Nice Point Sets Can Have Nasty Delaunay Triangulations

   Abstract. We consider the complexity of Delaunay triangulations of sets of points in R ³ under certain practical geometric constraints. The spread of a set of points is the ratio between the longest and shortest pairwise distances. We show that in the worst case, the Delaunay triangulation of n points in R ³ with spread Δ has complexity Ω(min{ Δ³, nΔ, n² }) and O(min{ Δ⁴, n ² }). For the case

Cryogenic operation of submillimeter quasioptical mixers

We report here the first results obtained by cooling a submillimeter quasioptical mixer, utilizing a Schottky diode in a corner reflector mixer structure. Measurements have been carried out at a wavelength of 434 microns. The diode inverse slope parameter V_o at low current decreases by a factor of 3 upon cooling to 50 K while the minimum system noise temperature of 5600 K (SSB), including the IF contribution, demonstrates a reduction of approximately 40% from the ambient temperature value. We also report improved system noise temperatures at 184 m and 119 m wavelengths of 38000 K and 64000 K (SSB), respectively.This work was supported by the Army Research Office and the Air Force Office of Scientific Research     

Sorption and partitioning parameters of benzotriazole compounds

Benzotriazole compounds have major commercial applications as anticorrosive agents in automotive antifreeze and airplane deicer fluids. This study assesses the sorption of benzotriazole (BT), 5-methylbenzotriazole (MBT), and 5-chlorobenzotriazole (CBT) from aqueous solutions to four top soils. The concentration range of 10-500 mg l⁻¹ was used with soils differing in total organic carbon content from 0.27 to 1.72%. Batch systems facilitated the equilibrium sorption with analysis by HPLC. The sorption of these compounds was as much as 60% by mass to a soil with 0.33% Org. C. The log octanol-water partition coefficients (log K_ow) were determined to be 1.23 for BT, 1.89 for MBT, and 2.17 for CBT. The relationship between the log of the sorption partition coefficient, log K_oc and log K_ow differed from previous correlations because hydrophobicity was not the only factor affecting sorption. These compounds have substantial permanent dipole moments as well as being hydrophobic. At high pH where CBT molecules approach their pK_a, sorption was approximately 50% less (by mass) than that of relatively non-ionized CBT molecules.     

Polymers from the iterated addition of hydrogen sulfide to diolefins

This paper describes polyesters and polyamides obtained by the base-catalyzed additions of hydrogen sulfide to α,β-unsaturated diesters and diamides. The compounds employed were ethylene diacrylate, the diacrylate of trans-1,4-bis(hydroxymethyl)cyclohexane, p-xylylene diacrylate, hydroquinone diacrylate, the diacrylate of 1,4-butanedithiol, tetraethylene glycol dimethacrylate, 1,4-butylene dicrotonate, 1,4-butylene dicinnamate, methylene bisacrylamide, and m-xylylene bisacrylamide. The polymers posses the general formula, , wherein R¹ is hydrogen, methyl, or phenyl, R² is hydrogen or methyl, R³ is an alkylene, aralkylene, or oxyalkylene group, and X is oxygen, sulfur, or the imino group. Polymers with as many as several hundred repeating units were obtained. Depending upon the structure, the products are liquids, rubbers, or solids, the polymers are obtained with vinyl or sulfhydryl termination and the efficiency of this termination is very high, as was shown by chain extension of a sulfhydryl-terminated polymer through oxidation to a polydisulfide, $$ \rlap{‐‐} ({\rm RSS\rlap{‐‐} )}_n $$, having a molecular weight 30 times as great as that of the parent dimercaptan. The syntheses of several new monomers are described.     

Structure property relationships in the ATi2O4 (A=Na, Ca) family of reduced titanates

Reduced titanates in the ATi₂O₄ (A=Li, Mg) spinel family exhibit a variety of interesting electronic and magnetic properties, most notably superconductivity in the mixed-valence spinel, Li_1+xTi_2−xO₄. The sodium and calcium analogs, NaTi₂O₄ and CaTi₂O₄, each differ in structure, the main features of which are double rutile-type chains composed of edge-sharing TiO₆ octahedra. We report for the first time, the properties and band structures of these two materials. XANES spectroscopy at the Ti K-edge was used to probe the titanium valence. The absorption edge position and the pre-edge spectral features observed in the XANES data confirm the assignment of Ti³⁺ in CaTi₂O₄ and mixed-valence Ti³⁺/Ti⁴⁺ in NaTi₂O₄. Temperature-dependent resistivity and magnetic susceptibility studies are consistent with the classification of both NaTi₂O₄ and CaTi₂O₄ as small band-gap semiconductors, although changes in the high-temperature magnetic susceptibility of CaTi₂O₄ suggest a possible insulator-metal transition near 700 K. Band structure calculations agree with the observed electronic properties of these materials and indicate that while Ti-Ti bonding is of minimal importance in NaTi₂O₄, the titanium atoms in CaTi₂O₄ are weakly dimerized at room temperature.     

