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.

     

A note on dual modules and the transpose

Archiv der Mathematik - It is a classical result in matrix algebra that any square matrix over a field can be conjugated to its transpose by a symmetric matrix. For F a non-Archimedean local field,...     

Beyond microstructures: Using the Kerr Effect to characterize the macrostructures of synthetic polymers

The macrostructures of synthetic polymers are essentially the complete molecular chain architectures, including the types and amounts of constituent short‐range microstructures, such as the regio‐ and stereosequences of the inserted monomers, the amounts and sequences of monomers found in co‐, ter‐, and tetra‐polymers, branching, inadvertent, and otherwise, etc. Currently, the best method for characterizing polymer microstructures uses high field, high resolution ¹³C‐nuclear magnetic resonance (NMR) spectroscopy observed in solution. However, even ¹³C‐NMR is incapable of determining the locations or positions of resident polymer microstructures, which are required to elucidate their complete macrostructures. The sequences of amino acid residues in proteins, or their primary structures, cannot be characterized by NMR or other short‐range spectroscopic methods, but only by decoding the DNA used in their syntheses or, if available, X‐ray analysis of their single crystals. Similarly, there are currently no experimental means to determine the sequences or locations of constituent microstructures along the chains of synthetic macromolecules. Thus, we are presently unable to determine their macrostructures. As protein tertiary and quaternary structures and their resulting ultimate functions are determined by their primary sequence of amino acids, so too are the behaviors and properties of synthetic polymers critically dependent on their macrostructures. We seek to raise the consciousness of both synthetic and physical polymer scientists and engineers to the importance of characterizing polymer macrostructures when attempting to develop structure–property relations. To help achieve this task, we suggest using the electrical birefringence or Kerr effects observed in their dilute solutions. The molar Kerr constants of polymer solutes contributing to the birefringence of their solutions, under the application of a strong electric field, are highly sensitive to both the types and locations of their constituent microstructures. As a consequence, we may begin to characterize the macrostructures of synthetic polymers by means of the Kerr effect. To simplify implementation of the Kerr effect to characterize polymer macrostructures, we suggest that NMR first be used to determine the types and amounts of constituent microstructures present. Subsequent comparison of observed Kerr effects with those predicted for different microstructural locations along the polymer chains can then be used to identify the most likely macrostructures. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 155–166     

HPLC–MS Profiling and Structural Identification of [14C]-Diclofenac Metabolites in Mouse Bile

Biliary metabolites present at 6 h post-dose following a single oral dose of [¹⁴C]-diclofenac (10 mg kg^?1) to male bile duct-cannulated C57BL/6 J mice were profiled and identified. Over the 6 h duration of the study ~19.5 % of the administered radioactivity was excreted into the bile as either [¹⁴C]-diclofenac or metabolites. When profiled using HPLC with online radiodetection, the presence of at least 13 radiolabelled components was indicated. These compounds were shown, by consecutive reaction mass spectrometry, to comprise a range of hydroxylated metabolites conjugated to either taurine, glucose and/or glucuronic acid. Both phenolic and acylglucuronide-containing metabolites were observed. The confirmation of the presence of these glucuronide conjugates in mouse bile may have important consequences in the light of emerging theories concerning the role of bacterial glucuronidases for the GI-tract toxicity of NSAIDs such as diclofenac.     

Isolation and Crystallographic Characterization of Two,Nonisolated Pentagon Endohedral Fullerenes: Ho3N@C2(22010)-C78 and Tb3N@C2(22010)-C78

Purified samples of Ho₃N@C₂(22010)-C₇₈ and Tb₃N@C₂(22010)-C₇₈ have been isolated by two distinct processes from the rich array of fullerenes and endohedral fullerenes present in carbon soot from graphite rods doped with Ho₂O₃ or Tb₄O₇. Crystallographic analysis of the endohedral fullerenes as cocrystals with Ni(OEP) (in which OEP is the dianion of octaethylporphyrin) shows that both molecules contain the chiral C₂(22010)-C₇₈ cage. This cage does not obey the isolated pentagon rule (IPR) but has two sites where two pentagons share a common C−C bond. These pentalene units bind two of the metal ions, whereas the third metal resides near a hexagon of the cage. Inside the cages, the Ho₃N or Tb₃N unit is planar. Ho₃N@C₂(22010)-C₇₈ and Tb₃N@C₂(22010)-C₇₈ use the same cage previously found for Gd₃N@C₂(22010)-C₇₈ rather than the IPR-obeying cage found in Sc₃N@D_3h-C₇₈.