A Particle-Mesh Method for the Shallow Water Equations Near Geostrophic Balance

In this paper we outline a new particle-mesh method for rapidly rotating shallow water flows based on a set of regularized equations of motion. The time-stepping method uses an operator splitting of the equations into an Eulerian gravity wave part and a Lagrangian advection part. An essential ingredient is the advection of absolute vorticity by means of translated radial basis functions. We show that this implies exact conservation of enstrophy. The method is tested on two model problems based on the qualitative features of the solutions obtained (i.e., dispersion or smoothness of potential vorticity contours) as well as on the increase in mean divergence level.     

Behaviors of the positive temperature coefficient of resistance of poly(styrene‐co‐n‐butylacrylate) filled with Ni‐plated core‐shell polymeric particles

Conductive composite films of poly(styrene‐co‐n‐butylacrylate) copolymers filled with low‐density, Ni‐plated core‐shell polymeric particles were prepared and their behaviors of positive temperature coefficient of resistance (PTCR) were investigated. When the conductive fillers in the composite film were loaded beyond the critical volume, 10 up to 25 vol %, composite films exhibited a unique electrical resistant transition behavior, which the electrical resistance rapidly increased by several orders of magnitude at the critical temperature. The PTCR transition temperature, in general, occurred before the glass transition temperature of polymer matrix. Further increased the conductive filler loading to 30 vol %, the overpacked conduction paths were formed in the entire composite and the PTCR effects became blurred. While the composite film treated with thermal cycle several times from room temperature up to 120 °C, the electrical resistivity increased accompanied with the shift of the PTCR transition to lower temperature. The reason might have been caused by the formed interfacial cracks within the composite film. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 322–329, 2007     

Product formulas and convolution structure for Fourier-Bessel series

One of the most far-reaching qualities of an orthogonal system is the presence of an explicit product formula. It can be utilized to establish a convolution structure and hence is essential for the harmonic analysis of the corresponding orthogonal expansion. As yet a convolution structure for Fourier-Bessel series is unknown, maybe in view of the unpractical nature of the corresponding expanding functions called Fourier-Bessel functions. It is shown in this paper that for the half-integral values of the parameter ,n=0, 1, 2,, the Fourier-Bessel functions possess a product formula, the kernel of which splits up into two different parts. While the first part is still the well-known kernel of Sonine's product formula of Bessel functions, the second part is new and reflects the boundary constraints of the Fourier-Bessel differential equation. It is given, essentially, as a finite sum over triple products of Bessel polynomials. The representation is explicit up to coefficients which are calculated here for the first two nontrivial cases and . As a consequence, a positive convolution structure is established for . The method of proof is based on solving a hyperbolic initial boundary value problem.Communicated by Tom H. Koornwinder.     

Derivatives of pentamidine designed to target the Leishmania lipophosphoglycan

The Leishmania lipophosphoglycan (LPG) is the most abundant cell surface glycoconjugate of a family of infectious protozoa. Pentamidine, a common drug used in the treatment of Leishmania infections, has been modified with boronic acids so that it might bind more selectively to the phosphodisaccharide repeating unit of the LPG. This could serve to target the drug to the protozoan surface and increase its efficacy in vivo.     