Raman and infrared spectroscopy of selected vanadates

Raman and infrared spectroscopy has been used to study the structure of selected vanadates including pascoite, huemulite, barnesite, hewettite, metahewettite, hummerite. Pascoite, rauvite and huemulite are examples of simple salts involving the decavanadates anion (V10O28)6-. Decavanadate consists of four distinct VO6 units which are reflected in Raman bands at the higher wavenumbers. The Raman spectra of these minerals are characterised by two intense bands at 991 and 965 cm(-1). Four pascoite Raman bands are observed at 991, 965, 958 and 905 cm(-1) and originate from four distinct VO6 sites. The other minerals namely barnesite, hewettite, metahewettite and hummerite have similar layered structures to the decavanadates but are based upon (V5O14)3- units. Barnesite is characterised by a single Raman band at 1010 cm(-1), whilst hummerite has Raman bands at 999 and 962 cm(-1). The absence of four distinct bands indicates the overlap of the vibrational modes from two of the VO6 sites. Metarossite is characterised by a strong band at 953 cm(-1). These bands are assigned to nu1 symmetric stretching modes of (V6O16)2- units and terminal VO3 units. In the infrared spectra of these minerals, bands are observed in the 837-860 cm(-1) and in the 803-833 cm(-1) region. In some of the Raman spectra bands are observed for pascoite, hummerite and metahewettite in similar positions. These bands are assigned to nu3 antisymmetric stretching of (V10O28)6- units or (V5O14)3- units. Because of the complexity of the spectra in the low wavenumber region assignment of bands is difficult. Bands are observed in the 404-458 cm(-1) region and are assigned to the nu2 bending modes of (V10O28)6- units or (V5O14)3- units. Raman bands are observed in the 530-620 cm(-1) region and are assigned to the nu4 bending modes of (V10O28)6- units or (V5O14)3- units. The Raman spectra of the vanadates in the low wavenumber region are complex with multiple overlapping bands which are probably due to VO subunits and MO bonds.     

Refinements of the crystal structures of 1,4-diphenylbutadiyne and its complex with two moles of Co2(CO)6

1,4-diphenylbutadiyne, C₁₆H₁₀, crystallizes in monoclinic space group P2₁/n witha=6.6152(6),b=6.0768(7),c=14.634(1) Å, =100.981(8)⁰,V=577.5(2) ų,Z=2. The structure was refined toR=0.077 andR _w=0.069 for 1007 observed reflections with CuK radiation. The molecule lies on an inversion center. Our determination represents and increase in precision of a factor of approximately three over the original determination. The 21 cobalt complex, C₁₆H₁₀[Co₂(CO)₆]₂, also crystallizes in monoclinic space group P2₁/n witha=8.9568(12),b=17.7057(10),c=18.5671(12) Å, =90.606(12)^o,V=2944.3(5) ų,Z=4. The structure was refined toR=0.032 andR _w=0.031 for 4312 observed reflections. The diphenylbutadiyne triple bonds elongate to 1.346(3) Å and the angles at the diyne C atoms decrease to 134.1(3)–144.9(3)^o upon complexation. The Co-Co distance is 2.4580(4)Å. Our data represent an increase in precision by a factor of 2–3 over the original determination.     

Bioenergetics and bioremediation of contaminated soil

The microbial biodegradation of xenobiotic compounds in soil and ground water is constrained by the laws of thermodynamics. Bioremediation is being investigated in a rhizosphere environment in which higher plants provide carbon and energy to sustain the microbial population. Toluene, phenol, trichloroethylene and trichloroethane have been fed in separate experiments to a pilot scale system with alfalfa growing in sandy soil containing less than 10% of silt. It is well known that microbial populations are numerous in the root zone of healthy vegetation. Root exudates can stimulate aerobic microbial biodegradation of compounds which by themselves support growth poorly or not at all. Polynuclear aromatic compounds such as phenanthrene, anthracene, and pyrene, which are not very soluble in water, and chlorinated aliphatic hydrocarbons such as trichloroethylene are examples of compounds that can be biodegraded in the rhizosphere when root exudates are present to enhance and sustain microbial activity. Solar driven transport processes such as water and solute movements due to evapotranspiration increase the likelihood that the contaminants will come into contact with the microorganisms and be degraded. The thermodynamic and bioenergetic aspects of transport and biodegradation in the rhizosphere are examined through a review of the literature and the analysis of experimental data collected in the pilot scale system.     

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