Far field velocity potential induced by a rapidly decaying vorticity distribution

We study the velocity field induced by a vorticity distribution decaying rapidly in the distancer from the origin. In the far field, the vector potential for the velocity field can be represented by a series A ⁽ⁿ⁾, withA ⁽ⁿ⁾ proportional tor ^–n–1, forn=1, 2, .... We show thatA ⁽ⁿ⁾ can be expressed as a linear combination ofM _n linearly independent vector functions. The numberM _n is equal to 3 forn=1 and 4n forn2 and the coefficient of a vector function is defined by a linear combination of nth moments of vorticity. We then show that only 2n+1 linear combinations of thoseM _n vector functions contribute to the far field velocity which is irrotational. The corresponding scalar potential ⁽ⁿ⁾ is then represented by a linear combination of 2n+1 spherical harmonics ofnth order whose coefficients are again linear combinations ofnth moments of vorticity.

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Zusammenfassung Die vorliegende Arbeit beschreibt das Geschwindigkeitsfeld fernab einer Wirbelverteilung, welche mit dem Abstandr vom Ursprung eines geeigneten Bezugssystems hinreichend schnell abklingt. Die Geschwindigkeit besitzt ein Vektorpotential, dessen Fernfeldverhalten einer Reihenentwicklung A ⁽ⁿ⁾, genügt. Dabei istA ⁽ⁿ⁾ proportional zur ^–n–1 fürn=1, 2, .... Wir entwickeln eine explizite Darstellung vonA ⁽ⁿ⁾ als Linearkombination vonM _n linear unabhängigen Vektorfunktionen. Die auftretenden Koeffizienten sind ihrerseits Kombinationenn-ter Momente der Wirbelverteilung. Die ZahlM ₁ ist gleich 3 und es istM _n=4n fürn2, während die Gesamtzahl dernten Momente beträgt. Weiterhin zeigen wir, da\ nur 2n+1 dieser Vektorfunktionen auch zum drehungsfreien Fernfeld der Geschwindigkeitn-ter Ordnung beitragen können und identifizieren die zugehörigen Kombinationen von Wirbelmomenten. Dieselben Kombinationen liefern dann auch die Koeffizienten in einer Entwicklung desskalaren Fernfeldpotentials nach Kugelfunktionen.

     

Anomalies in the one-dimensional Anderson model at weak disorder

We show that at the special energiesE=2cosp/q, the invariant measure, the Lyapunov exponent, and the density of states can be extended to zero disorder as C functions in the disorder parameter. In particular, we obtain asymptotic series in the disorder parameter. This gives a rigorous proof of the existence of the anomalies originally discovered by Kappus and Wegner and studied by Derrida and Gardner and by Bovier and Klein.Partially supported by NSF grant DMS 87-02301     

Low-concentration series in general dimension

We discuss recent work on the development and analysis of low-concentration series. For many models, the recent breakthrough in the extremely efficient no- free-end method of series generation facilitates the derivation of 15th-order series for multiple moments in general dimension. The 15th-order series have been obtained for lattice animals, percolation, and the Edwards-Anderson Ising spin glass. In the latter cases multiple moments have been found. From complete graph tables through to 13th order, general dimension 13th-order series have been derived for the resistive susceptibility, the moments of the logarithms of the distribution of currents in resistor networks, and the average transmission coefficient in the quantum percolation problem, 11th-order series have been found for several other systems, including the crossover from animals to percolation, the full resistance distribution, nonlinear resistive susceptibility and current distribution in dilute resistor networks, diffusion on percolation clusters, the dilute Ising model, dilute antiferromagnet in a field, and random field Ising model and self-avoiding walks on percolation clusters. Series for the dilute spin-1/2 quantum Heisenberg ferromagnet are in the process of development. Analysis of these series gives estimates for critical thresholds, amplitude ratios, and critical exponents for all dimensions. Where comparisons are possible, our series results are in good agreement with both-expansion results near the upper critical dimension and with exact results (when available) in low dimensions, and are competitive with other numerical approaches in intermediate realistic dimensions.     

