Path integral for the relativistic particle and harmonic oscillators

The action for a massive particle in special relativity can be expressed as the invariant proper length between the end points. In principle, one should be able to construct the quantum theory for such a system by the path integral approach using this action. On the other hand, it is well known that the dynamics of a free, relativistic, spinless massive particle is best described by a scalar field which is equivalent to an infinite number of harmonic oscillators. We clarify the connection between these two—apparently dissimilar—approaches by obtaining the Green function for the system of oscillators from that of the relativistic particle. This is achieved through defining the path integral for a relativistic particle rigorously by two separate approaches. This analysis also shows a connection between square root Lagrangians and the system of harmonic oscillators which is likely to be of value in more general context.     

Parametric identification of nonlinear systems using multiple trials

It is observed that the harmonic balance (HB) method of parametric identification of nonlinear system may not give right identification results for a single test data. A multiple-trial HB scheme is suggested to obtain improved results in the identification, compared with a single sample test. Several independent tests are conducted by subjecting the system to a range of harmonic excitations. The individual data sets are combined to obtain the matrix for inversion. This leads to the mean square error minimization of the entire set of periodic orbits. It is shown that the combination of independent test data gives correct results even in the case where the individual data sets give wrong results.     

Ultrafast Electron Transfer Kinetics of Graphene Grown by Chemical Vapor Deposition

High electrochemical reactivity is required for various energy and sensing applications of graphene grown by chemical vapor deposition (CVD). Herein, we report that heterogeneous electron transfer can be remarkably fast at CVD‐grown graphene electrodes that are fabricated without using the conventional poly(methyl methacrylate) (PMMA) for graphene transfer from a growth substrate. We use nanogap voltammetry based on scanning electrochemical microscopy to obtain very high standard rate constants k⁰≥25 cm s^?1 for ferrocenemethanol oxidation at polystyrene‐supported graphene. The rate constants are at least 2–3 orders of magnitude higher than those at PMMA‐transferred graphene, which demonstrates an anomalously weak dependence of electron‐transfer rates on the potential. Slow kinetics at PMMA‐transferred graphene is attributed to the presence of residual PMMA. This unprecedentedly high reactivity of PMMA‐free CVD‐grown graphene electrodes is fundamentally and practically important.     

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.     

Exploring the effect of radiation crosslinking on the physico‐mechanical,dynamic mechanical and dielectric properties of EOC–PDMS blends for cable insulation applications

This work focuses on the effect of electron beam irradiation on the physico‐mechanical, dynamic mechanical and dielectric properties of blends based on ethylene octene copolymer (EOC) and poly dimethyl siloxane (PDMS) rubber. It is found that electron beam irradiation caused considerable improvement in the physico‐mechanical properties; the tensile strength was enhanced by nearly 35% for 70:30 EOC:PDMS blend. Phase morphology of the blends analyzed before irradiation by scanning electron microscopy (SEM) exhibited droplet/matrix morphology with sizes of the PDMS rubber domain varying from 0.55 µm to 0.47 µm as the amount of PDMS rubber decreased from 30 wt% to 10 wt%. This reduction in the PDMS rubber domain has been correlated with the physico‐mechanical properties of the blends. Further, the dynamic mechanical properties and creep behavior of these EOC:PDMS blends before and after irradiation has been studied. It is inferred that the 70:30 blend after radiation crosslinking shows a 17% decrease in the creep compliance, i.e. higher creep resistance compared to neat blends. All the radiation crosslinked blends exhibited lower dielectric constant, lower dielectric loss and higher electrical resistivity as compared to the virgin blends which makes it suitable for cable insulating application. Copyright © 2016 John Wiley & Sons, Ltd.     

Inelastic constitutive equations for complex flows

A new class of inelastic constitutive equations is presented and discussed. In addition to the rate-of-strain tensor, the stress is assumed to depend also on the relative-rate-of-rotation tensor, a frame-indifferent quantity that brings information about the nature of the flow. The material functions predicted by these constitutive equations are given for simple shear and uniaxial extension. A special case of these equations takes the Newtonian form, except that the viscosity is a function of the invariants of both kinematic tensors on which the stress depends. This simple constitutive equation has potential applications in liquid flow process simulations, since it combines simplicity with the capability of responding independently to shear and extension, as real liquids seem to do. Finally, possible forms for the new viscosity function are discussed.     

Synthesis, complexation studies and biological activity of some novel mono and tricyclic cyclophane amides and cyclophane sulfonamides

A series of mono, tricyclic cyclophane tetraamides and cyclophane sulfonamides have been synthesized and characterized from spectral and XRD studies. All the cyclophane amides form charge transfer (CT) complex with TCNQ. The cyclophane amides show moderate to good anti-inflammatory activity. Some of them were active against Gram positive (Klebsiella pneumonia) and Gram negative (Escherichia coli and Staphylococcus aureus) human pathogens.