical shape centered at every lattice site but with non-overlapping supports and with randomly varying coupling constants. Both types of bounds only involve scattering data for the single-site potential. They show in particular that both $\gamma(E)$ and $N(E)-\sqrt{E}/\pi$ decay at infinity at least like $1/\sqrt{E}$. As an example we consider the random Kronig-Penney model.Comment: 9 page

Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

Mars Exploration Rover APXS Results from Matijevic Hill

Correlation analysis of APXS results on the eastern slope rocks indicate that the Matijevic Hill rocks are overall compositionally distinct from the Shoemaker Formation rocks [6]. Compared to the Shoemaker impactites, Matijevic Hill rocks are higher in Al, Si, and Ni, and lower in Ti, Fe, and Zn. No significant variation is evident in the APXS analyses that indicate the presence of a smectite or other phyllosilicate, as opposed to basaltic rocks. However, APXS data cannot in themselves rule out phyllosilicates. If indeed this material contains smectite, as seen from orbit, it implies that the rock has been isochemically altered to create the phyllosilicate content. The Cl content of the Cape York rocks is relatively high, and whereas the S/Cl ratio in the Burns Formation is 4x higher than in soil, in the Cape York rocks it is lower than in soil. These trends indicate that the alteration processes and types of aqueous salt loads were different between Cape York and Meridiani. In addition, significant deviations from the Martian Mn/Fe ratio are observed in Whitewater Lake coatings and the altered Grasford/Deadwood rocks (Fig. 3). These variations indicate that the redox/pH conditions during alteration of the Shoemaker Formation rocks and the Matijevic Hill rocks were similar, but that the Deadwood/Grasberg unit may have undergone alteration under different conditions, possibly at a later time. The Matijevic Hill outcrops appear to share a common genetic origin. It is not yet clear whether both the Shoemaker impactites and Matijevic Hill rocks are related to the formation of Endeavour Crater, or whether the Matijevic Hill suite represents a prior episode of Martian impact or volcanism. Opportunity continues to investigate both hypotheses

Power Spectrum Analysis of Physikalisch-Technische Bundesanstalt Decay-Rate Data: Evidence for Solar Rotational Modulation

Evidence for an anomalous annual periodicity in certain nuclear decay data has led to speculation concerning a possible solar influence on nuclear processes. We have recently analyzed data concerning the decay rates of Cl-36 and Si-32, acquired at the Brookhaven National Laboratory (BNL), to search for evidence that might be indicative of a process involving solar rotation. Smoothing of the power spectrum by weighted-running-mean analysis leads to a significant peak at frequency 11.18/yr, which is lower than the equatorial synodic rotation rates of the convection and radiative zones. This article concerns measurements of the decay rates of Ra-226 acquired at the Physikalisch-Technische Bundesanstalt (PTB) in Germany. We find that a similar (but not identical) analysis yields a significant peak in the PTB dataset at frequency 11.21/yr, and a peak in the BNL dataset at 11.25/yr. The change in the BNL result is not significant since the uncertainties in the BNL and PTB analyses are estimated to be 0.13/yr and 0.07/yr, respectively. Combining the two running means by forming the joint power statistic leads to a highly significant peak at frequency 11.23/yr. We comment briefly on the possible implications of these results for solar physics and for particle physics.Comment: 15 pages, 13 figure

The Berry-Keating operator on L^2(\rz_>, x) and on compact quantum graphs with general self-adjoint realizations

The Berry-Keating operator H_{\mathrm{BK}}:= -\ui\hbar(x\frac{ \phantom{x}}{ x}+{1/2}) [M. V. Berry and J. P. Keating, SIAM Rev. 41 (1999) 236] governing the Schr\"odinger dynamics is discussed in the Hilbert space L^2(\rz_>, x) and on compact quantum graphs. It is proved that the spectrum of $H_{\mathrm{BK}}$ defined on L^2(\rz_>, x) is purely continuous and thus this quantization of $H_{\mathrm{BK}}$ cannot yield the hypothetical Hilbert-Polya operator possessing as eigenvalues the nontrivial zeros of the Riemann zeta function. A complete classification of all self-adjoint extensions of $H_{\mathrm{BK}}$ acting on compact quantum graphs is given together with the corresponding secular equation in form of a determinant whose zeros determine the discrete spectrum of $H_{\mathrm{BK}}$. In addition, an exact trace formula and the Weyl asymptotics of the eigenvalue counting function are derived. Furthermore, we introduce the "squared" Berry-Keating operator $H_{\mathrm{BK}}^2:= -x^2\frac{ ^2\phantom{x}}{ x^2}-2x\frac{ \phantom{x}}{ x}-{1/4}$ which is a special case of the Black-Scholes operator used in financial theory of option pricing. Again, all self-adjoint extensions, the corresponding secular equation, the trace formula and the Weyl asymptotics are derived for $H_{\mathrm{BK}}^2$ on compact quantum graphs. While the spectra of both $H_{\mathrm{BK}}$ and $H_{\mathrm{BK}}^2$ on any compact quantum graph are discrete, their Weyl asymptotics demonstrate that neither $H_{\mathrm{BK}}$ nor $H_{\mathrm{BK}}^2$ can yield as eigenvalues the nontrivial Riemann zeros. Some simple examples are worked out in detail.Comment: 33p

An advanced expiratory circuit for the recovery of perfluorocarbon liquid from non-saturated perfluorocarbon vapour during partial liquid ventilation: an experimental model

BACKGROUND: The loss of perfluorocarbon (PFC) vapour in the expired gases during partial liquid ventilation should be minimized both to prevent perfluorocarbon vapour entering the atmosphere and to re-use the recovered PFC liquid. Using a substantially modified design of our previously described condenser, we aimed to determine how much perfluorocarbon liquid could be recovered from gases containing PFC and water vapour, at concentrations found during partial liquid ventilation, and to determine if the amount recovered differed with background flow rate (at flow rates suitable for use in neonates). METHODS: The expiratory line of a standard ventilator circuit set-up was mimicked, with the addition of two condensers. Perfluorocarbon (30 mL of FC-77) and water vapour, at concentrations found during partial liquid ventilation, were passed through the circuit at a number of flow rates and the percentage recovery of the liquids measured. RESULTS: From 14.2 mL (47%) to 27.3 mL (91%) of the infused 30 mL of FC-77 was recovered at the flow rates studied. Significantly higher FC-77 recovery was obtained at lower flow rates (ANOVA with Bonferroni's multiple comparison test, p < 0.0001). As a percentage of the theoretical maximum recovery, 64 to 95% of the FC-77 was recovered. Statistically significantly less FC-77 was recovered at 5 Lmin(-1 )(ANOVA with Bonferroni's multiple comparison test, p < 0.0001). Amounts of perfluorocarbon vapour recovered were 47%, 50%, 81% and 91% at flow rates of 10, 5, 2 and 1 Lmin(-1), respectively. CONCLUSION: Using two condensers in series 47% to 91% of perfluorocarbon liquid can be recovered, from gases containing perfluorocarbon and water vapour, at concentrations found during partial liquid ventilation

Search for Flavoured Multiquarks in a Simple Bag Model

We use a bag model to study flavoured mesonic $(Qq\bar q\bar q)$ and baryonic $({\overline Q}qqqq)$ states, where one heavy quark $Q$ is associated with light quarks or antiquarks, and search for possible stable multiquarks. No bound state is found. However some states lie not too high above their dissociation threshold, suggesting the possibility of resonances, or perhaps bound states in improved models.Comment: REVTEX, VERSION 3.