Oxidation of nitrided si(100) by gaseous atomic and molecular oxygen

The nitridation of Si(100) by ammonia and the subsequent oxidation of the nitrided surface by both gaseous atomic and molecular oxygen was investigated under ultrahigh vacuum (UHV) conditions using X-ray photoelectron spectroscopy (XPS). Nitridation of Si(100) by the thermal decomposition of NH3 results in the formation of a subsurface nitride and a decrease in the concentration of surface dangling bond sites. On the basis of changes in the N1s spectra obtained after NH3 adsorption and decomposition, we estimate that the nitride resides about four to five layers below the vacuum-solid interface and that the concentration of surface dangling bonds after nitridation is only 59% of its value on Si(100)-(2 x 1). Oxidation of the nitrided surface is found to produce an oxide phase that remains in the outer layers of the solid and interacts only weakly with the underlying nitride for oxygen coverages up to 2.5 ML. Slight changes in the N1s spectra observed after oxidizing at 300 K are suggested to arise primarily from the introduction of strain within the nitride, and by the formation of a small amount of Si2=N-O species near the nitride-oxide interface. The nitrogen bonding environment changes negligibly after oxidizing at 800 K, which is indicative of greater phase separation at elevated surface temperature. Nitridation is also found to significantly reduce the reactivity of the Si(100) surface toward both atomic and molecular oxygen. A comparison of the oxygen uptake on the clean and nitrided surfaces shows quantitatively that the decrease in dangling bond concentration is responsible for the reduced activity of the nitrided surface toward oxidation, and therefore that dangling bonds are the initial adsorption site for both gaseous oxygen atoms and molecules. Increasing the surface temperature is found to promote the uptake of oxygen when O2 is used as the oxidant, but brings about only a small enhancement in the uptake of gaseous O-atoms. The different effects of surface temperature on the uptake of O versus O2 are interpreted in terms of the efficiency at which dangling bond pairs are regenerated on the surface at elevated temperature and the different site requirements for the adsorption of O and O2.     

Reactions of N-heterocyclic carbenes (NHCs) with one-electron oxidants: possible formation of a carbene cation radical

One-electron oxidation of N-heterocyclic carbenes (NHCs) has been carried out using oxidising agents such as tetracyanoethylene (TCNE) and ferrocenium [Cp(2)Fe](+); the formation of carbene radical cations is postulated.     

Formation and structure of 1:1 complexes between aryl hydroxamic acids and vanadate at neutral pH

Although aryl hydroxamic acids are well-known to form coordination complexes with vanadate (V(V)), the nature of these complexes at neutral pH and submillimolar concentrations, the conditions under which such complexes inhibit various serine amidohydrolases, is not well established. A series of qualitative and quantitative experiments, involving UV/vis, (1)H NMR, and (51)V NMR spectroscopies, established that both 1:1 and 1:2 vanadate/hydroxamate complexes form at pH 7.5, with the former dominating at submillimolar concentrations. Formation constants for the complexes of several aryl and alkyl hydroxamic acids were determined; for example, for benzohydroxamic acid, the stepwise formation constants of the 1:1 and 1:2 complexes were 3000 and 400 M(-1), respectively. The (51)V chemical shift of the 1:1 4-nitrobenzohydroxamic acid complex was -497 ppm, and that of its unsubstituted analogue was -498 ppm. A (1)H-(15)N HSQC spectrum of the 4-nitrobenzo-(15)N-hydroxamic acid/vanadate complex indicated the presence of an N-H group with (15)N and (1)H chemical shifts of 115 and 5.83 ppm, respectively. A (13)C NMR spectrum of the complex of 4-nitrobenzo-(13)C-hydroxamic acid with vanadate displayed a resonance at 170.1 ppm and thus a coordination-induced shift (CIS) of +3.8 ppm. In contrast, the CIS value of an established 1:2 complex, thought to contain chelated hydroxamic acid ligands, was +11.9 ppm. These spectral data led to the following structural picture of 1:1 complexes of vanadate and aryl hydroxamic acids. They contain penta- or hexa-coordinated vanadium. The ligand is in the hydroxamate rather than hydroximate form. The ligand is presumably bound to vanadium through the hydroxamic hydroxyl oxygen, but the hydroxamic acid carbonyl oxygen interacts weakly with vanadium. These species are the most likely candidates for the inhibitors of serine amidohydrolases found in vanadate/hydroxamic acid mixtures.     

