Investigation of the phase transition at the nematic liquid crystal-wall interface within nonextensivity

In this study, the nematic-isotropic phase transition is investigated for a sample in the shape of a slab of thickness d, using nonextensive formalism. The interaction potential is written as the sum of the direct interaction of a given nematic molecule with the substrate and of its incomplete interaction with the other nematic molecules due to the presence of the limiting surface. In this framework, we show the effects of the nonextensivity on the nematic-isotropic transition at the nematic-wall interface. The generalized model can shed light on the properties of nematic liquid crystal confined in small-scale structures.     

Cellular automata for the spreading of technologies in socio-economic systems

We introduce an agent-based model for the spreading of technological developments in socio-economic systems where the technology is mainly used for the collaboration/interaction of agents. Agents use products of different technologies to collaborate with each other which induce costs proportional to the difference of technological levels. Additional costs arise when technologies of different providers are used. Agents can adopt technologies and providers of their interacting partners in order to reduce their costs leading to microscopic rearrangements of the system. Analytical calculations and computer simulations revealed that starting from a random configuration of different technological levels a complex time evolution emerges where the spreading of advanced technologies and the overall technological progress of the system are determined by the amount of advantages more advanced technologies provide, and by the structure of the social environment of agents. We show that agents tend to form clusters of identical technological level with a power law size distribution. When technological progress arises, the spreading of technologies in the system can be described by extreme order statistics.     

对规范粒子极化矢量的一些讨论

对规范粒子的极化矢量做了较为系统的论述. 讨论内容包括极化矢量的具体形式和性质、求和规则和规范传播子之间的关系以及由其张成的投影算子的性质. 通过若干精选的例子, 进一步演示了计算牵涉规范粒子的过程时采用的基本方法和应当注意事项.     

Relationship between different approaches to derive weighting functions related to atmospheric remote sensing problems

The paper is devoted to the investigation of the relationship between different methods used to derive weighting functions required to solve numerous inverse problems related to the remote sensing of the Earth's atmosphere by means of scattered solar light observations. The first method commonly referred to as the forward-adjoint approach is based on a joint solution of the forward and adjoint radiative transfer equations and the second one requires the linearized forward radiative transfer equation to be solved. In the framework of the forward-adjoint method we consider two approaches commonly used to derive the weighting functions. These approaches are referenced as the “response function” and the “formal solution” techniques, respectively. We demonstrate here that the weighting functions derived employing the formal solution technique can also be obtained substituting the analytical representations for the direct forward and direct adjoint intensities into corresponding expressions obtained in the framework of the response function technique. The advantages and disadvantages of different techniques are discussed.     

Notes on Superadditivity of Wigner–Yanase–Dyson Information

The classical Fisher information is superadditive in the sense that the Fisher information of a bivariate probability density is always not less than the sum of those of the marginals. The longstanding conjecture concerning the superadditivity of the Wigner–Yanase–Dyson information is a quantum analogue of this property. It is remarkable that Hansen constructed a numerical counterexample to the quantum case (J. Stat. Phys. 126: 643–648, 2007). However, the requirement of superadditivity of an information-theoretic quantity such as the Wigner–Yanase–Dyson information seems so intuitive, it is desirable to identify conditions as general as possible such that the superadditivity holds. In this paper, we establish the superadditivity in several physically significant cases.     

A note on the disjunctive index of joined a-perfect graphs

In this paper we present a lower bound of the disjunctive rank of the facets describing the stable set polytope of joined a-perfect graphs. This class contains near-bipartite, t-perfect, h-perfect and complement of fuzzy interval graphs, among others. The stable set polytope of joined a-perfect graphs is described by means of full rank constraints of its node induced prime antiwebs. As a first step, we completely determine the disjunctive rank of all these constraints. Using this result we obtain a lower bound of the disjunctive index of joined a-perfect graphs and prove that this bound can be achieved. In addition, we completely determine the disjunctive index of every antiweb and observe that it does not always coincide with the disjunctive rank of its full rank constraint.     

On the efficient application of weighted essentially nonoscillatory scheme

In this paper, the efficient application of high‐order weighted essentially nonoscillatory (WENO) reconstruction to the subsonic and transonic engineering problems is studied. On the basis of the physical considerations, two techniques are proposed to enhance the accuracy and efficiency of the WENO reconstruction. First, it is observed that the WENO scheme using characteristic variable has better accuracy and convergence speed than the scheme using primitive variable. For engineering problems with shock of moderate amplitude, on the basis of the Rankine–Hugoniot conditions, a simplified characteristic‐variable‐based WENO is developed. The simplified version significantly reduces the cost overhead without sacrificing the shock‐capturing capability. Second, in this work, it is found for viscous case that it is better to include the viscous effect. On the basis of a simple analysis, the viscous correction to the parameter ε in the WENO reconstruction is proposed. Numerical results indicate, with the proposed simplified characteristic‐variable‐based reconstruction and the viscous correction, that the nonlinear WENO interpolation is sharply activated in the region of shock jump, whereas in the shockless area, the WENO interpolation weights are tuned towards the designed optimal value for better accuracy. Compared with the original characteristic‐variable‐based WENO, the current implementation has similar accuracy and reduced cost. At the same time, compared with the primitive variable‐based WENO, better accuracy and convergence speed are obtained at marginal cost overhead. Several practical cases are calculated to demonstrate the accuracy and efficiency of the current methodology. Copyright © 2012 John Wiley & Sons, Ltd.     

Convergence of mann iteration processes for nonexpansive operators in equi-connected metric spaces

The paper deals with various conditions implying the convergence of a Mann type iteration process constructed for a non-expansive operator in an equi-connected space (i. e. metric space equipped with a connecting function; so the iterates are taken along certain curves). Coefficients of the iterates do not have to be separated from 0 or 1. 1].     

Correlation of charge transport with structural order in highly ordered melt‐crystallized poly(3‐hexylthiophene) thin films

A series of well‐defined poly(3‐hexylthiophene)s (P3HT) of different molecular weight (MW) and high regioregularity was investigated for charge transport properties in as‐cast and melt‐crystallized films. The semicrystalline structure of the P3HT was characterized by X‐ray scattering and Atomic force microscopy. Crystallization by cooling from the melt led to a substantial increase in crystallinity and a stronger alignment of the crystals in comparison to as‐cast films. The increase in crystallinity went along with an increase in hole mobility of up to an order of magnitude as measured by the space charge limited current method. Additionally, the hole mobility depended on the long period of P3HT lamellae and consequently on the MW. In compliance with the long period, the charge carrier mobility first increased with the MW before decreasing again at the onset of chain folding. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 943–951