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81.
An elegant quaternionic formulation is given for the Lagrangian advection equation for velocity vector potential in fluid dynamics. At first we study the topological significance of a restricted conserved quantity viz., stream-helicity and later more realistic configuration of open streamlines is figured out. Also, using Clebsch parameterisation of the velocity vector potential yet another physical significance for the stream-helicity is provided. Finally we give a Nambu-Poisson formalism of the Lagrangian advection equation for velocity vector potential. 相似文献
82.
Lauren Marbella Barbara Serli‐Mitasev Dr. Partha Basu Dr. 《Angewandte Chemie (International ed. in English)》2009,48(22):3996-3998
A real turn‐on : The emission intensity of heterocycle 1 increases upon binding to Pb2+. Thus, 1 acts as a small‐molecule “turn‐on” fluorescent sensor for lead. The sensor is highly selective and is functional over a wide range of pH values.
83.
A. Ghose Choudhury Partha Guha Barun Khanra 《Journal of Mathematical Analysis and Applications》2009,360(2):45-664
We use a formula derived almost seventy years ago by Madhav Rao connecting the Jacobi Last Multiplier of a second-order ordinary differential equation and its Lagrangian and determine the Lagrangians of the Painlevé equations. Indeed this method yields the Lagrangians of many of the equations of the Painlevé–Gambier classification. Using the standard Legendre transformation we deduce the corresponding Hamiltonian functions. While such Hamiltonians are generally of non-standard form, they are found to be constants of motion. On the other hand for second-order equations of the Liénard class we employ a novel transformation to deduce their corresponding Lagrangians. We illustrate some particular cases and determine the conserved quantity (first integral) resulting from the associated Noetherian symmetry. Finally we consider a few systems of second-order ordinary differential equations and deduce their Lagrangians by exploiting again the relation between the Jacobi Last Multiplier and the Lagrangian. 相似文献
84.
Kail BW Pérez LM Zarić SD Millar AJ Young CG Hall MB Basu P 《Chemistry (Weinheim an der Bergstrasse, Germany)》2006,12(28):7501-7509
The oxygen-atom-transfer (OAT) reactivity of [LiPrMoO2(OPh)] (1, LiPr=hydrotris(3-isopropylpyrazol-1-yl)borate) with the tertiary phosphines PEt3 and PPh2Me in acetonitrile was investigated. The first step, [LiPrMoO2(OPh)]+PR3-->[LiPrMoO(OPh)(OPR3)], follows a second-order rate law with an associative transition state (PEt3, DeltaH not equal=48.4 (+/-1.9) kJ mol-1, DeltaS not equal=-149.2 (+/-6.4) J mol-1 K-1, DeltaG not equal=92.9 kJ mol-1; PPh2Me, DeltaH not equal=73.4 (+/-3.7) kJ mol-1, DeltaS not equal=-71.9 (+/-2.3) J mol-1 K-1, DeltaG not equal=94.8 kJ mol-1). With PMe3 as a model substrate, the geometry and the free energy of the transition state (TS) for the formation of the phosphine oxide-coordinated intermediate were calculated. The latter, 95 kJ mol-1, is in good agreement with the experimental values. An unexpectedly large O-P-C angle calculated for the TS suggests that there is significant O-nucleophilic attack on the P--C sigma* in addition to the expected nucleophilic attack of the P on the Mo==O pi*. The second step of the reaction, that is, the exchange of the coordinated phosphine oxide with acetonitrile, [LiPrMoO(OPh)(OPR3)]+MeCN-->[LiPrMoO(OPh)(MeCN)]+OPR3, follows a first-order rate law in MeCN. A dissociative interchange (Id) mechanism, with activation parameters of DeltaH not equal=93.5 (+/-0.9) kJ mol-1, DeltaS not equal=18.2 (+/-3.3) J mol-1 K-1, DeltaG not equal=88.1 kJ mol-1 and DeltaH not equal=97.9 (+/-3.4) kJ mol-1, DeltaS not equal=47.3 (+/-11.8) J mol-1 K-1, DeltaG not equal=83.8 kJ mol-1, for [LiPrMoO(OPh)(OPEt3)] (2 a) and [LiPrMoO(OPh)(OPPh2Me)] (2 b), respectively, is consistent with the experimental data. Although gas-phase calculations indicate that the Mo--OPMe3 bond is stronger than the Mo--NCMe bond, solvation provides the driving force for the release of the phosphine oxide and formation of [LiPrMoO(OPh)(MeCN)] (3). 相似文献
85.
Selective separation of pyrite and galena from mixture of the two minerals was achieved through interaction with cells and metabolic products from a culture of Paenibacillus polymyxa. Adsorption of cells and metabolic products onto minerals and electrokinetic studies of minerals after interaction with cells and metabolic products were carried out to examine the resulting surface modification on the mineral surfaces. Flocculation and flotation techniques were successfully applied in the selective separation of minerals after bacterial interaction. The effect of varying conditions for production of extracellular polysaccharides and protein provided an insight into the possible mechanism involved in microbially induced flocculation and flotation of pyrite and galena. 相似文献
86.