N(nPr)4[B5O6(OH)4][B(OH)3]2 and N(nBu)4[B5O6(OH)4][B(OH)3]2: Clathrates with a diamondoid arrangement of hydrogen-bonded pentaborate anions

Single-crystal X-ray structure analyses of N(nPr)₄[B₅O₆(OH)₄][B(OH)₃]₂,1, and N(nBu)₄ [B₅O₆(OH)₄][B(OH)₃]₂,2, reveal that these materials are novel clathrates, the isotypic host structures of which are three-dimensional assemblies of hydrogen-bonded [B₅O₆(OH)₄]^– ionsand B(OH)₃ molecules. The assembly of only the pentaborate anions is a distorted (i.e., along [102] elongated) fourconnected diamond-related network. The N(nPr) ₄ ⁺ and N(nBu) ₄ ⁺ ions are trapped within the complex three-dimensional channel systems of the host frameworks. Both1 and2 crystallize monoclinically with space groupP2₁/c andZ=4. The cell constants are:1:a=13.592(5),b=12.082(2),c=17.355(6) Å, =106.60(2)° (298K);2:a=13.874(3),b=12.585(1),c=17.588(4) Å, =107.04(1)° (238 K). The results obtained by both¹¹B and¹³C MAS NMR spectroscopy are discussed. Thermogravimetric studies under a flowing inert-gas atmosphere suggest that water, stemming from polycondensation of the hydrous borate species, is released from the clathrates at ca. 443 K (1) and 398 K (2) before the decomposition of the organic cations starts at ca. 603 K (1) and 603 K (2).Author for correspondence. Supplementary Data relating to this article are deposited with the British Library as supplementary publication No. SUP 82172 (82 pages).     

Tantalum Clusters in Oxidic Matrices — Synthesis,Crystal Structure and Magnetic Properties of Eu1.83Ta15O32

The mixed‐valent oxotantalate Eu_1.83Ta₁₅O₃₂ was prepared from a compressed mixture of Ta₂O₅ and the metals in a sealed Ta ampoule at 1400 °C. The crystal structure was determined by means of single crystal X‐ray diffraction: space group R3¯, a = 777.2(6) pm and c = 3523.5(3) pm, Z = 3, 984 symmetrically independent reflections, 83 variables, R_F = 0.027 for I > 2σ (I). The structure is isotypic to Ba₂Nb₁₅O₃₂. The salient feature is a [Ta(+8/3)₆O₁₂ⁱO₆^a] cluster consisting of an octahedral Ta₆ core bonded to 12 edge‐bridging inner and six outer oxygen atoms. The clusters are arranged to slabs which are sandwiched by layers of [Ta(+5)₃O₁₃] triple octahedra. Additional Ta(+5) and Eu(+2) atoms provide the cohesion of these structural units. Twelve‐fold coordinated Eu(+2) atoms are situated on a triply degenerate position 33 pm displaced from the threefold axis of symmetry. A depletion of the Eu(+2) site from 6 to 5.5 atoms per unit cell reduces the number of electrons available for Ta‐Ta bonding from 15 to 14.67 electrons per cluster. Between 125 and 320 K Eu_1.83Ta₁₅O₃₂ is semi‐conducting with a band gap of 0.23 eV. The course of the magnetization is consistently described with the Brillouin function in terms of a M_mol/(N_Aμ_B) versus B/T plot in the temperature range 5 K — 320 K and at magnetic flux densities 0.1 T — 5 T. At moderate flux densities (< 1 T) the magnetic moment agrees fairly well with the expected value of 7.94 μ_B for free Eu (2+) ions with 4f⁷ configuration in ⁸S_7/2 ground state. Below 5 K, anisotropic magnetization measurements at flux densities B < 1 T point to an onset of an antiferromagnetic ordering of Eu spins within the layers and an incipient ferromagnetic ordering perpendicular to the layers.     

Calculation of the Entropy of Lattice Polymer Models from Monte Carlo Trajectories

While lattice models are used extensively for macromolecules (synthetic polymers proteins, etc.), calculation of the absolute entropy, S, and the free energy, F, from a given Monte Carlo (MC) trajectory is not straightforward. Recently, we have developed the hypothetical scanning MC (HSMC) method for calculating S and F of fluids. Here we extend HSMC to self-avoiding walks on a square lattice and discuss its wide applicability to complex polymer lattice models. HSMC is independent of existing techniques and thus constitutes an independent research tool; it provides rigorous upper and lower bounds for F, which can be obtained from a very small sample and even from a single chain conformation.