Power-law falloff in the kosterlitz-Thouless phase of a two-dimensional lattice Coulomb gas

We give a rigorous proof of power-law falloff in the Kosterlitz-Thouless phase of a two-dimensional Coulomb gas in the sense that there exists a critical inverse temperaturegb and a constant >0 such that for all> and all external charges R we have , whereG (x) is the two-point external charges correlation function,=dist(, Z), and for 0$$ " align="middle" border="0"> . In the case of a hard-core or standard Coulomb gas with activityz, we may choose=(z) such that(z)24 asz0.     

Trace analysis of airborne haloacetates

Haloacetates in various environmental compartments can be determined by gas chromatography-negative-ion chemical-ionization mass spectrometry after derivatization with 1-pentafluorophenyl diazoethane. Detection limits in absolute amounts per injection are between 0.01 fg (chlorodifluoroacetate) and 80 fg (monofluoroacetate). Sampling of haloacetates in urban air was performed by means of cylindrical denuders coated with alkalized glycerol. The haloacetates detected are trifluoro-, monochloro-, dichloro-, trichloro-, monobromo-, and dibromoacetate. The concentrations in ambient air fluctuate strongly, e.g. between 20 and 3000 pg/m³ for TFA. Haloacetates are also found in river waters and tree foliage. A major problem is interference from contamination with trifluoro- and trichloroacetate.     

The IL-10 gene is not involved in the predisposition to inflammatory bowel disease

Although genetic predisposition for inflammatory bowel disease (IBD) is well established, little is known about the accountable genes. The pathogenesis of IBD is characterized by an imbalanced activation of Th1- and Th2-lymphocytes. IL-10 represents an anti-inflammatory cytokine which downregulates the production of Th1-derived cytokines. To evaluate the role of the IL-10 gene in IBD, two polymorphisms in the promoter region (G/A at position -1082 and C/A at position -592) were genotyped in 142 patients with Crohn's disease (CD), 104 patients with ulcerative colitis (UC), and 400 healthy controls. Significant differences were not apparent, neither in the allele frequencies of either polymorphism, nor in the haplotype frequencies. Screening of the coding region of the IL-10 gene by polymerase chain reaction--single strand conformation polymorphism (PCR-SSCP) analysis revealed a rare sequence variation in exon 1 leading to an amino acid exchange (G-->A; G15R) in two patients with CD and five healthy controls. Therefore, polymorphisms of the IL-10 gene are not demonstrably involved in the predisposition of IBD in our cohorts of patients.     

Analysis of volatiles emitted by potato plants by means of a Colorado beetle electroantennographic detector

An electroantennographic detector based on the antenna of the Colorado potato beetle (Leptinotarsa decemlineata Say, 1824) was used to investigate volatile organic compounds emitted by injured potato plants (Solanum tuberosum L., 1753). Samples were collected on charcoal traps using the CLSA method. Analyses were performed with a GC-EAD-FID setup as well as a GC-MS system. The experiments revealed that several groups of compounds are perceptible to the Colorado potato beetle. The ability of the Colorado potato beetle to detect green leaf odours (e.g. (Z)-3-hexen-1-ol and (E)-2-hexenal), linalool and some terpenes has been noticed before [Visser et al., J. Chem. Ecol. 5 (1979) 13]. In this work the presence of (Z)-3-hexen-1-ol, (E)-2-hexenal and linalool in the potato odour could be confirmed. Moreover, β-myrcene, benzeneethanol, and several sesquiterpenes (e.g. caryophyllene and germacrene-D) were identified. The GC-EAD experiments reveal that apart from the green leaf odours and linalool prominent reactions of the Colorado bettle antenna are induced by benzeneethanol and the sesquiterpene fraction.