Molecular dynamics simulations of ion-irradiation induced deflection of 2D graphene films

Ion-irradiation induced surface stress generation and the resulting deflection of 2D cantilever graphene films is studied using molecular dynamics (MD) simulations. The simulation results show that the free-end deflection is strongly dependent on the kinetic energy of the incident ions. At low incident energies (?10 eV), the graphene film bends towards the irradiated side (upward deflection in our simulations); a transition from bending towards the irradiated side (upward deflection) to bending away from the irradiated side (downward deflection) occurs when the incident energy is ～10 eV; the downward deflection peaks at ～50 eV. Further increases of the incident energy cause the magnitude of downward deflection to decrease. The evolution of free-end deflection with respect to the number of incidences is also dependent on the incident energy. The dependence of the deflection behavior of the graphene films on the incident energy revealed by our atomistic simulations suggests the generation of intrinsic stress of different levels in the growing films. Such behavior may be attributed to competing mechanisms of production and annihilation of interstitial- and vacancy-like defects in the growing film. Understanding the dependence of thin film deflection on the incident energy provides guidelines for controlling thin film shapes at the nanometer scale using ion-beam machining.     

Non-linear dynamic intertwining of rods with self-contact

Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or ‘hockles’ are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively, by the dynamic conversion of twist (Tw) to writhe (Wr).     

Interfacially active particles in droplet/matrix blends of model immiscible homopolymers: Particles can increase or decrease drop size

Particles have been shown to adsorb at the interface between immiscible homopolymer melts and to affect the morphology of blends of those homopolymers. We examined the effect of such interfacially active particles on the morphology of droplet/matrix blends of model immiscible homopolymers. Experiments were conducted on blends of polydimethylsiloxane and 1,4-polyisoprene blended in either a 20:80 or 80:20 weight ratio. The effects of three different particle types, fluoropolymer particles, iron particles, and iron oxyhydroxide particles, all at a loading of 0.5 vol.%, were examined by rheology and by direct flow visualization. Particles were found to significantly affect the strain recovery behavior of polymer blends, increasing or decreasing the ultimate recovery, slowing down or accelerating the recovery kinetics, and changing the dependence of these parameters on the applied stress prior to cessation of shear. These rheological observations were found to correlate reasonably well with particle-induced changes in drop size. The particles can both increase as well as decrease the drop size, depending on the particle type, as well as on which phase is continuous. The cases in which particles cause a decrease in drop size are analogous to the particle stabilization of “Pickering emulsions” well-known from the literature on oil/water systems. We hypothesize that cases in which particles increase drop size are analogous to the “bridging–dewetting” mechanism known in the aqueous foam literature.     

Simultaneous spectrophotometric determination of mefenamic acid and paracetamol in pharmaceutical preparations

A spectrophotometric procedure for the simultaneous determination of mefenamic acid and paracetamol in a mixture is described. Using 0.01 M methanolic hydrochloric acid as solvent, the absorbance of the mixture is measured at 248, 279 and 351 nm. The concentration of each component can be calculated by solving two equations using two wavelengths, either 248 and 279 nm or 248 and 351 nm.     

An Efficient Enantioselective Synthesis of Natural Gingerols,the Active Principles of Ginger

A straightforward synthesis of (S)‐gingerols 1 – 3 has been described. The requisite stereogenic center in the target molecules was introduced by Sharpless asymmetric dihydroxylation using a chiral complex, AD‐mix β. This route is simple and efficient to prepare the products in very good yields.     

Asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers

We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established.     

Self‐diffusion coefficient of ring polymers in semidilute solution

In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self‐diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008     

Infinite-horizon investment consumption model with a nonterminal bankruptcy

This paper solves a general continuous-time consumption and portfolio decision problem for a single agent for whom there exists, upon bankruptcy, a possibility of recovery from his bankruptcy. The main contribution of the paper is in the modeling of the recovery process. Moreover, it is shown that the model with recovery has a one-to-one correspondence with the model with terminal bankruptcy treated in the literature.This research was supported by Grants SSHRC-410-83-9888 and NSERC-A4619 to the first author and by Grants NSF-DMS-86-01510 and AFOSR-88-0183 to the second author. Comments from E. Presman are gratefully acknowledged.     

The polarography of oximes: II. 1,2-Acenaphthaquinone monoxime

Polarography of 1,2-acenaphthaquinone monoxime has been carried out in buffers (pH 3.5–13.0) of constant ionic strength 0.5 M and 40% alcohol $\text{v}\text{v}$ at 25 ± 0.5 °C. The oxime group underwent diffusion-controlled reduction (4e) over the whole pH range. The number of electrons involved in the reduction was found by coulometric method as well as by incorporating the values of diffusion coefficients, obtained by using a McBain-Dawson cell, into the Ilkovi? equation. Koutecky's method has been used to compute the kinetic parameters (αn_aand ?log K_f.h) for the reduction of the oxime group and a reduction mechanism is proposed.     

Relations between generalised Hankel and modified Hypergeometric function operators

The object of the present note is to investigate the relations that exist between the generalized Hankel and Hypergeometric function operators. The results established here can be used in the theory of Integral equations also. This is illustrated by means of an example. The results established in this paper are of general character and includes, as particular cases, the results of Sneddon and Kalla and Saxena.