Stationary turbulent closure via the Hopf functional equation

Exact closed-form solutions are exhibited for the Hopf equation for stationary incompressible 3D Navier-Stokes flow, for the cases of homogeneous forced flow (including a solution with depleted nonlinearity) and inhomogeneous flow with arbitrary boundary conditions. This provides an exact method for computing two- and higher-point moments, given the mean flow.     

Electrophilic reactions of chlorin derivatives and a comprehensive collection of 13c data of these products and closely related compounds

Vilsmeier-formylation of the copper(II) complex of chlorin-e₆ trimethyl ester (2), under mild conditions, gives selective substitution in the 3-vinyl group. In contrast chlorination of 2 is shown to lead to selective substitution at position 20 of the macrocycle. A similar result is found for [3-ethyl]-isochlorin-e₄ dimethyl ester (17) although further reaction leads to more highly chlorinated products which have been isolated and identified. ¹³C NMR data for some of these compounds and several related chlorin derivatives are reported. In particular, after correction of the literature, many of the quaternary carbon signals of the macrocycle are assigned and substituent effects assessed. Consideration of the shifts of the α-pyrrolic carbons confirms that chlorin and its derivatives exist in a tautomeric form with the two inner H atoms on diagonally opposite pyrrole rings A and C. Such a form allows a satisfactory explanation of the substituent chemical shifts of the formyl group at positions 15 and 20 to be made.     

Structure Determination of a New Spirobicyclic Triterpenoid from Iris foetidissima

The novel iridal 10 has been isolated from rhizome extracts of Iris foetidissima. Its structure was established by spectroscopic methods and oxidative degradation. Final proof of the spirobicyclic nature of the compound – a new feature in the triterpenoid field – was afforded by the correlations observed in the 2D-HMBC- (¹H-detected multiple-bond heteronuclear multiple-quantum coherence) spectrum. The possible biogenesis of this unusual compound is discussed.     

Structure and Stereochemistry of New Sesquiterpene Esters from Echinacea purpurea (L.) MOENCH. (Preliminary communication)

The structure elucidation of four new constituents from the roots of Echinacea purpurea is described. They are shown to be cinnamoyl esters of sesquiterpene alcohols with a germacrane or a guaiane skeleton. First pharmacological results indicate immunological activities.     

Dipolar interactions and origin of spin ice in ising pyrochlore magnets

Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the nearest-neighbor "spin ice" model. We discuss the dipolar energy scale present in both these materials and discuss how spin-ice behavior can occur despite the presence of long-range dipolar interactions. We present results of numerical simulations and a mean field analysis of Ising pyrochlore systems. Based on our quantitative theory, we suggest that the spin-ice behavior in these systems is due to long-range dipolar interactions, and that the nearest-neighbor exchange in Dy2Ti2O7 is antiferromagnetic.     

Pinensins: The First Antifungal Lantibiotics

Lantibiotics (lanthionine‐containing antibiotics) from Gram‐positive bacteria typically exhibit activity against Gram‐positive bacteria. The activity and structure of pinensin A ( 1 ) and B ( 2 ), lantibiotics isolated from a native Gram‐negative producer Chitinophaga pinensis are described. Surprisingly, the pinensins were found to be highly active against many filamentous fungi and yeasts but show only weak antibacterial activity. To the best of our knowledge, lantibiotic fungicides have not been described before. An in‐depth bioinformatic analysis of the biosynthetic gene cluster established the ribosomal origin of these compounds and identified candidate genes encoding all of the enzymes required for post‐translational modification. Additional encoded functions enabled us to build up a hypothesis for the biosynthesis, export, sensing, and import of this intriguing lantibiotic.     

Columnar vortices in isotropic turbulence

The structure of the intense vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers, in the rangeRe =35–170, and is found to be organized in coherent, cylindrical or ribbon-like, vortices (worms). At the Reynolds numbers studied, they are responsible for much of the extreme intermittent tails observed in the statistics of the velocity gradients, but their importance seems to decrease at higherRe . Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow, while their circulation increases monotonically withRe . An explanation is offered for this latter scaling, based in the assumed presence of axial inertial waves along their cores, excited by a random background strain of the order of the root mean square vorticity. This explanation is consistent with the presence of comparable amounts of stretching and compression along the vortex cores.

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Sommario La struttura di regioni ad intensa vorticità in campi di flusso turbolento omogenei, isotropi ed in equilibrio, simulati numericamente, viene studiata per quattro differenti numeri di Reynolds nell'intervalloRe =35÷170, e si trova che tali regioni si organizzano in vortici coerenti, cilindrici o a forma di nastro (vermi). Con rifermento ai numeri di Reynolds studiati, si vede che tali vortici sono responsabili per gran parte delle code estreme ed intermittenti, osservate nelle statistiche dei gradienti di velocità, ma la loro importanza sembra decrescere a più altiRe . I loro raggi scalano con la microscala di Kolmogorov e le loro lunghezze con la scala integrale del flusso, mentre la loro circolazione cresce monotonicamente conRe . Per quest'ultimo riscalamento viene offerta una spiegazione basata sull'assunzione della presenza di onde inerziali assiali lungo i loro nuclei, eccitate da una deformazione di fondo casuale dell'ordine della radice quadrata della velocità media. Questa spiegazione è consistente con la presenza di incrementi paragonabili di allungamenti e compressioni lungo i nuclei dei vortici.

     

The temperature dependence of the 13C nuclear magnetic resonance spectra of porphyrins

The high temperature ¹³C NMR spectra of the methyl esters of deuteroporphyrin-IX and protoporphyrin-IX, and octaethylporphyrin show sharp discrete signals for the inner macrocycle carbon resonances. The temperature dependence of these shifts is discussed.     

Spin effects in hadron scattering at very high energies

In this paper a spin-dependent diffractive model is studied for πN and NN elastic scattering. We find non-trivial results for spin correlation parameters which persist at high energies and have very distinct features in the dip region. It is stressed that these parameters provide good tests of pomeron factorization.