On dynamics of velocity vector potential in incompressible fluids

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.     

Accelerating molecular dynamic simulation on the cell processor and Playstation 3

Implementation of molecular dynamics (MD) calculations on novel architectures will vastly increase its power to calculate the physical properties of complex systems. Herein, we detail algorithmic advances developed to accelerate MD simulations on the Cell processor, a commodity processor found in PlayStation 3 (PS3). In particular, we discuss issues regarding memory access versus computation and the types of calculations which are best suited for streaming processors such as the Cell, focusing on implicit solvation models. We conclude with a comparison of improved performance on the PS3's Cell processor over more traditional processors.     

On the Jacobi Last Multiplier, integrating factors and the Lagrangian formulation of differential equations of the Painlevé–Gambier classification

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.     

Adsorption behavior of rhodamine B on Rhizopus oryzae biomass

The removal of a carcinogenic dye rhodamine B (C. I. 45170) from wastewater by biomass of different moulds and yeasts is described. Among all of the fungal species tested, the biomass of Rhizopus oryzae MTCC 262 is found to be the most effective. Dye adsorption reaches maximum with the biomass harvested from the early stationary phase of growth. The optimum temperature and pH for adsorption are observed to be 40 degrees C and 7.0, respectively. The adsorption rate is very fast initially and attains equilibrium after 5 h. The adsorption isotherm follows the Langmuir isotherm model satisfactorily within the studied dye concentration range. Of the different metabolic inhibitors tested, 2,4-ditrophenol (DNP) and N,N'-dicyclohexylcarbodiimide (DCCD) decrease dye adsorption by approximately 30% suggesting the role of energy metabolism in the process. Spectrophotometric study indicates that the removal of rhodamine B by R. oryzae biomass involves an adsorption process. Scanning (SEM) and transmission (TEM) electron microscopic investigations have been carried out to understand the probable mechanism of the dye-biomass interaction.     

Parallelized-over-parts computation of absolute binding free energy with docking and molecular dynamics

We present a technique for biomolecular free energy calculations that exploits highly parallelized sampling to significantly reduce the time to results. The technique combines free energies for multiple, nonoverlapping configurational macrostates and is naturally suited to distributed computing. We describe a methodology that uses this technique with docking, molecular dynamics, and free energy perturbation to compute absolute free energies of binding quickly compared to previous methods. The method does not require a priori knowledge of the binding pose as long as the docking technique used can generate reasonable binding modes. We demonstrate the method on the protein FKBP12 and eight of its inhibitors.     

Cd(ii)-triggered excimer-monomer conversion of a pyrene derivative: time dependent red-shift of monomer emission with cell staining application

An efficient fluorescent probe (E)-N1-((E)-2-((pyren-7-yl)methyleneamino)ethyl)-N2-((pyren-7-yl)methylene)ethane-1,2-diamine (L) has been synthesized by a facile one-step condensation reaction. L can selectively detect Cd(2+) in presence of other common metal ions in 0.1 M HEPES buffered DMSO-water (4?:?1, v/v) medium. The detection limit of Cd(2+) is 1.8 × 10(-8) M. Cd(2+) can effectively convert the excimer emission of L into its monomer emission which in turn exhibits a time-dependent red-shift.     

Information trade-offs for optical quantum communication

Recent work has precisely characterized the achievable trade-offs between three key information processing tasks-classical communication (generation or consumption), quantum communication (generation or consumption), and shared entanglement (distribution or consumption), measured in bits, qubits, and ebits per channel use, respectively. Slices and corner points of this three-dimensional region reduce to well-known protocols for quantum channels. A trade-off coding technique can attain any point in the region and can outperform time sharing between the best-known protocols for accomplishing each information processing task by itself. Previously, the benefits of trade-off coding that had been found were too small to be of practical value (viz., for the dephasing and the universal cloning machine channels). In this Letter, we demonstrate that the associated performance gains are in fact remarkably high for several physically relevant bosonic channels that model free-space or fiber-optic links, thermal-noise channels, and amplifiers. We show that significant performance gains from trade-off coding also apply when trading photon-number resources between transmitting public and private classical information simultaneously over secret-key-assisted bosonic channels.     

Solid supported palladium(0) nano/microparticle: a ligand-free efficient recyclable heterogeneous catalyst for mono- and β,β-double-Heck reaction

Solid supported palladium nano/microparticles were found to be active catalysts to perform mono- and β,β-double-Heck reactions. Different β-unsubstituted and substituted alkenes including acrylate, methacrylate, crotonate, styrene, acrylonitrile, and acrylamide were investigated successfully for mono- and β,β-double-Heck reactions with aryl iodide under milder reaction condition. One-pot β,β-double-Heck reaction of aryl iodides with α,β-unsaturated ester, amide, nitrile, and styrene derivatives were also performed under standard reaction conditions. Wide functional group tolerance, easy catalyst recovery, and recyclability up to twelve times without significant loss of catalytic activity added extra importance to the present process.     

Protein adsorption-desorption on electrospray capillary walls--no influence on aggregate distribution

Adsorbed proteins on walls of glass capillaries used for electrospray (ES) can desorb and potentially affect size distributions and, thus, quantification of aggregates of proteins. In this study we use differential mobility analysis (DMA) to investigate the size distribution of various proteins eluting from bare and passivated glass capillaries. We found no significant differences in aggregate distributions from unpassivated capillaries at 'steady state' when compared to aggregate distributions from passivated capillaries implying that desorbing proteins do not influence protein aggregate distribution. Surface passivation with gelatin was found to be considerably more effective in limiting adsorption of two antibodies (Rituxan and polyclonal human IgG) compared to passivation with BSA. Gelatin passivation was also found to be stable for a few days and from a pH range of 4.8-9.0.     

On solutions of third and fourth-order time dependent Riccati equations and the generalized Chazy system

We introduce a new transformation (nonlocal) to find the general solutions of some equations belonging to the third and fourth-order time dependent Riccati class of equations. These are in turn related to the Chazy polynomial class and the time dependent F-XVI Bureau symbol PI equations respectively.