Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.     

The area within a curve

The area of a simple closed convex curve can be estimated in terms of the number of points of a square lattice that lie within the curve. We obtain the usual error bound without integration using a form of the Hardy—Littlewood—Ramanujan circle method, and also present simple estimates for the mean square error.     

Lp径向Blaschke-Minkowski同态的Lp对偶几何表面积

2006年，Schuster提出了径向Blaschke-Minkowski同态的概念.随后，汪卫等人将其推广到L_p径向Blaschke-Minkowski同态.本文结合L_p对偶几何表面积，建立了L_p径向Blaschke-Minkowski同态的若干不等式，包括Brunn-Minkowski型不等式和单调不等式.并给出了L_p径向Blaschke-Minkowski同态的Busemann-Petty问题的肯定和否定形式.     

Interfacial change on morphological transitions in styrene-isoprene diblock copolymer

The specific interfacial area (S/V) and interfacial thickness in each microstructure of styrene-isoprene diblock copolymer were estimated by analyzing the deviations from Porod’s law. The thermally induced phase transitions proceeded from lamellae (L) to hexagonally ordered cylinder (HEX), via hexagonally perforated layer (HPL) and gyroid (G). The S/V ratio increased stepwise at the order-order transition (OOT) from L to HEX, via HPL and G. The S/V data can be utilized for OOT determination.     

The affine Plateau problem

In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.

     

Quantitative surface analysis performed with an imaging photoelectron spectrometer

The paper gives an outline of the basic principle of our imaging technique for XPS. The advantage of the concept is its excellent applicability to quantitative pixel information. This idea is verified by two examples which are representative for routine problems in XPS. These are quantitative surface analysis and determination of overlayer thicknesses. A lateral resolution of at least 0.2 mm is achieved and thus a pixel size of 0.2 mm × 0.2 mm can be quantified automatically by means of numerical algorithms without need of reference samples.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday     

Geometrically nonlinear analysis with a 4-node membrane element formulated by the quadrilateral area coordinate method

Recently, a 4-node quadrilateral membrane element AGQ6-I, has been successfully developed for analysis of linear plane problems. Since this model is formulated by the quadrilateral area coordinate method (QACM), a new natural coordinate system for developing quadrilateral finite element models, it is much less sensitive to mesh distortion than other 4-node isoparametric elements and free of various locking problems that arise from irregular mesh geometries. In order to extend these advantages of QACM to nonlinear applications, the total Lagrangian (TL) formulations of element AGQ6-I was established in this paper, which is also the first time that a plane QACM element being applied in the implicit geometrically nonlinear analysis. Numerical examples of geometrically nonlinear analysis show that the presented formulations can prevent loss of accuracy in severely distorted meshes, and therefore, are superior to those of other 4-node isoparametric elements. The efficiency of QACM for developing simple, effective and reliable serendipity plane membrane elements in geometrically nonlinear analysis is demonstrated clearly.     

pyMolDyn: Identification,structure, and properties of cavities/vacancies in condensed matter and molecules

pyMolDyn is an interactive viewer of atomic systems defined in a unit cell and is particularly useful for crystalline and amorphous materials. It identifies and visualizes cavities (vacancies, voids) in simulation cells corresponding to all seven 3D Bravais lattices, makes no assumptions about cavity shapes, allows for atoms of different size, and locates the cavity centers (the centers of the largest spheres not including an atom center). We define three types of cavity and develop a method based on the split and merge algorithm to calculate all three. The visualization of the cavities uses the marching cubes algorithm. The program allows one to calculate and export pair distribution functions (between atoms and/or cavities), as well as bonding and dihedral angles, cavity volumes and surface areas, and measures of cavity shapes, including asphericity, acylindricity, and relative shape anisotropy. The open source Python program is based on GR framework and GR3 routines and can be used to generate high resolution graphics and videos. © 2016 Wiley Periodicals, Inc.     

Synthesis, characterization and hydrodesulfurization activity of silica-dispersed NiMoW trimetallic catalysts

Silica-dispersed NiMoW trimetallic hydrodesulfurization catalysts were prepared by deposition-precipitation method. For comparative purposes, bulk NiMoW trimetallic catalysts were obtained by co-precipitation. Silica was employed to disperse active metals for full utilization of active components and silica-dispersed NiMoW catalyst had high active metal content. BET analysis showed that silica-dispersed NiMoW trimetallic catalysts had a high surface area (165.1 m²/g) and pore volume (0.27 ml/g). Transmission electron microscopy results proved that active components were well dispersed. Hydrodesulfurization activity of silica-dispersed NiMoW catalysts was much higher than that of comparative catalysts and up to twice greater than those of commercial NiMo alumina-supported systems per gram of catalyst.     

UNIQUAC correlation of liquid–liquid equilibrium in systems involving ionic liquids: The DFT–PCM approach. Part II

In this work, new UNIQUAC structural parameters r and q for the ionic liquids were determined by quantum chemistry calculations performed with the Gaussian 03 and GAMESS 7.1 packages, including the density functional theory (DFT) for the optimization of the structures and the polarizable continuum method (PCM) for the calculation of molecular areas and volumes. Data liquid–liquid equilibrium (LLE) of 41 ternary systems involving 15 different ionic liquids, comprising 379 experimental tie-lines, was correlated by the UNIQUAC model for the activity coefficient. The results, expressed by deviations between experimental and calculated compositions, are very satisfactory, with deviation values about 1.93%.