Microscopic theory of vortex dynamics

An approach to vortex dynamics is outlined, a new form being obtained for the pair potential forces on a vortex. A microscopic calculation of the vortex inertial mass is presented. Quantum effects on vortex lattice melting are briefly discussed.

Non-uniform slot injection (suction) or wall enthalpy into a steady nonsimilar compressible laminar boundary layer

Steady two-dimensional and axisymmetric compressible nonsimilar laminar boundary-layer flows with non-uniform slot injection (or suction) and non-uniform wall enthalpy have been studied from the starting point of the streamwise co-ordinate to the exact point of separation. The effect of different free stream Mach number has also been considered. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) or wall enthalpy are removed by choosing appropriate non-uniform slot injection (suction) or wall enthalpy. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is observed that the non-uniform slot injection moves the point of separation downstream but the non-uniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) along the streamwise co-ordinate has very little effect on the skin friction and thus on the point of separation.

Solution structure of BTK-2, a novel hK(v)1.1 inhibiting scorpion toxin, from the eastern Indian scorpion Mesobuthus tamulus

The three dimensional structure of a 32 residue three disulfide scorpion toxin, BTK-2, from the Indian red scorpion Mesobuthus tamulus has been determined using isotope edited solution NMR methods. Samples for structural and electrophysiological studies were prepared using recombinant DNA methods. Electrophysiological studies show that the peptide is active against hK(v)1.1 channels. The structure of BTK-2 was determined using 373 distance restraints from NOE data, 66 dihedral angle restraints from NOE, chemical shift and scalar coupling data, 6 constraints based on disulfide linkages and 8 constraints based on hydrogen bonds. The root mean square deviation (r.m.s.d) about the averaged co-ordinates of the backbone (N, C-alpha, C') and all heavy atoms are 0.81 +/- 0.23 angstrom and 1.51 +/- 0.29 angstrom respectively. The backbone dihedral angles (phi and psi) for all residues occupy the favorable and allowed regions of the Ramachandran map. The three dimensional structure of BTK-2 is composed of three well defined secondary structural regions that constitute the alpha-beta-beta, structural motif. Comparisons between the structure of BTK-2 and other closely related scorpion toxins pointed towards distinct differences in surface properties that provide insights into the structure-function relationships among this important class of voltage-gated potassium channel inhibiting peptides. (C) 2011 Elsevier B.V. All rights reserved.

Structure of N-tert-butyloxycarbonyl-[alpha]-aminoisobutyryl-DL-pipecolyl-[alpha]-aminoisobutyric acid methyl ester

C20H35N3O6 (Boc-Aib-DL-Pip-Aib-OMe, Boc = tert-butyloxycarbonyl, Aib = alpha-aminoisobutyric acid, Pip = pipecolic acid, OMe = methoxy), M(r) = 413.5, monoclinic, P2(1)/c, a = 18.055 (3), b = 15.048 (3), c = 17.173 (3) angstrom, beta = 91.7 (1)-degrees, V = 4663.8 (9) angstrom3, Z = 8, D(m) = 1.16, D(x) = 1.178 Mg m-3, lambda(Mo Kalpha) = 0.71069 angstrom, mu = 0.081 mm-1, F(000) = 1792, T = 297 K. The final R value for 4925 [I greater-than-or-equal-to 3sigma(I)] reflections is 0.065 (wR = 0.067). The peptide backbone of the two independent molecules in the asymmetric unit is folded at the -Aib-Pip- sequence to form a type-I (I') beta-bend stabilized by a 1 <-- 4 intramolecular N-H...O=C hydrogen bond between the Aib(3) peptide N-H and Boc urethane C=O groups.

Cascades of Selective Pulses on Connected Single-Quantum Transitions Leading to the Selective Excitation of Multiple-Quantum Coherences

A symmetric cascade of selective pulses applied on connected transitions leads to the excitation of a selected multiple-quantum coherence by a well-defined angle. This cascade selectively operates on the subspace of the multiple-quantum coherence and acts as a generator of rotation selectively on the multiple-quantum subspace. Single-transition operator algebra has been used to explain these experiments. Experiments have been performed on two- and three-spin systems. It is shown that such experiments can be utilized to measure the relaxation times of selected multiple-quantum coherences or of a specifically prepared initial longitudinal state of the spin system.

