Morphology and physical properties of a liquid–crystalline main-chain polymer with flexible side chains

A molecular laminate model is used to explain the properties of unoriented and oriented films of poly(p-phenylene-2,5-didodecyloxyterephthalate) cast from solution. In oriented films the two different crystal modifications, A and B, give rise to room temperature tensile moduli of 15 and 30 GPa respectively. The packing (in clusters) of the side chains in modification A, leading to a glass–like transition in the side-chain regions around ?40°C, is largely responsible for this difference. Oriented films of modification A and B have coefficients of thermal expansion of +0.3×10^?5 and ?1× 10^?5 K^?1 respectively. It is concluded that the properties of this class of polymers can be adjusted in a systematic way.     

Verifying exactness of relaxations for robust semi-definite programs by solving polynomial systems

In this paper, robust semi-definite programs are considered with the goal of verifying whether a particular LMI relaxation is exact. A procedure is presented showing that verifying exactness amounts to solving a polynomial system. The main contribution of the paper is a new algorithm to compute all isolated solutions of a system of polynomials. Standard techniques in computational algebra, often referred to as Stetter’s method [H.J. Stetter, Numerical Polynomial Algebra, SIAM, 2004], involve the computation of a Gröbner basis of the ideal generated by the polynomials and further require joint eigenvector computations in order to arrive at the zeros of the polynomial system. Our algorithm does neither require structural knowledge on the polynomial system, nor does it rely on the computation of joint eigenvectors.     

Wavenumber dependence of structural relaxation in a molecular liquid

Structural relaxation in liquid orthoterphenyl is studied by means of coherent neutron time-of-flight and backscattering spectroscopy over a large temperature range. Not only amplitude and relaxation time but also the spectral line shape show a significant variation with wavenumber. These variations are correlated with the static structure factor, in qualitative accord with mode-coupling results for simple liquids. Even far above the melting point, relaxation remains non-exponential. Received: 5 January 1998 / Revised: 3 April 1998 / Accepted: 19 June 1998     

Optical and electrical characteristics of (LiCl) x (P2O5)1 − x glass

Homogeneous (LiCl) _x (P₂O₅)_1 − x glasses were synthesised using a melt-quenching method for x = 0.1–0.6 in the interval of 0.05. The amorphous structure of the samples was evident by the X-ray diffraction spectrum. The short range structures of the binary phosphate samples were examined by Fourier transform infrared spectroscopy, whilst the density of the samples was measured as supportive data for the investigations. The results of refractive indices as measured using an ellipsometer reveal the homogeneity of samples and was found to depend on the glass composition. The electrical properties of the glasses were investigated by ac impedance spectroscopy from 10 mHz to 1 MHz for temperatures ranging from room temperature to 573 K. An estimation of the bulk resistivity was obtained by taking the intercepts on the real axis at low frequencies of the complex impedance plot. The dc conductivities derived from the reciprocal of resistivity values were found to obey the Arrhenius relationship, and its activation energy shows a decreasing trend with the increase in LiCl content in the glass. Lastly, an equivalent circuits consisting of real and complex capacitors is proposed to describe the dielectric response of the glass.     

Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques

In a recent work, we introduced the concept of convex extensions for lower semi-continuous functions and studied their properties. In this work, we present new techniques for constructing convex and concave envelopes of nonlinear functions using the theory of convex extensions. In particular, we develop the convex envelope and concave envelope of z=x/y over a hypercube. We show that the convex envelope is strictly tighter than previously known convex underestimators of x/y. We then propose a new relaxation technique for fractional programs which includes the derived envelopes. The resulting relaxation is shown to be a semidefinite program. Finally, we derive the convex envelope for a class of functions of the type f(x,y) over a hypercube under the assumption that f is concave in x and convex in y.     

A semidefinite programming approach to the generalized problem of moments

We consider the generalized problem of moments (GPM) from a computational point of view and provide a hierarchy of semidefinite programming relaxations whose sequence of optimal values converges to the optimal value of the GPM. We then investigate in detail various examples of applications in optimization, probability, financial economics and optimal control, which all can be viewed as particular instances of the GPM. This work was supported by french ANR-grant NT05-3-41612, and part of it was completed in January 2006 while the author was a member of IMS, the Institute for Mathematical Sciences of NUS (The National University of Singapore).     

Hilbertian convex feasibility problem: Convergence of projection methods

The classical problem of finding a point in the intersection of countably many closed and convex sets in a Hilbert space is considered. Extrapolated iterations of convex combinations of approximate projections onto subfamilies of sets are investigated to solve this problem. General hypotheses are made on the regularity of the sets and various strategies are considered to control the order in which the sets are selected. Weak and strong convergence results are established within thisbroad framework, which provides a unified view of projection methods for solving hilbertian convex feasibility problems. This work was supported by the National Science Foundation under Grant MIP-9308609.     

The capacitated distribution and waste disposal problem

We study the problem of the simultaneous design of a distribution network with plants and waste disposal units, and the coordination of product flows and waste flows within this network. The objective is to minimize the sum of fixed costs for opening plants and waste disposal units, and variable costs related to product and waste flows. The problem is complicated by (i) capacity constraints on plants and waste disposal units, (ii) service requirements (i.e. production must cover total demand) and (iii) waste, arising from production, to be disposed of at waste disposal units. We discuss alternative mathematical model formulations for the two-level distribution and waste disposal problem with capacity constraints. Lower bounding and upper bounding procedures are analyzed. The bounds are shown to be quite effective when embedded in a standard branch and bound algorithm. Finally, the results of a computational study are reported.     

Effect of mesoscopic misfit on growth,morphology, electronic properties and magnetism of nanostructures at metallic surfaces

Stress and strain originating from mesoscopic misfit at interfaces can have diverse effects on the properties of surfaces and nanostructures thereon. We review the sources and consequences of mesoscopic misfit at metallic surfaces and elucidate various ways in which it affects growth, morphology, electronic properties and magnetism of thin films in early stages of epitaxy and epitaxial nanostructures.     

Using mechanical spectroscopies to study the glass transition dynamics in unsaturated polyester resins cured with different styrene contents

The control of chemical architecture has been one relevant parameter in the study of glass transition dynamics in macromolecular systems. In this study, two polyester resins differing in the styrene content that was added in the curing process were studied using two complementary mechanical spectroscopy techniques: dynamic mechanical analysis (DMA) and thermally stimulated recovery (TSR). Both techniques showed that the -relaxation is shifted to higher temperatures (longer times) with increasing styrene content. Master curves were obtained from the DMA data. The shift factors were used to obtain the temperature dependence of the apparent activation energy, E_a(T). The TSR results also permitted to obtain E_a(T) that also exhibited a maximum around T_g. This behaviour, apparently universally observed in thermally stimulated techniques, was explained by the shift from a Vogel-Fulcher-Tamman-Hesse to an Arrhenius regime. The data also allowed to calculate the fragility index of the two materials, which was found to be higher for the one with higher styrene content. Remarks are made on the dependency of the values of this parameter obtained from different techniques.