Schloegl’s Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis

Schloegl’s second model for autocatalysis on a hypercubic lattice of dimension d≥2 involves: (i) spontaneous annihilation of particles at lattice sites with rate p; and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of diagonal pairs of particles on neighboring sites. Kinetic Monte Carlo simulations for a d=3 cubic lattice reveal a discontinuous transition from a populated state to a vacuum state as p increases above p=p _e . However, stationary points, p=p _eq (≤p _e ), for planar interfaces separating these states depend on interface orientation. Our focus is on analysis of interface dynamics via discrete reaction-diffusion equations (dRDE’s) obtained from mean-field type approximations to the exact master equations for spatially inhomogeneous states. These dRDE can display propagation failure absent due to fluctuations in the stochastic model. However, accounting for this anomaly, dRDE analysis elucidates exact behavior with quantitative accuracy for higher-level approximations.     

Intensity and spatial correlation properties of tightly focused partially coherent radially polarized vortex beams

By expanding the Debye theory into the tight focusing of partially coherent field, the intensity and spatial correlation properties of partially coherent radially polarized vortex beams are studied. Expressions are derived for the intensity distribution and the spectral degree of coherence in the focal region. It is found that the intensity and the transverse and longitudinal coherence degrees in the focal region change with the variation of the topological charge and coherence length of the vortex beam. In addition, the degree of coherence is shown to exhibit phase singularities.     

Parallel characteristic finite element method for time‐dependent convection–diffusion problem

Based on the overlapping‐domain decomposition and parallel subspace correction method, a new parallel algorithm is established for solving time‐dependent convection–diffusion problem with characteristic finite element scheme. The algorithm is fully parallel. We analyze the convergence of this algorithm, and study the dependence of the convergent rate on the spacial mesh size, time increment, iteration times and sub‐domains overlapping degree. Both theoretical analysis and numerical results suggest that only one or two iterations are needed to reach to optimal accuracy at each time step. Copyright © 2010 John Wiley & Sons, Ltd.     

Some sufficient conditions for tunnel numbers of connected sum of two knots not to go down

In this paper, we show the following result: Let K _i be a knot in a closed orientable 3-manifold M _i such that (M _i ,K _i ) is not homeomorphic to (S ₂ ×S ₁, x ₀ ×S ₁), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K _i ) is less than the difference of one and twice of the tunnel number of K _i . Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive.     

Morita contexts and Galois theory for weak Hopf comodulelike algebras

We investigate the Morita context and graded cases for weak group corings and derive some equivalent conditions for μ to be surjective. Furthermore, we develop Galois theory for weak group corings. As an application, we give Galois theory for comodulelike algebras over a weak Hopf group coalgebra.     

Some further <Emphasis Type="Italic">q</Emphasis>-series identities related to divisor functions

We give new generalizations of some q-series identities of Dilcher and Prodinger related to divisor functions. Some interesting special cases are also deduced, including an identity related to overpartitions studied by Corteel and Lovejoy.     

关于Parseval框架小波的刻画

In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜det A｜ = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.     

Red top-emitting organic light-emitting device with improved efficiency and saturated color

In this work, characteristics of microcavity top-emitting red organic light-emitting device (TEROLED) having metallic electrodes had been examined. The TEOLED shows the higher efficiency in comparison with that of the bottom OLED. However, color variation with the increasing view angles is also observed. For the purpose of diminishing the blue-shift of resonant wavelength (RW) in the device with increasing view angle, the effect of out-coupling layer on the emission properties of the TEOLED is discussed in detail. Finally, the out-coupling layer was introduced in theory without sacrificing the efficiency through precise optical simulation.     

Experimental investigation of a modified Beckmann-Kirchhoff scattering theory for the in-process optical measurement of surface quality

An experimental investigation of a modified Beckmann-Kirchhoff scattering theory applied in an in-process optical measurement of surface quality is described. The proposed theory describes the scattered light intensity distribution from a surface with the additional layers, and can be employed to analyze the surface characteristics in in-process measurement. Based on light scattering principle and machine vision method, the surface roughness is extracted to testify the correction of the modified Beckmann-Kirchhoff scattering theory. The experimental apparatus consists of a collimated laser diode, a beam splitter, a screen, a measuring lens and a camera. Test specimens with different surface roughness are studied. The results obtained demonstrate the feasibility of in-process optical measurement of surface quality using the modified model.     

Ag-mediated charge transfer from electron-doped SrTiO3 to CO and NO: A first-principles study

Ag-mediated charge transfer from electron-doped SrTiO₃ to molecules CO and NO has been studied through the first-principles calculations based on density functional theory (DFT). Evaluation of Fukui functions indicates that Ag atom on SrTiO₃ (001) surface is presented as an active reduction and oxidation site. It shows that Ag prefers to mediate the charge transfer from electronically excited SrTiO₃ to target species. It illustrates that electron initially transfers from electron-doped SrTiO₃ to Ag, i.e., Ag is negatively charged. Interfacial charge transfer induces dipole moment and changes the surface work function. SrO-termination of SrTiO₃ (001) surface has weak activity to CO and NO while CO and NO can be strongly adsorbed on the negatively charged Ag atom. Negatively charged Ag donates its charge to the molecules. Charge occupies the molecule π_2p* orbital, which is responsible for the activation of the molecular bonds. Evidence that deposited metals on photocatalyst surface can efficiently separate the photogenerated electron-hole pairs has been addressed in this study.