Non-linear optical response of rutile-related oxides, LiM(V)M(VI)O(6), and their derivatives obtained by ion-exchange and intercalation

Polycrystalline samples of oxides of the general formula LiM(V)M(VI)O(6) (M(V) = Nb, Ta; M(VI) = Mo, W), crystallizing in a non-centrosymmetric (space group P (4) over bar 2(1)m) trirutile structure, exhibit second harmonic generation (SHG) of 1064 nm radiation with efficiencies 15-45 times that of alpha-quartz; interestingly, the SHG response is retained by the protonated derivatives HM(V)M(VI)O(6) . xH(2)O, and their n-alkylamine intercalates as well.

Tunable Brownian vortex at the interface

A general kind of Brownian vortices is demonstrated by applying an external nonconservative force field to a colloidal particle bound by a conservative optical trapping force at a liquid-air interface. As the liquid medium is translated at a constant velocity with the bead trapped at the interface, the drag force near the surface provides enough rotational component to bias the particle's thermal fluctuations in a circulatory motion. The interplay between the thermal fluctuations and the advection of the bead in constituting the vortex motions is studied, and we infer that the angular velocity of the circulatory motion offers a comparative measure of the interface fluctuations.

Translational velocity oscillations of piston generated vortex rings

Experimental results are presented that show that the translational velocities of piston generated vortex rings often undergo oscillations, similar to those recently discovered for drop generated rings. An attempt has been made to minimize uncertainties by utilizing both dye and hydrogen bubbles for visualization and carefully repeating measurements on the same ring and on different realizations under the same nominal piston conditions. The results unambiguously show that under most conditions, both for laminar and turbulent rings and for rings generated from pipes and orifices, the oscillations are present. The present results, together with the earlier results on drop generated rings, give support to the view that translational velocity oscillations are probably an inherent feature of translating vortex ring fields. (C) 1995 American Institute of Physics.

Diphenylantimony(V) oxo/chloro carboxylates and phosphinates: crystal structures of {SbPh2Cl[O2P(C6H11)2]}2O and [SbPh2(O2CPh)2]2O

Reaction of SbPh(2)Cl(3) (1 mol) with the silver salt of dicyclohexylphosphinic acid (2 mol) afforded {SbPh(2)Cl[O2P(C6H11)(2)]}O-2 1, a similar reaction with AgO2P(C8H15)(2) gave a product formulated as {SbPh(2)Cl[O2P(C8H15)(2)]}O-2 2. Similar reactions with silver carboxylates (1:3 stoichiometry) led to the crystalline derivatives [SbPh(2)(O(2)CR)(2)]O-2 (R = Ph 3, CHPh(2) 4, 2,4,6-Me(3)C(6)H(2) 5, 2-MeC(6)H(4) 6 or 4-MeC(6)H(4) 7), whereas the 1:2 reaction afforded crystalline SbPh(2)Cl(O(2)CR)(2) (R = Ph 8, 2-MeC(6)H(4) 9 or 4-MeC(6)H(4) 10). Interconversion of the previously known compounds [SbPh(2)(O(2)CMe)(2)]O and Sb(4)Ph(8)O(6) . 3MeCO(2)H was achieved and established by H-1 NMR spectroscopy. Compounds 1 and 3 were further characterized by X-ray diffraction; the antimony in 1 is six-co-ordinated with bridging phosphinates whereas in 3 it is seven-co-ordinated with chelating benzoates. Short Sb-O (oxo) distances (1.923 Angstrom) and near linearity at the bridging ox

