Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement

Influence of experimental parameters on in vitro human skin permeation of Bisphenol A.

Bisphenol A (BPA) in vitro skin permeation studies have shown inconsistent results, which could be due to experimental conditions. We studied the impact of in vitro parameters on BPA skin permeation using flow-through diffusion cells with ex-vivo human skin (12 donors, 3-12 replicates). We varied skin status (viable or frozen skin) and thickness (200, 400, 800 μm), BPA concentrations (18, 250 mg/l) and vehicle volumes (10, 100 and 1000 μl/cm <sup>2</sup> ). These conditions led to a wide range of BPA absorption (2%-24% after 24 h exposure), peak permeation rates (J = 0.02-1.31 μg/cm <sup>2</sup> /h), and permeability coefficients (K <sub>p</sub> = 1.6-5.2 × 10 <sup>-3</sup> cm/h). This is the first time steady state conditions were reached for BPA aqueous solutions in vitro (1000 μl/cm <sup>2</sup> applied at concentration 250 mg/l). A reduction of the skin thickness from 800 and 400 μm to 200 μm led to a 3-fold increase of J (P < 0.05). A reduction of the vehicle volume from 1000 to 100 led to a 2-fold decrease in J (P > 0.05). Previously frozen skin led to a 3-fold increase in J compared to viable skin (P < 0.001). We found that results from published studies were consistent when adjusting J according to experimental parameters. We propose appropriate J values for different exposure scenarios to calculate BPA internal exposures for use in risk assessment

A Quantum Approach to Classical Statistical Mechanics

We present a new approach to study the thermodynamic properties of $d$-dimensional classical systems by reducing the problem to the computation of ground state properties of a $d$-dimensional quantum model. This classical-to-quantum mapping allows us to deal with standard optimization methods, such as simulated and quantum annealing, on an equal basis. Consequently, we extend the quantum annealing method to simulate classical systems at finite temperatures. Using the adiabatic theorem of quantum mechanics, we derive the rates to assure convergence to the optimal thermodynamic state. For simulated and quantum annealing, we obtain the asymptotic rates of $T(t) \approx (p N) /(k_B \log t)$ and $\gamma(t) \approx (Nt)^{-\bar{c}/N}$, for the temperature and magnetic field, respectively. Other annealing strategies, as well as their potential speed-up, are also discussed.Comment: 4 pages, no figure

Aquifer thermal energy storage : A well doublet experiment at increased temperatures

This is the published version. Copyright 1983 American Geophysical UnionThe two main objectives of this communication are to present a study of potential advantages and disadvantages of the doublet supply-injection well configuration in an aquifer thermal energy storage (ATES) system and to report on aquifer storage problems with injection temperatures in the 80°C range. A 3-month injection-storage-recovery cycle followed by a 7.3-month cycle constituted the main experiment. The injection volumes were 25,402 m3 and 58,063 m3 at average temperatures of 58.5°C and 81°C respectively. Unlikely previous experiments at the Mobile site, no clogging of the injection well due to clay particle swelling, dispersion, and migration was observed. This is attributed to the fact that the supply water used for injection contained a cation concentration equal to or slightly greater than that in the native groundwater. For cycles I and II, the fraction of injected energy recovered in a volume of water equal to the injection volume was 0.56 and 0.45 respectively. Both groundwater temperature and tracer data support the conclusion that this relatively low recovery was due to the detrimental effects of free thermal convection, possibly augmented by longitudinal zones of high permeability. Construction of a partially penetrating recovery well improved recovery efficiency but is not thought to be an adequate solution to thermal stratification. A maximum increase of 1.24 cm in relative land surface elevation was recorded near the end of second cycle injection. The engineering implications of such an elevation change would have to be considered, especially if an ATES system were being designed in an urban environment. A third cycle was started at the Mobile site on April 7, 1982. This final experiment contains a partially penetrating, dual-recovery well system which is expected to maximize energy recovery from a thermally stratified storage aquifer

Aspects of the Noisy Burgers Equation

The noisy Burgers equation describing for example the growth of an interface subject to noise is one of the simplest model governing an intrinsically nonequilibrium problem. In one dimension this equation is analyzed by means of the Martin-Siggia-Rose technique. In a canonical formulation the morphology and scaling behavior are accessed by a principle of least action in the weak noise limit. The growth morphology is characterized by a dilute gas of nonlinear soliton modes with gapless dispersion law with exponent z=3/2 and a superposed gas of diffusive modes with a gap. The scaling exponents and a heuristic expression for the scaling function follow from a spectral representation.Comment: 23 pages,LAMUPHYS LaTeX-file (Springer), 13 figures, and 1 table, to appear in the Proceedings of the XI Max Born Symposium on "Anomalous Diffusion: From Basics to Applications", May 20-24, 1998, Ladek Zdroj, Polan

A note on the extension of the polar decomposition for the multidimensional Burgers equation

It is shown that the generalizations to more than one space dimension of the pole decomposition for the Burgers equation with finite viscosity and no force are of the form u = -2 viscosity grad log P, where the P's are explicitly known algebraic (or trigonometric) polynomials in the space variables with polynomial (or exponential) dependence on time. Such solutions have polar singularities on complex algebraic varieties.Comment: 3 pages; minor formatting and typos corrected. Submitted to Phys. Rev. E (Rapid Comm.

Reconstructing the global topology of the universe from the cosmic microwave background

If the universe is multiply-connected and sufficiently small, then the last scattering surface wraps around the universe and intersects itself. Each circle of intersection appears as two distinct circles on the microwave sky. The present article shows how to use the matched circles to explicitly reconstruct the global topology of space.Comment: 6 pages, 2 figures, IOP format. To be published in the proceedings of the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to Class. Quant. Gra

Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary differential equation to govern the functional dependence of the principal curvatures. Employing the scaling and translation (offsetting) symmetry, we give a general solution of the governing equation in terms of elliptic integrals. We show that the instances when the elliptic integrals degenerate to elementary functions were known to nineteenth century geometers. Finally, we characterize the associated normal congruences