一个带阻尼项Josephson振动的半经典模型

在双势阱模型的基础上考虑了Josephson流与凝聚体的相互作用而引起的阻尼效应,得出相对粒子数Z(t)的表达式,并用一个简单的碰撞模型得出Josephson振动的振幅和能量及随时间呈指数衰减,以及凝聚体的质量越大,衰减越慢。     

Analytical solution of the linear fractional differential equation by Adomian decomposition method

In this paper, we consider the n-term linear fractional-order differential equation with constant coefficients and obtain the solution of this kind of fractional differential equations by Adomian decomposition method. With the equivalent transmutation, we show that the solution by Adomian decomposition method is the same as the solution by the Green's function. Finally, we illustrate our result with some examples.     

Low temperature fabrication of efficient porous carbon counter electrode for dye-sensitized solar cells

Porous carbon counter electrodes have been fabricated at low temperature by coating an organic binder free carbon slurry onto F-doped tin oxide conducting glass. The carbon slurry is prepared by ball-milling a dispersion of activated carbon in aqueous SnCl₄ solution. During ball-milling, SnCl₄ hydrolyzes and transforms into stannic acid gel, which acts as an inorganic “glue” to connect the carbon particles during film preparation. Dye-sensitized solar cells employing this carbon electrode achieve efficiency as high as 6.1% which is comparable to that of the cells using sputtering Pt as counter electrode.     

Synthesis of PMMA‐b‐PBA block copolymer in homogeneous and miniemulsion systems by DPE controlled radical polymerization

In this research, poly(methyl methacrylate)‐b‐poly(butyl acrylate) (PMMA‐b‐PBA) block copolymers were prepared by 1,1‐diphenylethene (DPE) controlled radical polymerization in homogeneous and miniemulsion systems. First, monomer methyl methacrylate (MMA), initiator 2,2′‐azobisisobutyronitrile (AIBN) and a control agent DPE were bulk polymerized to form the DPE‐containing PMMA macroinitiator. Then the DPE‐containing PMMA was heated in the presence of a second monomer BA, the block copolymer was synthesized successfully. The effects of solvent and polymerization methods (homogeneous polymerization or miniemulsion polymerization) on the reaction rate, controlled living character, molecular weight (M_n) and molecular weight distribution (PDI) of polymers throughout the polymerization were studied and discussed. The results showed that, increasing the amounts of solvent reduced the reaction rate and viscosity of the polymerization system. It allowed more activation–deactivation cycles to occur at a given conversion thus better controlled living character and narrower molecular weight distribution of polymers were demonstrated throughout the polymerization. Furthermore, the polymerization carried out in miniemulsion system exhibited higher reaction rate and better controlled living character than those in homogeneous system. It was attributed to the compartmentalization of growing radicals and the enhanced deactivation reaction of DPE controlled radical polymerization in miniemulsified droplets. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4435–4445, 2009     

Model‐based design and synthesis of gradient MMA/tBMA copolymers by computer‐programmed semibatch atom transfer radical copolymerization

Methyl methacrylate (MMA)/tert‐butyl methacrylate (tBMA) gradient copolymers having linear and hyperbolic composition profiles were synthesized. These special copolymer products were achieved via a model‐based computer‐controlled semibatch atom transfer radical copolymerization (ATRcoP) process. A simple ATRcoP model was developed based on the terminal model. The equilibrium constants in the ATRP of MMA and tBMA were estimated by the data correlation. The model was verified by batch experiments and was found to give good correlation for the polymerization rate, molecular weight, and copolymer composition data. The model coupled with a reactor model was then applied to the semibatch ATRcoP and was used to calculate comonomer feeding rates for the targeted gradient composition profiles. It was found that the experimental monomer conversion, molecular weight, and cumulative copolymer composition were in good agreement with their targeted theoretical values. The gradient copolymers had low polydispersities close to 1.1. This work demonstrated the feasibility of the model‐based semibatch ATRcoP in fine‐tuning gradient copolymer composition profiles. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 69–79, 2009     

Directly suspended droplet microextraction in a rotating vial

In this paper, a novel suspended droplet microextraction method was developed for the detection of trace of organic compounds in water samples. The process was executed in a rotating extraction vial without the use of a stir bar. A single drop of octan-1-ol placed on top of the water sample was used as the solvent. The droplet remained on top of the water sample as a thin layer with an expanding surface area during the extraction stage, while during the sampling stage, the droplet was collected and sampled by inserting a needle. The volume of the microdroplet used was 3 μL or less, to ensure high organic compound sensitivity. The microextraction experimental setup was simple, utilizing centrifugal forces and possesses the advantages of low cross-contaminant/interference and applicability to water samples apt to emulsification. Nitrobenzene was selected as a model organic compound, and samples were analyzed using gas chromatography (GC) or UV-vis spectrometry. Analysis of the microextraction method results showed a relative standard deviation (RSD) less than 3.82%.     

Structure elucidation and complete NMR spectral assignments of new furostanol glycosides from Solanum torvum

Two new furostanol glycosides, torvosides O (1) and P (2), were isolated from leaves of Solanum torvum. Their structures were completely and unambiguously assigned by one‐ and two‐dimensional NMR techniques (¹H NMR, ¹³C NMR, TOCSY, HSQC, ROESY and HMBC), ESI‐MS spectrometry and chemical methods. Copyright © 2009 John Wiley & Sons, Ltd.     

Improvement of Steroid Biotransformation with Hydroxypropyl-β-Cyclodextrin Induced Complexation

The inclusion complexes induced by cyclodextrins and its derivates have been shown previously to enhance the biotransformation of hydrophobic compounds. Using hydroxypropyl-β-cyclodextrin (HP-β-CD; 20% w/v), the water solubility of cortisone acetate increased from 0.039 to 7.382 g L⁻¹ at 32 °C. The solubilization effect of HP-β-CD was far superior to dimethylformamide (DMF) and ethanol. The dissolution rate also significantly increased in the presence of HP-β-CD. The enzymatic stability of Δ¹-dehydrogenase from Arthrobacter simplex TCCC 11037 was not influenced by the increasing concentrations of HP-β-CD contrary to the organic cosolvents which negatively influenced in the order DMF > ethanol. The activity inhibition effect caused by HP-β-CD was not so conspicuous as ethanol and DMF. Inactivation constants of ethanol, DMF, and HP-β-CD were 5.832, 4.541, and 1.216, respectively. The inactivation energy (E _a) was in the order of HP-β-CD (55.1 kJ mol⁻¹) > ethanol (39.9 kJ mol⁻¹) > DMF (37.1 kJ mol⁻¹).     

Geodesic ideal triangulations exist virtually

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability of peripheral subgroups.

     

GLOBAL SUPERCONVERGENCES OF THE DOMAIN DECOMPOSITION METHODS WITH NONMATCHING GRIDS

1. IlltroductionA nonconforming domain decomposition method with Lagrangian multipliers was proposedin [13]. The basic idea of this method is to deal with the nonconforming of nonmatching gridsby illtroducing the Lagrangian multipliers on interfaces of subdomains and its advalltages arethat it allows not only the incompatibility of the internal variables on the interface betweensubdomains, but also the discolltinuity of the boundary variables on the common venices ofsubdomains. Thus one can c…