Rod–coil block copolymers: An iterative synthetic approach via living free-radical procedures

A modular approach has been developed for the synthesis of rod–coil block copolymers involving the initial preparation of a macroinitiator based on the rod block followed by the growth of the coil segment with living free-radical procedures. The key feature of this strategy is the utilization of an alkoxyamine group from the beginning of the synthesis, which serves as a solubilizing group and ensures that each rod block contains a single initiating fragment. Using this approach permits block copolymers based on insoluble biphenyl ester oligomers to be conveniently prepared with coil segments that range from styrenes to acrylates to 1,3-dienes. The tendency of the rod segments to crystallize is strongly dependent on the weight fraction of the rod segment and the chemical nature of the coil segment. Rod–coil molecules containing at least 25–35 wt % polystyrene or poly(n-butyl acrylate) coil segments show a two-dimensional hexagonal arrangement of rod aggregates, as characterized by transmission electron microscopy and small-angle X-ray scattering. Polyisoprene block copolymers exhibit a lamellar microstructure with short rigid domains in which the rod units lie in an interdigitated smectic C arrangement. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3640–3656, 2003     

Synthesis of side‐chain liquid‐crystalline homopolymers and triblock copolymers with p‐methoxyazobenzene moieties and poly(ethylene glycol) as coil segments by atom transfer radical polymerization and their thermotropic phase behavior

A series of side‐chain liquid‐crystalline (LC) homopolymers of poly[6‐(4‐methoxy‐4′‐oxy‐azobenzene) hexyl methacrylate] with different degrees of polymerization were synthesized by atom transfer radical polymerization (ATRP), which were prepared with a wide range of number‐average molecular weights from 5.1 × 10³ to 20.6 × 10³ with narrow polydispersities of around 1.17. Thermal investigation showed that the homopolymers exhibit two mesophases, a smectic phase, and a nematic phase, and the phase‐transition temperatures of the homopolymers increase clearly with increasing molecular weights. A series of novel LC coil triblock copolymers with narrow polydispersities was synthesized by ATRP, and their thermotropic phase behavior was investigated with differential scanning calorimetry and polarized optical microscopy. The LC coil triblocks were designed to have an LC conformation of poly[6‐(4‐methoxy‐4′‐oxy‐azobenzene) hexyl methacrylate] with a wide range of molecular weights from 3.5 × 10³ to 1.7 × 10⁴ and the coil conformation of poly(ethylene glycol) (PEG) (number‐average molecular weight: 6000 or 12,000) segment. Their characterization was investigated with ¹H NMR, Fourier transform infrared spectra, and gel permeation chromatography. Triblock copolymers exhibited a crystalline phase, a smectic phase, and a nematic phase. The phase‐transition temperatures from the smectic to nematic phase and from the nematic to isotropic phase increased, and the crystallization of PEG depressed with increasing molecular weight of the LC block. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2854–2864, 2003     

The Resonance Phenomena Associated with the Time Asymmetry in Non-Hermitian Quantum Mechanics

Resonances are defined as the poles of the scattering matrix. The poles are associated with the complex eigenvalues of the Hamiltonian which are embedded in the lower half of the complex plane. The asymptotes of the corresponding eigenfunctions are exponentially diverged. Therefore, the resonance eigenfunctions are not embedded in the Hermitian domain of the Hamiltonian. The time asymmetric problem is discussed for these types of non-Hermitian Hamiltonians and several solutions of this problem are proposed.     

B(A)CKLUND TRANSFORMATION ON SURFACES WITH CONSTANT MEAN CURVATURE IN R2'1

In this paper,the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2,1.Using this transformation,families of surfaces with constant mean curvature from known ones can be constructed.     

Magneto-Optical Measurement of Organic Conductor Using Rotational Cavity System

We have developed a new magneto-optical measurement system using a rotational cavity system equipped with a millimeter vector network analyzer and a 14 T solenoid type super conducting magnet. The measurement can be performed in the transmission configuration down to 1.6 K. The results of the precise angular dependence measurement of quasi-one-dimensional organic conductor (DMET)₂I₃ using the new system are shown, and its Fermi surface will be discussed in connection with the previous reports.     

Efficient discretization of pressure‐correction equations on non‐orthogonal grids

An alternative discretization of pressure‐correction equations within pressure‐correction schemes for the solution of the incompressible Navier–Stokes equations is introduced, which improves the convergence and robustness properties of such schemes for non‐orthogonal grids. As against standard approaches, where the non‐orthogonal terms usually are just neglected, the approach allows for a simplification of the pressure‐correction equation to correspond to 5‐point or 7‐point computational molecules in two or three dimensions, respectively, but still incorporates the effects of non‐orthogonality. As a result a wide range (including rather high values) of underrelaxation factors can be used, resulting in an increased overall performance of the underlying pressure‐correction schemes. Within this context, a second issue of the paper is the investigation of the accuracy to which the pressure‐correction equation should be solved in each pressure‐correction iteration. The scheme is investigated for standard test cases and, in order to show its applicability to practical flow problems, for a more complex configuration of a micro heat exchanger. Copyright © 2003 John Wiley & Sons, Ltd.     

On a dynamic fractional game

Consider a two-person zero-sum game constructed by a dynamic fractional form. We establish the upper value as well as the lower value of a dynamic fractional game, and prove that the dual gap is equal to zero under certain conditions. It is also established that the saddle point function exists in the fractional game system under certain conditions so that the equilibrium point exists in this game system.     

Higher-order radiative perturbation theory

As a computationally effective tool, the first-order term of the radiative perturbation theory has been computed successfully, and has been applied in a number of areas. In this article, we develop the computational expressions for the higher-order terms of the perturbation expansion in a plane parallel atmosphere. These expressions are then implemented, and numerical results for some typical cases are presented. These results indicate that the computation is successful and that the higher-order terms are essential in cases where the first-order term alone cannot predict the perturbation with sufficient accuracy.     

Analysis of a Duopoly Supply Chain and its Application in Electricity Spot Markets

This paper studies a supply chain consisting of two suppliers and one retailer in a spot market, where the retailer uses the newsvendor solution as its purchase policy, and suppliers compete for the retailer’s purchase. Since each supplier’s bidding strategy affects the other’s profit, a game theory approach is used to identify optimal bidding strategies. We prove the existence and uniqueness of a Nash solution. It is also shown that the competition between the supplier leads to a lower market clearing price, and as a result, the retailer benefits from it. Finally, we demonstrate the applicability of the obtained results by deriving optimal bidding strategies for power generator plants in the deregulated California energy market. Supported in part by RGC (Hong Kong) Competitive Earmarked Research Grants (CUHK4167/04E and CUHK4239/03E), a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of China, and a grant from Hundred Talents Program of the Chinese Academy of Sciences.