Symmetric boundary integral formulations for Helmholtz transmission problems

In this work we propose and analyze numerical methods for the approximation of the solution of Helmholtz transmission problems in two or three dimensions. This kind of problems arises in many applications related to scattering of acoustic, thermal and electromagnetic waves. Formulations based on boundary integral methods are powerful tools to deal with transmission problems in unbounded media. Different formulations using boundary integral equations can be found in the literature. We propose here new symmetric formulations based on a paper by Martin Costabel and Ernst P. Stephan (1985), that uses the Calderón projector for the interior and exterior problems to develop closed expressions for the interior and exterior Dirichlet-to-Neumann operators. These operators are then matched to obtain an integral system that is equivalent to the Helmholtz transmission problem and uses Cauchy data on the transmission boundary as unknowns. We show how to simplify the aspect and analysis of the method by employing an additional mortar unknown with respect to the ones used in the original paper, writing it in an appropriate way to devise Krylov type iterations based on the separate Dirichlet-to-Neumann operators.     

一类具有隔离的脉冲免疫接种SIQR传染病模型的全局动力学行为

建立了一类具有隔离和垂直传染的SIQR传染病模型,在脉冲免疫接种条件下,分析了其全局动力学行为.利用频闪映射,获得了无病周期解,给出了此周期解的全局稳定性分析.并获得了系统一致持续生存的条件.     

Interference of Data Transmission in Access and Backbone Networks by High-Power Sensor System

Currently, individual optical fibers are mostly used for each non-data application, which is very inefficient and uneconomical. Sharing a single fiber for multiple applications is a promising solution. However, in the case of a non-data application, the situation is much more complicated compared to data because of special application´s requirements. In laboratory setup, we performed a measurement with a standard G.652D optical fiber for analyzing possible interaction of stable frequency/accurate time transmission, 1.25/10Gbps data transmission (typical bitrates for access point-to-point networks), and high-power sensor signal for different channel spacing and different pulse duration of sensor signal.     

Sound transmission from stiffened double laminated composite plates

An analytical model is developed to investigate the sound transmission loss from orthogonally rib-stiffened double laminated composite plates structure under a plane sound wave excitation, in which first order shear deformation theory is presented for laminated composite plates. By using the space harmonic approach and virtual work principle, the sound transmission loss is described analytically. The validity and feasibility of the model are verified by comparing the present theoretical predictions with numerical results published previously. The influences of structure geometrical parameters on sound transmission loss are subsequently presented. Through numerical results, it can be concluded that the proposed analytical model is accurate and simple in solving the vibroacoustic behavior of an orthogonally rib-stiffened double laminated composite plates.     

Heavy‐Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial,and Bell's Formula Closely Approximates Multidimensional Tunneling at ≥250 K

Multidimensional tunneling calculations are carried out for 13 reactions, to test the scope of heavy‐atom tunneling in organic chemistry, and to check the accuracy of one‐dimensional tunneling models. The reactions include pericyclic, cycloaromatization, radical cyclization and ring opening, and S_N2. When compared at the temperatures that give the same effective rate constant of 3×10⁻⁵ s⁻¹, tunneling accounts for 25–95 % of the rate in 8 of the 13 reactions. Values of transmission coefficients predicted by Bell's formula, κ_Bell , agree well with multidimensional tunneling (canonical variational transition state theory with small curvature tunneling), κ_SCT. Mean unsigned deviations of κ_Bell vs. κ_SCT are 0.08, 0.04, 0.02 at 250, 300 and 400 K. This suggests that κ_Bell is a useful first choice for predicting transmission coefficients in heavy‐atom tunnelling.     

Pyrolysis synthesis of magnetic - and -MnO2 nanostructures and the polymorph discrimination

The concentration of the Mn(NO₃)₂ solution has significant influence on the morphologies and the phases of the MnO₂ products. A large number of ε- MnO₂ nanowires were prepared via a simple pyrolysis under lower reaction concentration. The nanowires have lengths up to tens of micrometers and diameters in the range of 20–100 nm. The β- MnO₂ nanobundles and nanoflowers were prepared by increasing the concentration of Mn(NO₃)₂ solution. The superparamagnetism of ε- MnO₂ nanowires and paramagnetism of β- MnO₂ nanoflowers indicate their potential applications in magnetic materials.     

