Diffusions on graphs, Poisson problems and spectral geometry

We study diffusions, variational principles and associated boundary value problems on directed graphs with natural weightings. We associate to certain subgraphs (domains) a pair of sequences, each of which is invariant under the action of the automorphism group of the underlying graph. We prove that these invariants differ by an explicit combinatorial factor given by Stirling numbers of the first and second kind. We prove that for any domain with a natural weighting, these invariants determine the eigenvalues of the Laplace operator corresponding to eigenvectors with nonzero mean. As a specific example, we investigate the relationship between our invariants and heat content asymptotics, expressing both as special values of an analog of a spectral zeta function.

     

Substituted selenourea–tellurium tetrahalide adducts: Precursors to selenium–tellurium alloys

N,N-Dimethylselenourea (DMSeU) yields, with TeX₄ (X = Cl or Br), a variety of compounds having bonds from selenium to tellurium. Excluding molecules of solvation these compounds display the following stoichiometries: [(DMSeU)₄Te]X₂, (DMSeU)₃(TeX₄)₂, and (DMSeU)₂Te₂X₆. Tetramethylselenourea (TMSeU) gives, with TeBr₄, crystals of (TMSeU)₂TeBr₄. Both the carbon–selenium and tellurium–halogen bonds undergo hydrolysis under mild conditions to yield precipitates that are alloys of selenium and tellurium. Thus, this group of compounds affords a new approach to the synthesis of selenium–tellurium alloys. Some of the properties of these compounds, as well as the crystal structure of [(DMSeU)₄Te]Cl₂, are described in this article.     

Characterization of the surface structural,mechanical, and thermal properties of benzocyclobutene dielectric polymers using scanned probe microscopy

Scanning probe microscopy (SPM) techniques are used to characterize surfaces related to the processing of benzocyclobutene (BCB) dielectric thin films. Thermally cured resins and photodefineable resins are sold under the trade name CYLCOTENE^TM1) for electronic applications. TappingMode AFM (TMAFM) imaging is used to follow changes in adhesion promoter morphology upon baking to help explain adhesion performance. Power spectral density (PSD) analysis of TMAFM images of plasma treated BCB surfaces are unique and can be used to ‘fingerprint’ processes. Selective oxidation of the BCB surface can be used to fabricate a phase imaging standard for TMAFM. Near surface modulus of the BCB materials is 3.6 ± 0.2 GPa and the hardness is 0.38 ± 0.2 GPa measured by depth‐sensing nanoindentation. Creep recovery of indents can be used to qualitatively distinguish between thermal and photocureable materials. A heated tip in a scanning thermal microscope can induce the thermal curing of BCB over micron sized areas. Local thermal analysis with the same probe allows the measurement of the changes in the glass transition, T_g, at the surface with cure temperature.