Mathematical Models for Unstable Quantum Systems and Gamow States

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo.     

ACTIVE CONTROL OF A FLEXIBLE CANTILEVER PLATE WITH MULTIPLE TIME DELAYS

Active control of a flexible cantilever plate with multiple time delays is investigated using the discrete optimal control method. A controller with multiple time delays is presented. In this controller, time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the controller derivation, so the system stability is easily guaranteed. Furthermore, this controller is available for both small time delays and large time delays. The feasibility and efficiency of the proposed controller are verified through numerical simulations in the end of this paper.     

串联组装双C60 的电子结构和输运特性

利用第一原理密度泛函理论计算组装C60形成能和电子结构,用半经典隧穿理论研究了串联C60的电子输运特性。结果显示：六边形对六边形双C60比边对边双C60稳定;库仑阻塞与系统的结构密切相关,并且只有阴极结比阳极结窄时,才会出现库仑阻塞;低温时出现非常明显库仑台阶,温度较高时其被热效应抑制。     

Configuration Design Sensitivity Analysis of Kinematic Responses of Mechanical Systems∗

Abstract

A continuum-based configuration design sensitivity analysis method is presented for kinematically driven mechanical systems. Configuration design variable for mechanical systems are defined. The 3-1-3 Euler angle is used as the orientation design variable. The reassembly process for a mechanical system after a configuration design change is eliminated by imposing kinematic admissibility conditions of the velocity field. The direct differentiation method is used to derive design sensitivity equations. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.     

Synthesis of well‐defined side chain fullerene polymers and study of their self‐aggregation behaviors

Monoalkynyl‐functionalized fullerene was precisely synthesized starting with pristine fullerene (C₆₀) and characterized by multiple techniques. Methyl methacrylate and 6‐azido hexyl methacrylate were then randomly copolymerized via reversible addition fragmentation chain transfer polymerization to build polymer backbones with well‐controlled molecular weights and copolymer compositions. Finally, these two moieties were covalently assembled into a series of well‐defined side chain fullerene polymers (SFPs) via the copper‐mediated click reaction which was verified by Fourier transform infrared spectroscopy and ¹H NMR. The fullerene loadings of the resultant polymers were estimated by thermogravimetric analysis and UV–vis spectroscopy, demonstrating consistent and high conversions in most of the samples. The morphology studies of the SFPs were performed both in solution and on solid substrates. Very intriguing self‐aggregation behaviors were detected by both gel permeation chromatography and dynamic light scattering analyses. Furthermore, the scanning electron microscopic images of these polymers showed the formation of various supramolecular nanoparticle assemblies and crystalline‐like clusters depending on the fullerene contents and polymer chain lengths. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3572–3582     

Clicked (AB)2C‐type miktoarm terpolymers: Synthesis,thermal and self‐assembly properties,and preparation of nanoporous materials

A well‐defined (PEO‐PS)₂‐PLA miktoarm terpolymer ( 1 ) was synthesized by stepwise click reactions of individually prepared poly(ethylene oxide) (PEO), polystyrene (PS, polymerized by atom transfer radical polymerization), and polylactide (PLA, polymerized by ring‐opening polymerization) blocks. As characterized by differential scanning calorimetry and small‐angle X‐ray scattering techniques, the terpolymer self‐assembled into a hexagonal columnar structure consisting of PLA/PEO cylindrical cores surrounded by PS chains. In contrast, the ion‐doped sample ( 1‐Li⁺ ) with lithium concentration per ethylene oxide = 0.2 exhibited a three‐phase lamellar structure, which was attributed to the microphase separation between PEO and PLA blocks and to the conformational stabilization of the longest PLA chain. The two‐phase columnar morphology before the ion doping was used to prepare a nanoporous material. PLA chains in the cylindrical core region were hydrolyzed by sodium hydroxide, producing nanopores with a pore diameter of about 14 nm. The resulted nanoporous material sank to the bottom in water, because of water‐compatible PEO chains on the walls. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Flexible active matrix addressed displays manufactured by printing and coating techniques

A flexible electrochromic active matrix addressed display, including 8 × 8 pixels, is demonstrated by using solution processing based on standard printing and coating manufacturing techniques. Each organic electrochromic display (OECD) pixel and its corresponding organic electrochemical transistor (OECT) are located on different sides of the flexible PET substrate. Electronic vias generated through the plastic substrate connects each OECD pixel with one addressing OECT. When comparing this display with actively addressed OECDs with all its components located on the same side, the present approach based on this electronic via substrate provides an enhanced pixel resolution and a relatively more simplified manufacturing process. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Nanoassemblies with light‐responsive size and density from linear flexible polyelectrolytes

This study presents electrostatically self‐assembled nanoparticles from linear flexible polyelectrolytes (poly(diallyldimethylammonium chloride or quarternized poly(4‐vinylpyridine)) and an ionic photo‐isomerizable azo dye (Acid Yellow 38) that can change their size upon UV‐light irradiation. Assemblies with narrow size distribution are stable in aqueous solution. For samples with under‐stoichiometric dye load, UV‐light exposure triggers a size decrease, e.g. from a hydrodynamic radius of R_h = 94 nm to R_h = 62 nm for an Ay38‐PDADMAC sample with a charge ratio of l_charge = 0.7. Size changes are caused by trans‐cis isomerization of the dye, accompanied by a change in hydrophilicity, binding enthalpy and entropy. Assemblies are characterized by static and dynamic light scattering, atomic force microscopy, UV–vis spectroscopy and isothermal titration calorimetry. Zeta potential measurements give insight into the electrostatic stabilization and size‐control of the ionic nano‐assemblies, revealing a master curve of effective surface charge density versus hydrodynamic radius. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys., 2013     

Synthesis and characterization of polythiophene block copolymer and fullerene derivative capable of “three‐point” complementary hydrogen bonding interactions and their application in bulk‐heterojunction solar cells

We report the synthesis and characterization of a polythiophene block copolymer (P4) selectively functionalized with diaminopyrimidine moieties and a thymine tethered fullerene derivative (F1). Self‐assembly between P4 and F1 through “three‐point” complementary hydrogen bonding is studied by ¹H NMR spectroscopy and differential scanning calorimetry. A large Stern‐Volmer constant (K_SV) of 1.2 × 10⁵ M^?1 is observed from fluorescence quenching experiments, revealing strong complexation between these two components. Solar cells employing P4 and F1 at different weight ratios as active layers are fabricated and tested; corresponding thin film morphologies are studied in detail by optical imaging and atomic force microscopy. Correlations between polymer complex structures, film morphologies, and device performance are discussed. Thermal stability of benchmark poly(3‐hexylthiophene) bulk heterojunction solar cells is found to be improved by the addition of a few weight percent of P4/F1 complexes as compatibilizers. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 3339–3350