On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ⁻¹. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx). Received: 30 June 2000 / Accepted: 25 June 2001     

基于Jiles-Atherton理论的铁磁材料塑性变形磁化模型修正

Jiles-Atherton(J-A)模型在磁化建模领域应用广泛,但不同文献给出的J-A模型并不一致,致使采用不同表达式建立的塑性变形磁化模型存在多种版本,其正确性难以甄别.通过对无磁滞磁化方程、能量守恒方程和等效磁场强度方程的梳理与比较,发现原有模型中存在将磁化强度和无磁滞磁化强度混用、将不可逆磁化能量等效于全部的磁化能量、等效磁场强度中应力磁化项界定不清等问题.在此基础上,对上述方程进行了修正,推导了基于J-A模型的塑性变形磁化修正模型.将修正模型计算结果与原模型计算结果、相关文献中的试验结果进行对比,结果表明:与原有计算模型相比,修正模型计算结果的饱和磁化强度和剩余磁化强度随塑性变形增加而减小,矫顽力随塑性变形增大而增大,达到饱和磁化强度时的外磁场强度随塑性变形增大而增大的趋势有所减弱,更符合试验结果,可更准确地反映塑性变形对材料磁化的影响.     

Existence and uniqueness of stabilized propagating wave segments in wave front interaction model

Recent experimental studies of photosensitive Belousov–Zhabotinskii reaction have revealed the existence of propagating wave segments. The propagating wave segments are unstable, but can be stabilized by using a feedback control to continually adjust the excitability of the medium. Experimental studies also indicate that the locus of the size of a stabilized wave segment as a function of the excitability of the medium gives the excitability boundary for the existence of 2D wave patterns with free ends in excitable media. To study the properties of this boundary curve, we use the wave front interaction model proposed by Zykov and Showalter. This is equivalent to study a first order system of three ordinary differential equations which includes a singular nonlinearity. Using two different reduced first order systems of two ordinary differential equations, we first show the existence of wave segments for any given propagating velocity. Then the wave profiles can be classified into two types, namely, convex and non-convex types. More precisely, when the normalized propagating velocity is small, we show that the wave profile is of convex type, while the wave profile is of non-convex type when the normalized velocity is close to 1.     

Optimization of microcrystalline silicon thin film solar cell isolation processing parameters using ultraviolet laser

This study used ultraviolet laser to perform the microcrystalline silicon thin film solar cell isolation scribing process, and applied the Taguchi method and an L₁₈ orthogonal array to plan the experiment. The isolation scribing materials included ZnO:Al, AZO transparent conductive film with a thickness of 200 nm, microcrystalline silicon thin film at 38% crystallinity and of thickness of 500 nm, and the aluminum back contact layer with a thickness of 300 nm. The main objective was to ensure the success of isolation scribing. After laser scribing isolation, using the minimum scribing line width, the flattest trough bottom, and the minimum processing edge surface bumps as the quality characteristics, this study performed main effect analysis and applied the ANOVA (analysis of variance) theory of the Taguchi method to identify the single quality optimal parameter. It then employed the hierarchical structure of the AHP (analytic hierarchy process) theory to establish the positive contrast matrix. After consistency verification, global weight calculation, and priority sequencing, the optimal multi-attribute parameters were obtained. Finally, the experimental results were verified by a Taguchi confirmation experiment and confidence interval calculation. The minimum scribing line width of AZO (200 nm) was 45.6 μm, the minimum scribing line width of the microcrystalline silicon (at 38% crystallinity) was 50.63 μm and the minimum line width of the aluminum thin film (300 nm) was 30.96 μm. The confirmation experiment results were within the 95% confidence interval, verifying that using ultraviolet laser in the isolation scribing process for microcrystalline silicon thin film solar cell has high reproducibility.     

Frenkel-Kontorova模型中基底势振动的影响

基于一维Frenkel-Kontorova模型, 研究了振动的基底势对系统纳米摩擦现象的影响. 分别在相邻原子间的距离与周期势场的周期比为不公度(incommensurate)、可公度(commensurate)两种情形下, 探讨了基底势振动的振幅和频率对滞回现象(hysteresis)、最大静摩擦力以及超滑现象的作用机理. 两种情形下, 固定频率, 随着振幅的增大, 滞回区域的面积以及最大静摩擦力都将减小, 对于不同的频率, 减小的趋势不同. 系统甚至产生了超滑现象. 但当频率过大时, 振幅的改变不会影响滞回区域的面积以及最大静摩擦力的大小, 此时与基底不加振动时的情形一致; 当振幅固定, 随着频率的增大, 滞回区域的面积将增大, 对于不同振幅, 增大的趋势不同. 特别地, 对于某些固定的振幅, 最大静摩擦力随着振动频率的增大先逐步减小直至出现超滑现象, 再进一步增大频率, 最大静摩擦力又转而逐步增大. 这一现象类似于共振, 表明存在最佳的振动频率促进系统内所有原子的共同运动, 使得整个系统的最大静摩擦力几乎消失. 另外, 两种情形的区别是, 对于某些固定的频率(如ω= 0.5)和不同的小振幅, 不可公度情形往往具有相同的平均终止速度, 而可公度情形则不同, 表明相同前提下后者具有更复杂的动力学行为. 关键词： Frenkel-Kontorova模型 滞回 最大静摩擦力 超润滑     