Sarkar M Banerjee A Pramanick PP Sarkar AR 《Journal of colloid and interface science》2006,302(2):432-441
The effects of different operational variables on the mechanistic function of laterite in removal of fluoride have been investigated. Thermodynamic parameters such as free energy change, enthalpy, and entropy of the process, as well as the sorption isotherm, were evaluated. The extent of solute removal is determined by initial solute concentration, operational conditions, laterite dose, and solution pH. For a fixed set of experimental conditions, a model equation is developed from which the percent removal corresponding to each load of fluoride is determined. The mechanism of fluoride adsorption is governed by the zero point charge of laterite and follows a first-order rate equation. pH has a vital role influencing the surface characteristics of laterite. To simulate the flow dynamics, fluoride solution was run through a fixed bed column. The pattern of breakthrough curves for different influent fluoride concentration, pH, and column bed height was characterized. The column efficiency was tested from the bed depth-service time model. The elution of the retained fluoride was studied and the effectiveness of column operation was determined by the retention-elution cycles. 相似文献
87.
Sengupta PS 《The Journal of chemical physics》2006,124(7):74511
The water exchange process of square planar tetraaquaplatinum(II) was computationally investigated at the Hartree-Fock, density-functional theory (B3LYP, PW91PW91, and mPW1PW91) and the second-order Moller-Plesset perturbation theory of levels of calculation. The stationary points on the gas phase and on the reaction field potential-energy surface were fully optimized and characterized. The self-consistent reaction field (SCRF) methods were also applied on the same system. The structures and energetic processes of all the species involved were investigated. The kinetic and thermodynamic properties for the gas phase and SCRF model data were compared with the available experimental data. The rate constants in MP2 level of theory and B3LYP isodensity polarized continuum model reaction field are in good agreement with the experimental data. 相似文献
88.
Neogi A Majhi TP Mukhopadhyay R Chattopadhyay P 《The Journal of organic chemistry》2006,71(8):3291-3294
Pd-catalyzed intramolecular arylamination on sugar derivatives has been accomplished by using bulky biaryl phosphine ligands. An application of this methodology on a variety of D-glucose-derived substrates, 2a-f, led to the synthesis of highly functionalized cis-fused tricyclic oxazocines, 3a-e. The products could subsequently be transformed to the optically active benzoxazocine derivative 4 and tricyclic nucleoside 6. This is the first example of the synthesis of eight-membered rings via intramolecular cycloamination of furanose derivatives, which provides a very useful method for the catalytic synthesis of medium-ring heterocycles. 相似文献
89.
An experimental study was conducted to characterize the dynamic wind loads and evolution of the unsteady vortex and turbulent
flow structures in the near wake of a horizontal axis wind turbine model placed in an atmospheric boundary layer wind tunnel.
In addition to measuring dynamic wind loads (i.e., aerodynamic forces and bending moments) acting on the wind turbine model
by using a high-sensitive force-moment sensor unit, a high-resolution digital particle image velocimetry (PIV) system was
used to achieve flow field measurements to quantify the characteristics of the turbulent vortex flow in the near wake of the
wind turbine model. Besides conducting “free-run” PIV measurements to determine the ensemble-averaged statistics of the flow
quantities such as mean velocity, Reynolds stress, and turbulence kinetic energy (TKE) distributions in the wake flow, “phase-locked”
PIV measurements were also performed to elucidate further details about evolution of the unsteady vortex structures in the
wake flow in relation to the position of the rotating turbine blades. The effects of the tip-speed-ratio of the wind turbine
model on the dynamic wind loads and wake flow characteristics were quantified in the terms of the variations of the aerodynamic
thrust and bending moment coefficients of the wind turbine model, the evolution of the helical tip vortices and the unsteady
vortices shedding from the blade roots and turbine nacelle, the deceleration of the incoming airflows after passing the rotation
disk of the turbine blades, the TKE and Reynolds stress distributions in the near wake of the wind turbine model. The detailed
flow field measurements were correlated with the dynamic wind load measurements to elucidate underlying physics in order to
gain further insight into the characteristics of the dynamic wind loads and turbulent vortex flows in the wakes of wind turbines
for the optimal design of the wind turbines operating in atmospheric boundary layer winds. 相似文献
90.
Kumar Abhinav Partha Guha 《The European Physical Journal B - Condensed Matter and Complex Systems》2018,91(3):52
Through the Hasimoto map, various dynamical systems can be mapped to different integrodifferential generalizations of Nonlinear Schrödinger (NLS) family of equations some of which are known to be integrable. Two such continuum limits, corresponding to the inhomogeneous XXX Heisenberg spin chain [J. Phys. C 15, L1305 (1982)] and that of a thin vortex filament moving in a superfluid with drag [Eur. Phys. J. B 86, 275 (2013) 86; Phys. Rev. E 91, 053201 (2015)], are shown to be particular non-holonomic deformations (NHDs) of the standard NLS system involving generalized parameterizations. Crucially, such NHDs of the NLS system are restricted to specific spectral orders that exactly complements NHDs of the original physical systems. The specific non-holonomic constraints associated with these integrodifferential generalizations additionally posses distinct semi-classical signature. 相似文献