Surface tension and density of liquid Sn-Ag alloys

The surface tension and density measurements for Sn-Ag alloys were carried out with the sessile drop method. Seven different compositions were investigated in the range from 0.011 to 0.5 mole fraction of Ag, in a broad range of temperature. With increasing concentrations of Ag, both density and the surface tension are increased. With increasing temperature the density decreases for all of the alloys. A decrease of the surface tension is observed for most of the composition except for the alloy of 0.5 mole fractions of Ag. The obtained results are compared with existing literature data and Butler model calculations and relatively good agreement is observed.     

Estimation of the transient interfacial heat flux between substrate/melt at the initiation of magnesium solidification on aluminum substrates using the lumped capacitance method

Interfacial heat flux (IHF) between solid pure aluminum/magnesium melt and solid 413 aluminum alloy/magnesium melt couples was evaluated using lumped capacitance method, and the interface microstructures were assessed by scanning electronic microscope. The variation of maximum IHF with surface roughness for these two couples also was evaluated. The results showed that, for both solid aluminum/magnesium melt couples, with increasing the surface roughness, the maximum IHF increases at first and then starts to decrease after reaching a maximum value. In addition the measured maximum IHF for solid 413 aluminum alloy/magnesium melt couples was found to be higher than those measured for solid pure aluminum/magnesium melt couples. That seems to be because of the better wettability of 413 aluminum alloy than pure aluminum, by magnesium melt.     

Effect of surface oxidation on the surface condition and deuterium permeability of a palladium membrane

Oxidation and deoxidation of a Pd membrane was conducted in a quartz tube oven in a temperature range of 23-500 °C. The micromorphology and chemical composition of the Pd membrane surface was characterized using scanning electronic microscopy (SEM) and X-ray photoelectron spectroscopy (XPS). Micropores and PdO began to form on the Pd membrane surface after oxidation at 240 °C for 1 h and their quantity increased gradually with increasing temperature. A rough Pd membrane surface was obtained when the temperature rose to 500 °C. The PdO on the Pd membrane surface was completely deoxidized once more using H₂ at room temperature, but the rough surface morphology caused by oxidation remained. The deuterium permeability of the Pd membrane was tested using special equipment in the China National Key Laboratory and the results indicated that the rough Pd membrane surface had higher deuterium permeability than the original membrane. The improved deuterium permeability could be attributed to the higher Pd membrane surface area, which provided deuterium atoms with more adsorption sites and dissociation sites.     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Prym Representations of Mapping Class Groups

Let S be a closed orientable surface of genus at least 2 and let to S be a connected finite abelian covering with covering group $G$. The lifts of liftable mapping classes of S determine a central extension (by G) of a subgroup of finite index of the mapping class group of S. This extension acts on H₁( ). With a few exceptions for genus 2, we determine the Zariski closure of the image of this representation, and prove that the image is an arithmetic group.     

Crossed Modules and Quantum Groups in Braided Categories

Let A be a Hopf algebra in a braided category . Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group the corresponding braided category of modules is identified with a full subcategory in . The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized.     

Geometric Analysis and Symbol Calculus: Fourier Transform Magnetic Resonance Imaging and Wavelets

Due to its unequalled advantages, the magnetic resonance imaging (MRI) modality has truly revolutionized the diagnosis and evaluation of pathology. Because many morphological anatomic details that may not be visualized by other high tech imaging methods can now be readily shown by diagnostic MRI, it has already become the standard modality by which all other clinical imaging techniques are measured. The unique quantum physical basis of the MRI modality combined with the imaging capabilities of current computer technology has made this imaging modality a target of interdisciplinary interest for clinicians, physicists, biologists, engineers, and mathematicians. Due to the fact that MRI scanners perform corticomorphic processing, this modality is by far more complex than all the other high tech clinical imaging techniques. The purpose of this paper is to outline a phase coherent wavelet approach to Fourier transform MRI. It is based on distributional harmonic analysis on the Heisenberg nilpotent Lie group G and the associated symplectically invariant symbol calculus of pseudodifferential operators. The contour and contrast resolution of MRI scans which is controlled by symplectic filter bank processing gives the noninvasive MRI modality superiority over X-ray computed tomography (CT) in soft tissue differentiation.     

Miniaturized 3-D surface profilometer using a fiber optic coupler

A 3-D surface profilometer is described which uses a simple fiber optic coupler to form a Young's double pinhole interferometer. The Young's fringes are projected onto a surface, captured by a camera and analyzed using the Fourier transform method. The phase of the fringe pattern on the object is used to reconstruct the surface profile. System analysis, results from a simulation, and preliminary experimental results are provided which indicate a system resolution on the order of a tenth of a millimeter.     

四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

本文研究了四元Heisenberg群上次拉普拉斯算子的m幂次的基本解,该结论是Heisenberg群上结果的推广.本文利用了四元Heisenberg群上的Fourier变换理论构造了该群上次拉普拉斯算子的m幂次的基本解,并且给出了基本解的积分表示.     

Curvature walls and focal conic domains in a lyotropic lamellar phase

In the quasi-ternary CPCl/brine/hexanol lyotropic system, the interface of the lamellar and L₃ sponge phases displays a phenomenon of epitaxy: the layers of the lamellar phase tend to make a constant non-trivial angle with the interface. Thin samples of lamellar phase embedded in the sponge phase are thus submitted to oblique anchoring conditions and defects are created in the lamellar phase in order to satisfy the bulk lamellar ordering and the boundary conditions. We have studied small droplets of lamellar phase in the sponge phase. They do not exhibit the classic defects (focal conic domains) but wall defects, which appear in order to satisfy the smectic elasticity and the boundary conditions. Moreover we show through experiments in controlled geometry that, even in the presence of focal conic domains, wall defects control the size and periodicity of the textures which are observed at the interface. Received 4 November 1998