Aggregation induced polyelectrolyte multilayer film containing cubic silsesquioxane nanoparticles

Polyelectrolyte multilayer (PEM) films offer a method to functionalize substrates with specific properties that enable the films to be used for a variety of purposes. Desirable qualities of PEM films can include mechanical strengths, ease of preparations, flexibility, and their abilities to have their properties tailored to suit a particular process. We present a simple method to fabricate a class of PEM films that incorporate cubic silsesquioxane nanoparticles (CSSQ). Through a spin self-assembly (SSA) process, a hybrid multilayered film with two-components, namely, poly(styrene sulfonate) (PSS) and octaammonium cubic silsesquioxane (CSSQ) nanoparticle have been fabricated. The formation of this multilayer film is further verified by ellipsometry, contact angle studies, and atomic force microscopy (AFM). The water contact angle and ellipsometric measurements exhibit that the (PSS/OA-CSSQ) films are deposited onto the substrate. The surface topography of the deposited bilayers of PSS/OA-CSSQ film appears to be uniformly distributed with extremely small granules but the film uniformity of the granular surface is diminished and clusters of granules are observed at above 5 bilayers due to the aggregation of the OA-CSSQ nanoparticles.     

Design and construction of a compact end-station at NSRRC for circular-dichroism spectra in the vacuum-ultraviolet region

A synchrotron‐radiation‐based circular‐dichroism end‐station has been implemented at beamline BL04B at the National Synchrotron Radiation Research Center (NSRRC) in Taiwan for biological research. The design and performance of this compact end‐station for measuring circular‐dichroism spectra in the vacuum‐ultraviolet region are described. The linearly polarized light from the beamline is converted to modulated circularly polarized light with a LiF photoelastic modulator to provide a usable wavelength region of 130–330 nm. The light spot at the sample position is 5 mm × 5 mm at a slit width of 300 µm and provides a flux greater than 1 × 10¹¹ photons s^?1 (0.1% bandwidth)^?1. A vacuum‐compatible cell made of two CaF₂ windows has a variable path length from 1.3 µm to 1 mm and a temperature range of 253–363 K. Measured CD spectra of (1S)‐(+)‐10‐camphorsulfonic acid and proteins demonstrated the ability of this system to extend the wavelength down to 172 nm in aqueous solution and 153 nm in hexafluoro‐2‐propanol.     

The structure and thermodynamics of binary microclusters: A Monte Carlo simulation

The Monte Carlo computer simulation technique of classical statistical mechanics is employed to determine the structure and thermodynamics of binary microclusters of Lennard-Jones atoms as a function of cluster size, composition and temperature. Further, amorphous microclusters are prepared by a Monte Carlo quench, and their structural properties are examined. The properties of interest include the internal energy, instantaneous “snapshot” pictures of the microcluster's atomic configuration, and the single-particle and pair distribution functions. The Lennard-Jones potential parameters are chosen to model Ar₁₃, Ar₇Kr₆, Ar₃₆Kr₁₉ and Ar₁₉Kr₃₆, as well as to crudely model the bimetallic clusters of Cu₁₉Ni₃₆, Cu₁₉Ru₃₆ and Cu₁₉Os₃₆. A large variety of interesting features associated with these systems are described.     

Asymptotic dynamics of nonlinear Schrödinger equations with many bound states

We consider a nonlinear Schrödinger equation with a bounded localized potential in . The linear Hamiltonian is assumed to have three or more bound states with the eigenvalues satisfying some resonance conditions. Suppose that the initial data is localized and small of order n in H¹, and that its ground state component is larger than n^3−ε with ε>0 small. We prove that the solution will converge locally to a nonlinear ground state as the time tends to infinity.     

estimate of a parabolic Monge-Ampère equation on

We consider a special type of parabolic Monge-Ampère equation on arising from convex hypersurfaces expansion in Euclidean spaces. We obtained a parabolic estimate of the support functions for the convex hypersurfaces assuming that we have already had a parabolic estimate.