Investigation of the effects of silicate modification on polymer‐layered silicate nanocomposite morphology

The morphological behavior of a series of polymer‐layered silicate nanocomposites (PLSNs) has been investigated. The goal was to probe the effect of “textured” silicate surfaces on PLSN morphology. The nanocomposites were fabricated by mixing montmorillonite clay that was carefully modified with tailor‐made polystyrene (PS) surfactants into a PS homopolymer matrix, where the chemical similarity of the matrix polymer and surfactants assures complete miscibility of surfactant and homopolymer. To examine the effect of silicate surface “texture,” clay was modified with combinations of long and short surfactants. The samples were then direct melt annealed to allow the equilibrium morphology to develop, and characterized by small‐angle X‐ray scattering. Based on the implications of the Balazs model and other work on the wetting behavior of polymer melts with longer surfactants and textured surfaces we expected that the intercalation of the homopolymer matrix material into the modified clay would be promoted. Extensive characterization of both the modified clays as well as the resultant nanocomposites clearly show that the modified clays exhibit a high degree of order, but also that only phase‐separated morphologies are formed in the corresponding nanocomposites. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4075–4083, 2004     

A simple approach to evaluation of lattice sums

It is shown that starting from a Fourier transform relation one can derive, in a surprisingly simple manner, all the well-known results of lattice summation, that have been obtained so far by a complicated use of the Ewald theta transformation. We show that the Ewald transformation follows directly from the Fourier transform relation.     

Non-𝒜belian Geometry

 Spatial noncommutativity is similar and can even be related to the non- Abelian nature of multiple D-branes. But they have so far seemed independent of each other. Reflecting this decoupling, the algebra of matrix valued fields on noncommutative space is thought to be the simple tensor product of constant matrix algebra and the Moyal-Weyl deformation. We propose scenarios in which the two become intertwined and inseparable. Therefore the usual separation of ordinary or noncommutative space from the internal discrete space responsible for non-Abelian symmetry is really the exceptional case of an unified structure. We call it non-Abelian geometry. This general structure emerges when multiple D-branes are configured suitably in a flat but varying B field background, or in the presence of non-Abelian gauge field background. It can also occur in connection with Taub-NUT geometry. We compute the deformed product of matrix valued functions using the lattice string quantum mechanical model developed earlier. The result is a new type of associative algebra defining non-Abelian geometry. A possible supergravity dual is also discussed. Received: 13 December 2000 / Accepted: 24 October 2002 Published online: 24 January 2003 Communicated by R. H. Dijkgraaf     

Optimum pump-pulse duration for optical parametric oscillators

It is shown that for pulsed optical parametric oscillators there is an optimum pumppulse duration at which the threshold fluence is a minimum. The dependence of the threshold fluence on pump laser pulse duration is found to be substantial for lossy narrowband optical parametric oscillators. The pulse energy requirement for the pump laser may be substantially lowered by operating it at a pulse duration close to the optimum.     

Invariant Measure and a Limit Theorem for Some Generalized Gauss Maps

Continued fractions w.r.t. a specified class of numbers is considered. The invariant measures of the corresponding transformations are identified connecting the continued fractions with geodesics on the upper half plane. A problem of convergence in distribution of sums of the coefficients of the continued fraction is also considered.     

Two colour multiphoton ionization spectroscopy of uranium from a metastable state

Using two pulsed tunable dye lasers, a two colour multiphoton ionization process has been utilised to explore the higher energy levels of uranium. One hundred and thirty eight new UI levels have been observed in the 37540–38420 cm^–1 region. J assignments of these levels have been suggested on the basis of their excitation from intermediate levels with known and contiguous J values. In eight cases the J assignments are unique.     

On de-globalization in quantum chromodynamics

The recent discovery and resummation of a class of single logarithmic effects (non-global logs), has a significant impact on several QCD observables ranging from the classic Sterman-Weinberg jet definition to currently studied event shapes and rapidity gap observables. The discovery of the above effects overturns, for example, the common wisdom that hadronic energy flow in limited inter-jet regions is dictatedprimarily by the colour flow of the underlying hard partonic subprocess. We discuss some features of non-global logs and the rapid progress being made in estimating and controlling such corrections.     

Numerical estimate of the phase diagram of finite ANNNI chains in transverse field

We have estimated numerically the phase diagram of a one dimensional spin 1/2 quantum Ising model with competing nearest and next nearest neighbour interactions in presence of a transverse field. The method essentially is to diagonalise exactly the Hamiltonian for finite (10 spins) open chains and calculate the spin-spin correlations from the ground state eigenvector. The results obtained confirm the transition between ferromagnetic and paramagnetic phases for <0.5 and between antiphase and paramagnetic phase for >0.5. ( is the ratio of next nearest and nearest neighbour interactions.) The results perhaps indicate furthermore that (i) there is a disorder line passing through =0.5; (ii) the zero point quantum fluctuations destroy the order near =0.5 as the transverse field is switched on; and (iii) there is probably also a floating phase with slowly decayling correlation near the order-disorder phase boundary for >0.5.