A note on the slow rotation of a disc in a bounded fluid with a surfactant surface layer

A method involving eigenfunction expansion and collocation is employed to solve the axisymmetric problem of a slowly and steadily rotating circular disc in a fluid of finite extent whose surface is covered with a surfactant film. The present method (originally described by Wang (Acta Mech. 94, 97, 1992)) is observed to produce results of practical importance associated with the problem more quickly and more easily than the one used earlier by Shail and Gooden (Int. J. Multiphase Flow 7, 245, 1992). (C) 1994 Academic Press, Inc.

Conformationally Restricted Criegee Intermediates: Evidence for Formation and Stereoelectronically Controlled Fragmentation

The Baeyer-Villiger reaction of 2-(2-oxocyclohexyl) acetic acid occurs via a bicyclic Criegee intermediate, which fragments with stereoelectronic control, as evidenced by product analysis; the reaction of the but-2-yl ester and of 2-(2-oxocyclopentyl) acetic acid also show evidence of such stereoelectronic control, but less convincingly.

Flat rotation curves: A result of the helical inverse cascade in turbulent media

We have modeled the rotation curves of 21 galaxies observed by Amram et al. (1992), by combining the effects of rigid rotation, gravity, and turbulence. The main motivation behind such modeling is to study the formation of coherent structures in turbulent media and explore its role in the large-scale structures of the universe. The values of the parameters such as mass, turbulent velocity, and angular velocity derived from the rotation curve fits are in good agreement with those derived from the prevalent models.

Adaptive optimal tuning of a general class of stable LTI systems with restricted inputs

The problem addressed is one of model reference adaptive control (MRAC) of asymptotically stable plants of unknown order with zeros located anywhere in the s-plane except at the origin. The reference model is also asymptotically stable and lacking zero(s) at s = 0. The control law is to be specified only in terms of the inputs to and outputs of the plant and the reference model. For inputs from a class of functions that approach a non-zero constant, the problem is formulated in an optimal control framework. By successive refinements of the sub-optimal laws proposed here, two schemes are finally design-ed. These schemes are characterized by boundedness, convergence and optimality. Simplicity and total time-domain implementation are the additional striking features. Simulations to demonstrate the efficacy of the control schemes are presented.

Inter And Intramolecular Interactions Of Porphyrins With 5,5′-Dithiobis(2-Nitrobenzoic Acid)

meso-Tetraphenylporphyrin and its metal [zinc(II) and copper(II)] derivatives form both inter and intramolecular complexes with 5,5′-dithiobis(2-nitrobenzoic acid) (DTNB). The nature of interaction is predominantly charge transfer (CT) in origin, with the porphyrin functioning as a II-donor and DTNB as an acceptor. Among the covalently linked intramolecular systems, the magnitude of CT interaction varies with the position (of one of the aryl groups of the porphyrin) to which DTNB is attached as ortho meta > para. Steady-state and time-resolved fluorescence studies revealed electron transfer to be the dominant pathway for the fluorescence quenching in these systems. Steady-state photolysis experiments probed using EPR and optical absorption studies have shown that electron transfer (from the excited singlet state of the porphyrin) to DTNB results in the formation of thiyl radical and production of free thiolate anion. It is found that the products of electrochemical reduction of covalently linked porphyrin-DTNB systems are different from those observed for the photochemical studies.

Photochemical intramolecular gamma-hydrogen abstraction in a ketone and an alkene and the role of tunneling of hydrogen

Intramolecular gamma-hydrogen abstraction reactions were examined in pentane-2-one and 2-methyl-1-pentene in their lowest triplet states using the AM1 semi-empirical molecular orbital method with the complete geometry optimization in the unrestricted Hartree-Fock frame. The results reveal that the oxygen atom of the carbonyl group and the end carbon atom of the olefinic bond acquire high free valence and spin density indices in their respective lowest triplet states, leading to abstraction of hydrogen from the gamma-position relative to the carbonyl and olefinic bonds. The theoretical energy profiles fit with a polynomial and the probability of tunneling of hydrogen was estimated by the WKB (Wentzel, Kramer and Brillouin) method. The results, after thermal averaging of the rate constants, reveal that tunneling of hydrogen is significant at room temperature.

Synthesis of chiral bicyclo[2.2.2]oct-5-en-2-ones via an intramolecular alkylation reaction

Generation of the thermodynamic dienolate of 9-bromocarvone derivatives 5, 7 and 11 furnished the chiral bicycle[2.2.2] octenones 6, 8 and 9 and 12 and 13 containing a bridgehead methyl group via an intramolecular alkylation reaction. In an analogous manner intramolecular alkylation reaction of the bromo enones 15a-e, obtained from carvone 2 by 1,3-alkylative enone transposition (-->14) followed by a regiospecific bromoetherification reaction, furnished the bicyclo[2.2.2]oct-5-en-2-ones 16a-e and 17a-e.

