Site-Specific Functionalization of Hyperbranched Polymers Using ``Click'' Chemistry

Different strategies for functionalization of the core region and periphery of core-shell type hyperbranched polymers (HBP) using the ``click'' reaction have been explored. For achieving periphera functionalization, an AB(2) + A-R-1 + A-R-2 type copolymerization approach was used, where A-R-1 is heptaethylene glycol monomethyl ether (HPEG-M) and A-R-2 is tetraethylene glycol monopropargyl ether (TEG-P). A very small mole fraction of the propargyl containing monomer, TEG-P, was used to ensure that the water-solubility of the hyperbranched polymer is minimally affected. Similarly, to incorporate propargyl groups in the core region, a new propargyl group bearing B-2-typ monomer was designed and utilized in an AB(2) + A(2) + B-2 + A-R-1 type copolymerization, such that the total mole fraction of B-2 + A(2) is small and their mole-ratio is 1: 1. Further, using a combination of both the above approaches, namely AB(2) + A(2) + B-2 + A-R-1 + A-R-2, hyperbranched structures that incorporate propargyl groups both at theperiphery and within the core were synthesized. Since the AB(2) monomer carries a hexamethylene spacer (C-6) and the periphery is PEGylated all the derivatized polymers form core-shell type structures in aqueous solutions. Attempts were made to ascertain and probe the location of the propargyl groups in these HBP's, by ``clicking'' azidomethylpyrene, onto them. However, the fluorescence spectra of aqueous solutions of the pyrene derivatized polymers were unable to discriminate between the various locations, possibly because the relatively hydrophobic pyrene units insert themselves into the core region to minimize exposure to water.

Absence of reptation in highly confined polymers

We present results of mechanical stress relaxation measurements on polymers confined at the air-water interface in the form of a monolayer. Systematic measurements allow, to our knowledge, for the first time, observation of the scaling of the stress relaxation time of the highly confined polymers as a function of both surface concentration and molecular weight. The observed scaling is found to be very close to that expected for motion of unentangled polymer solutions with hydrodynamic interactions. Our experimental observations thus clearly rule out the possibility of entanglement and hence reptation as a mode of relaxation in such highly confined polymeric systems.

Heat transfer with solid liquid phase change initiating at a point in a semi infinite mold

Short-time analytical solutions of temperature and moving boundary in two-dimensional two-phase freezing due to a cold spot are presented in this paper. The melt occupies a semi-infinite region. Although the method of solution is valid for various other types of boundary conditions, the results in this paper are given only for the prescribed flux boundary conditions which could be space and time dependent. The freezing front propagations along the interior of the melt region exhibit well known behaviours but the propagations along the surface are of new type. The freezing front always depends on material parameters. Several interesting results can be obtained as particular cases of the general results.

Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

Pressure shocks in relativistic viscous heat-conducting fluids

In this paper we have studied the propagation of pressure shocks in viscous, heat-conducting, relativistic fluids. Velocities of wave fronts and growth equations for the strength of the waves are obtained in the case of low and high temperatures with variable transport coefficients. On the basis of numerical integrations the growth equation results have been discussed. In the case of constant transport coefficients and for all admissible values of ratio of specific heats of the fluid, an analytical solution for the velocity of the wave as a function of distance along the normal trajectory to the wave front, has been obtained.

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.

Unsteady flow of a dilute suspension in a semi-infinite contracting or expanding pipe

In the present paper an exact similar solution of the Navier-Stokes equation for unsteady flow of a dilute suspension in a semi-infinite contracting or expanding circular pipe is presented. The effects of the Schmidt number (Sc), Reynolds number (|ε|), the volume fraction (α) and the relaxation time (τ) of the particulate phase on the flow characteristics are examined. The presence of the solid particles has been observed to influence the flow behaviour significantly. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained fully. The results may help understanding the flow near the heart and certain forced contractions or expansions of valved veins.