Radiation damage in soft X-ray microscopy

The rates of chemical transformation by radiation damage of polystyrene (PS), poly(methyl methacrylate) (PMMA), and fibrinogen (Fg) in a X-ray photoemission electron microscope (X-PEEM) and in a scanning transmission X-ray microscope (STXM) have been measured quantitatively using synchrotron radiation. As part of the method of dose evaluation in X-PEEM, the characteristic (1/e) sampling depth of X-PEEM for polystyrene in the C 1s region was measured to be 4 ± 1 nm. Critical doses for chemical change as monitored by changes in the X-ray absorption spectra are 80 (12), 280 (40) and 1230 (180) MGy (1 MGy = 6.242*ρ eV/nm³, where ρ is the polymer density in g/cm³) at 300 eV photon energy for PMMA, Fg and PS, respectively. The critical dose for each material is comparable in X-PEEM and STXM and the values cited are thus the mean of the values determined by X-PEEM and STXM. C 1s, N 1s and O 1s spectroscopy of the damaged materials is used to gain insight into the chemical changes that soft X-rays induce in these materials.     

The influence of substrate surface roughness on microstrip transmission line loss using conventional analyses and length‐scale fractal analysis

Two components of conductor topography can impact conductor loss for signals in the GHz frequency range: conductor–ceramic interface roughness and conductor edge angle. This study is an experimental investigation of the influence of these conductor topographies on conductor loss in microstrip circuits produced by thick‐film technology. The aluminum nitride ceramic substrates have different surface roughnesses due to different surface finish processes. The substrate surfaces were characterized using conventional and length‐scale fractal analysis. The conductor–ceramic interface was measured with a contact profilometer. The conductor edge angle and conductor edge profile were measured optically. It was found that there is a direct correlation between conductor loss and conductor edge angle, whereas there is an inverse correlation between loss and substrate roughness or relative length of the conductor–ceramic interface. This is the opposite result to the conventional expectation of surface roughness effects on conductor loss. There is also a negative correlation between conductor edge angle and surface roughness or relative length. The loss behavior can be explained by the interaction of the conductor paste with the surfaces during processing. The paste tends to spread more on the smoother surfaces, and thus creates an elongated edge of diminishing cross‐section and a small edge angle. This leads to greater conductor loss. Copyright © 2009 John Wiley & Sons, Ltd.     

输电线路等效电阻的计算

本文通过对趋肤效应的分析 ,讨论了输电线路中的焦耳热 ,并给出其等效电阻的计算结果     

A Schr(o)idinger formulation research for light beam propagation

The wave equation of light beam propagation was written in the form of an axial-coordinate-dependent Schrdinger equation, and the expectation value of a dynamical variable, the trial function of variational approach and the ABCD law were discussed by use of quantum mechanics approach. In view of the evolution equations of expectation values of dynamical variables in the framework of quantum mechanics, the definition of a potential function representing the beam propagation stability and its universal formula with the quality factor, the universal formula of beam width and curvature radius for a paraxial beam and cylindrically symmetric non-paraxial beam, the general formula of second derivative of beam width with respect to the axial coordinate of beam for a paraxial beam, and the general criteria of the conservation of beam quality factor and the existence of a potential well of a potential function for a paraxial beam, were given or derived, respectively. Starting with the same trial function, the comparative research of our formulation with variational approach was done, which gave some further insight into the physical nature of a beam propagation parameters. The ABCD law of non-paraxial beam was discussed in terms of the definition of the non-paraxial expectation value of a dynamical variable for the first time. The applications to the media of constant second derivative of beam width with respect to the axial coordinate of a beam, square law media and the media of constant refractive index in the momentum representation were discussed, respectively.