Convective Heat Transfer past Small Cylindrical Bodies

Convective heat transfer from an array of small, cylindrical bodies of arbitrary shape in an unbounded, two-dimensional domain is a singular perturbation problem involving an infinite logarithmic expansion in the small parameter ε, representing the order of magnitude of the size of the bodies. Using the method of matched asymptotic expansions, we formulate a hybrid asymptotic-numerical method to solve for the dimensionless, steady-state temperature. We assume that the velocity field of the fluid surrounding the bodies is arbitrary but known. From our asymptotic solution for an arbitrary velocity field, we present the results for two special cases: a uniform flow field and a simple shear flow field. We demonstrate the asymptotic results of the hybrid method through a number of examples and, in a particular case, we compare these results to an exact analytical solution.     

Enumeration of three-dimensional convex polygons

A self-avoiding polygon (SAP) on a graph is an elementary cycle. Counting SAPs on the hypercubic lattice ℤ ^d withd≥2, is a well-known unsolved problem, which is studied both for its combinatorial and probabilistic interest and its connections with statistical mechanics. Of course, polygons on ℤ ^d are defined up to a translation, and the relevant statistic is their perimeter. A SAP on ℤ ^d is said to beconvex if its perimeter is “minimal”, that is, is exactly twice the sum of the side lengths of the smallest hyper-rectangle containing it. In 1984, Delest and Viennot enumerated convex SAPs on the square lattice [6], but no result was available in a higher dimension. We present an elementar approach to enumerate convex SAPs in any dimension. We first obtain a new proof of Delest and Viennot's result, which explains combinatorially the form of the generating function. We then compute the generating function for convex SAPs on the cubic lattice. In a dimension larger than 3, the details of the calculations become very cumbersome. However, our method suggests that the generating function for convex SAPs on ℤ ^d is always a quotient ofdifferentiably finite power series.     

On Discrete Zariski-Dense Subgroups of Algebraic Groups

We investigate under which conditions an algebraic group G defined over a locally compact field k admitr a subgroup Γ? G(k) which is dense in the Zariski topology, but discerte in the topology induced by the locally compact topology on k. For non—solvable groups we provide a complete answer.     

Preparation and Eh--pH diagrams of Fe(II)--Fe(III) green rust compounds; hyperfine interaction characteristics and stoichiometry of hydroxy-chloride, -sulphate and -carbonate

Fe(II)--Fe(III) hydroxy-chloride, -sulphate and -carbonate were prepared by oxidation of a ferrous hydroxide precipitate in anion-containing aqueous solutions. The compounds are characterized by monitoring the redox potential E_h and the pH of stochiometric suspension vs time with the appropriate concentration ratios. X-ray diffraction allows us to characterize the crystal structure by distinguishing “green rust one” (GR1) from “green rust two” (GR2). Since green rusts (GRs) are of a pyroaurite-sjögrenite-like structure, i.e., consisting of intercalated foreign anions and water molecules in the interlayers between the brucite-like layers of Fe(OH)₂, their chemical formulae can be determined from the Mössbauer spectra. Three quadrupole doublets are observed: D₁ and D₂ correspond to a ferrous state with isomershift IS of about 1.27 mm s^-1 and quadrupole splittings QS of about 2.85 and 2.60 mm s^-1, respectively, whereas D₃ corresponds to a ferric state with IS and QS of about 0.4 mm s^-1. The hyperfine parameters of these doublets are similar from one green rust to another but their intensity ratios vary considerably. Finally, E_h and pH equilibrium diagrams of the Fe species in the presence of chloride, sulphate and carbonate anions contained within the water solution are drawn and the thermodynamic conditions of existence and degrees of oxidation of green rusts are discussed.     

Algorithm for cosine transform of Toeplitz matrices

An algorithm for calculating the 2D cosine transform of a Toeplitz matrix is presented. The algorithm is based on the application of 1D cosine transforms. More specifically, four 1D cosine transforms of size N are needed to obtain the transform of a Toeplitz matrix of size N×N. This is an improvement over previously published algorithms. The algorithm is also simple and regular     

Chaotic oscillator in wavelength: a new setup for investigatingdifferential difference equations describing nonlinear dynamics

A generator of chaos in wavelength is reported. It is formed by a wavelength-tunable laser diode with a time delayed feedback loop in which a wavelength nonlinear-linear device is introduced. The dynamical regime of wavelength emission thus obtained is ruled by a differential difference equation. Experimental results are compared with numerical simulations and with previous theoretical and experimental results     

Determination of land and ocean reflective, radiative, andbiophysical properties using multiangle imaging

Knowledge of the directional and hemispherical reflectance properties of natural surfaces, such as soils and vegetation canopies, is essential for classification studies and canopy model inversion. The Multi-angle Imaging SpectroRadiometer (MISR), an instrument to be launched in 1998 onboard the EOS-AM1 platform, will make global observations of the Earth's surface at 1.1-km spatial resolution, with the objective of determining the atmospherically corrected reflectance properties of most of the land surface and the tropical ocean. The algorithms to retrieve surface directional reflectances, albedos, and selected biophysical parameters using MISR data are described. Since part of the MISR data analyses includes an aerosol retrieval, it is assumed that the optical properties of the atmosphere (i.e. aerosol characteristics) have been determined well enough to accurately model the radiative transfer process. The core surface retrieval algorithms are tested on simulated MISR data, computed using realistic surface reflectance and aerosol models, and the sensitivity of the retrieved directional and hemispherical reflectances to aerosol type and column amount is illustrated. Included is a summary list of the MISR surface products     

A Deformation-Theoretical Approach to Weyl Quantization on Riemannian Manifolds

By using a sheaf-theoretical language, we introduce a notion of deformation quantization allowing not only for formal deformation parameters but also for real or complex ones as well. As a model for this approach to deformation quantization, we construct a quantization scheme for cotangent bundles of Riemannian manifolds. Here, we essentially use a complete symbol calculus for pseudodifferential operators on a Riemannian manifold. Depending on a scaling parameter, our quantization scheme corresponds to normally ordered, Weyl or antinormally ordered quantization. Finally, it is shown that our quantization scheme induces a family of pairwise isomorphic strongly closed star products on a cotangent bundle.     

Fixed-frequency and threshold molecular photoelectron spectra of S 1s, Si 1s and Cl 1s core levels

Fixed-frequency and threshold photoelectron spectra have been recorded for ionization from the S ls shells in SF₆, CS₂ and COS, the Si 1s shells in SiH₄ and SiCl₄ and the Cl 1s shell in SiCl₄ using synchrotron radiation. Fixed-frequency spectra generally showed a single strong ionization feature with associated weak satellite structure due to excited ionized states. Threshold spectra closely resembled X-ray absorption spectra but with an additional feature due to direct ionization. In cases where resonant process enhanced the NEXAFS spectrum direct ionization was not observed.