Laboratory Test Methods For The Evaluation Of Flammability Of Polymers

Combustion is a complex phenomena involving a multiplicity of variables. Some important variables measured in flame tests follow [1]. In order to characterize ignition, such related parameters as ignition time, ease of ignition, flash ignition temperature, and self-ignition temperature are measured. For studying the propagation of the flame, parameters such as distance burned or charred, area of flame spread, time of flame spread, burning rate, charred or melted area, and fire endurance are measured. Smoke characteristics are studied by determining such parameters as specific optical density, maximum specific optical density, time of occurrence of the densities, maximum rate of density increase, visual obscuration time, and smoke obscuration index. In addition to the above variables, there are a number of specific properties of the combustible system which could be measured. These are soot formation, toxicity of combustion gases, heat of combustion, dripping phenomena during the burning of thermoplastics, afterglow, flame intensity, fuel contribution, visual characteristics, limiting oxygen concentration (OI), products of pyrolysis and combustion, and so forth. A multitude of flammability tests measuring one or more of these properties have been developed [2]. Admittedly, no one small scale test is adequate to mimic or assess the performance of a plastic in a real fire situation. The conditions are much too complicated [3, 4]. Some conceptual problems associated with flammability testing of polymers have been reviewed [5, 6].

Theoretical studies on the conformations of higher gangliosides

The possible conformations of higher gangliosides (GD3, GT1a. GT1b, GQ1b) have been determined by computing their potential energy using semi-empirical potential functions. The favoured conformation of the disialic acid fragment in these gangliosides is independent of its position (internal or terminal). The favoured conformations of these gangliosides have also been correlated to their biological activity. The results suggest that tetanus toxin and sendai virus may have a large binding site which can accommodate at least four sugar residues.

Theoretical studies on the conformations of higher gangliosides

The possible conformations of higher gangliosides (GD3, GT1a. GT1b, GQ1b) have been determined by computing their potential energy using semi-empirical potential functions. The favoured conformation of the disialic acid fragment in these gangliosides is independent of its position (internal or terminal). The favoured conformations of these gangliosides have also been correlated to their biological activity. The results suggest that tetanus toxin and sendai virus may have a large binding site which can accommodate at least four sugar residues.

A simple and inexpensive technique to study the flammability of polymers

A simple and inexpensive technique is described for the study of flammability of polymers, wherein the samples can be weighed continuously during their combustion in controlled atmosphere. The mass versus time curves for burning and quenching process in polystyrene samples are discussed. The experimental data indicates the efficiency of Monoammonium phosphate and ammonium halides in quenching of polystyrene.

Spinup or spindown of a rotating electrically conducting fluid in a magnetic field

The hydromagnetic spinup or spindown of an incompressible, rotating, electrically conducting fluid over an infinite insulated disk with an applied magnetic field is studied when the impulsive motion is imparted either to the fluid or to the disk. The nonlinear partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. It is found that the spinup (or spindown) time due to impulsive motion of the disk is much shorter than the spinup (or spindown) time due to the impulsive motion of the distant fluid. The spinup (or spindown) time for the hydromagnetic case is comparatively smaller than the corresponding nonmagnetic case. Spindown is not merely a mirror reflection of spinup. Physics of Fluids is copyrighted by The American Institute of Physics.

Optimal dynamic inversion-based semi-active control of benchmark bridge using MR dampers

A new two-stage state feedback control design approach has been developed to monitor the voltage supplied to magnetorheological (MR) dampers for semi-active vibration control of the benchmark highway bridge. The first stage contains a primary controller, which provides the force required to obtain a desired closed-loop response of the system. In the second stage, an optimal dynamic inversion (ODI) approach has been developed to obtain the amount of voltage to be supplied to each of the MR dampers such that it provides the required force prescribed by the primary controller. ODI is formulated by optimization with dynamic inversion, such that an optimal voltage is supplied to each damper in a set. The proposed control design has been simulated for both phase-I and phase-II study of the recently developed benchmark highway bridge problem. The efficiency of the proposed controller is analyzed in terms of the performance indices defined in the benchmark problem definition. Simulation results demonstrate that the proposed approach generally reduces peak response quantities over those obtained from the sample semi-active controller, although some response quantities have been seen to be increasing. Overall, the proposed control approach is quite competitive as compared with the sample semi-active control approach.

Surface instability in a semi-infinite plasma in the presence of high frequency fields

The surface instability of a semi-infinite plasma immersed in a high frequency field is investigated. When the natural Langmuir frequency of the surface is nearly equal to the frequency of the high frequency field, the dispersion relation predicts build-up of oscillations with a growth rate comparable with the real part of the frequency. Threshold values above which the instability is possible are derived.