Vortex sheet simulation of a plane �canonical� mixing layer

Discrete vortex simulations of the mixing layer carried out in the past have usually involved large induced velocity fluctuations, and thus demanded rather long time-averaging to obtain satisfactory values of Reynolds stresses and third-order moments. This difficulty has been traced here, in part, to the use of discrete vortices to model what in actuality are continuous vortex sheets. We propose here a novel two-dimensional vortex sheet technique for computing mixing layer flow in the limit of infinite Reynolds number. The method divides the vortex sheet into constant-strength linear elements, whose motions are computed using the Biot-Savart law. The downstream far-field is modelled by a steady vorticity distribution derived by application of conical similarity from the solution obtained in a finite computational domain. The boundary condition on the splitter plate is satisfied rigorously using a doublet sheet. The computed large-scale roll-up of the vortex sheet is qualitatively similar to experimentally obtained shadow-graphs of the plane turbulent mixing layer. The mean streamwise velocity profile and the growth rate agree well with experimental data. The presently computed Reynolds stresses and third-order moments are comparable with experimental and previous vortex-dynamical results, without using any external parameter (such as the vortex core-size) of the kind often used in the latter. The computed autocorrelations are qualitatively similar to experimental results along the top and bottom edges of the mixing layer, and show a well-defined periodicity along the centreline. The accuracy of the present computation is independently established by demonstrating negligibly small changes in the five invariants (including the Hamiltonian) in vortex dynamics.

Modelling plane mixing layers using vortex points and sheets

We present here a critical assessment of two vortex approaches (both two-dimensional) to the modelling of turbulent mixing layers. In the first approach the flow is represented by point vortices, and in the second it is simulated as the evolution of a continuous vortex sheet composed of short linear elements or ''panels''. The comparison is based on fresh simulations using approximately the same number of elements in either model, paying due attention in both to the boundary conditions far downstream as well as those on the splitter plate from which the mixing layer issues. The comparisons show that, while both models satisfy the well-known invariants of vortex dynamics approximately to the same accuracy, the vortex panel model, although ultimately not convergent, leads to smoother roll-up and values of stresses and moments that are in closer agreement with the experiment, and has a higher computational efficiency for a given degree of convergence on moments. The point vortex model, while faster for a given number of elements, produces an unsatisfactory roll-up which (for the number of elements used) is rendered worse by the incorporation of the Van der Vooren correction for sheet curvature.

On the improvement of chimney weirs

This paper is devoted to the improvement in the range of operation (linearity range) of chimney weir (consisting of a rectangular weir or vertical slot over an inward trapezium), A new and more elegant optimization procedure is developed to analyse the discharge-head relationship in the weir. It is shown that a rectangular weir placed over an inverted V-notch of depth 0.90d gives the maximum operating range, where d is the overall depth of the inward trapezoidal weir (from the crest to the vertex). For all flows in the rectangular portion, the discharge is proportional to the linear power of the head, h, measured above a reference plane located at 0.292d below the weir crest, in the range 0.90d less than or equal to h less than or equal to 7.474: within a maximum error of +/-1.5% from the theoretical discharge. The optimum range of operation of the newly designed weir is 200% greater than that in the chimney weir designed by Keshava Murthy and Giridhar, and is nearly 950% greater than that in the inverted V-notch. Experiments with two weirs having half crest widths of 0.10 and 0.12 m yield a constant average coefficient of discharge of 0.634 and confirm the theory. The application of the weir in the design of rectangular grit chamber outlet is emphasized, in that the datum for the linear discharge-head relationship is below the crest level of the weir.

Synthesis of Ti, Ga, and V nitrides: Microwave-assisted carbothermal reduction and nitridation

A simple, novel, and fast method of preparation of metal nitride powders (GaN, TiN, and VN) using microwave-assisted carbothermal reduction and nitridation has been demonstrated. The procedure uses the respective oxides and amorphous carbon powder as the starting materials. Ammonia gas is found to be more effective in nitridation than high-purity N-2 gas. Complete nitridation is achieved by the use of a slight excess of amorphous carbon. Metals themselves are not found to be effectively nitrided. The products were characterized using XRD, TEM, and SAED and found to possess good crystallinity and phase purity. The method can be of general applicability for the preparation of metal nitrides.

Nonresonant edge slot antenna for phased array applications: Theory and experiment

The design and development of nonresonant edge slot antenna for phased array applications has been presented. The radiating element is a slot cut on the narrow wall of rectangular waveguide (edge slot). The admittance characteristics of the edge slot have been rigorously studied using a novel hybrid method. Nonresonant arrays have been fabricated using the present slot characterization data and the earlier published data. The experimentally measured electrical characteristics of the antenna are presented which clearly brings out the accuracy of the present method.