Unsteady compressible flow due to relative rotation and translation of a viscous fluid on a disk

The modification of the axisymmetric viscous flow due to relative rotation of the disk or fluid by a translation of the boundary is studied. The fluid is taken to be compressible, and the relative rotation and translation velocity of the disk or fluid are time-dependent. The nonlinear partial differential equations governing the motion are solved numerically using an implicit finite difference scheme and Newton's linearisation technique. Numerical solutions are obtained at various non-dimensional times and disk temperatures. The non-symmetric part of the flow (secondary flow) describing the translation effect generates a velocity field at each plane parallel to the disk. The cartesian components of velocity due to secondary flow exhibit oscillations when the motion is due to rotation of the fluid on a translating disk. Increase in translation velocity produces an increment in the radial skin friction but reduces the tangential skin friction.

Dynamic Behavior of Poly(2-vinylpyridine) in Solution Studied by 13C Nuclear Magnetic Relaxation

Abstract: The dynamics of poly(2-vinylpyridine) in chloroform solution has been examined by C-13 spin-lattice relaxation time and NOE measurements as a function of temperature. The experiments were performed at 50.3 and 100.6 MHz. The backbone carbon relaxation data have been analyzed in terms of six motional models. Among these models, the models which consider conformational transitions and bond librations for the backbone were found to be more successful. Pyridyl ring motion has been modeled as a restricted rotation with the rotational amplitude varying with temperature. The activation energy parameters obtained from the relaxation data of the pyridyl ring carbon have been compared with the energy barrier for ring rotation estimated from conformational energy calculations using the AM1 semiempirical quantum chemical method. The results of the conformational energy calculations support the description of pyridyl ring motion as a restricted rotation.

Intramolecular Reactivity - Keto Participation in the Hydrolysis of N-Methyl-N-(9-Oxobicyclo[3.3.1]Nonan-2-Alpha-YL) Morpholinium Iodide, and A Cannizzaro-Type Reaction of 3-(2-Oxocyclohexyl)Propanal

Mechanistic studies of two intramolecular processes, nucleophilic displacement of N-methylmorpholinium in N-methyl-N-{9-oxobicyclo[3,3,1]nonan-2 alpha-yl}morpholinium iodide, anchimerically assisted by keto carbonyl, and a Cannizzaro-type reaction of 3-(2-oxocyclohexyl)propanal, occurring via axial hydride transfer onto the cyclohexanone, are reported.

Isomerisation of 4-aryl-4-methylhex-5-en-2-ones to 5-aryl-4-methylhex-5-en-2-ones by an intramolecular ene-retro ene reaction sequence

Acid-catalysed thermal rearrangement of 4-aryl-4-methylhex-5-en-2-ones (products of the Claisen rearrangement of beta-methylcinnamyl alcohols and 2-methoxypropene) to isomeric 5-aryl-4-methylhex-5-en-2-ones via an intramolecular ene reaction of the enol tautomer followed by a retro ene reaction of the resultant acetylcyclopropane is described. Formation of the known diketone 13 via the ozonolysis of the rearrangement product 10, confirmed the structures of the rearranged enones, whereas formation of the enone 15 containing an extra methyl group on the styrene double bond confirmed the proposed mechanism. Finally, the rearrangement has been extended to the formal synthesis of beta-cuparenone 20 via the enones 22 and 23.

Ultrafast Solvation Dynamics Of An Ion In A Restricted Environment

The solvation dynamics of an excited coumarin dye molecule (C-480) enclosed within a restricted space have been studied using molecular hydrodynamic theory (MHT) and compared with the recent experimental findings. The solvation dynamics of the dye molecule within the cavity of a toroidal gamma-cyclodextrin molecule have been shown to be explained only in terms of the freezing of the solvent translational modes using MHT. The results of the theoretical calculation are in good agreement with the experimental results. The inertial components of the solvation time correlation function remain the same in both the restricted environment and in the free space. These results are interesting in the light of the simulation studies of Maroncelli and Fleming [J chem Phys, 89 (1988) 5044] which concludes that the participation of the different solvation shells in controlling the dynamics are much different. The earlier studies have been reviewed and the recent findings are discussed.

Chopped nonlinear magneto-optic rotation: A technique for precision measurements

We have developed a technique for precise measurement of small magnetic fields using nonlinear magneto-optic rotation (NMOR). The technique relies on the resonant laser beam being chopped. During the on time, the atoms are optically pumped into an aligned ground state (Delta m=2 coherence). During the off time, they freely precess around the magnetic field at the Larmor frequency. If the on-off modulation frequency matches (twice) the Larmor precession frequency, the rotation is resonantly enhanced in every cycle, thereby making the process like a repeated Ramsey measurement of the Larmor frequency. We study chopped-NMOR in a paraffin-coated Cs vapor cell. The out-of-phase demodulated rotation shows a Lorentzian peak of linewidth 85 mu G, corresponding to a sensitivity of 0.15nG/root Hz. We discuss the potential of this technique for the measurement of an atomic electric-dipole moment. Copyright (C) EPLA, 2011