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     

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.     

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.

     

A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations

We introduce two types of finite difference methods to compute the L-solution and the proper viscosity solution recently proposed by the second author for semi-discontinuous solutions to a class of Hamilton-Jacobi equations. By regarding the graph of the solution as the zero level curve of a continuous function in one dimension higher, we can treat the corresponding level set equation using the viscosity theory introduced by Crandall and Lions. However, we need to pay special attention both analytically and numerically to prevent the zero level curve from overturning so that it can be interpreted as the graph of a function. We demonstrate our Lax-Friedrichs type numerical methods for computing the L-solution using its original level set formulation. In addition, we couple our numerical methods with a singular diffusive term which is essential to computing solutions to a more general class of HJ equations that includes conservation laws. With this singular viscosity, our numerical methods do not require the divergence structure of equations and do apply to more general equations developing shocks other than conservation laws. These numerical methods are generalized to higher order accuracy using weighted ENO local Lax-Friedrichs methods as developed recently by Jiang and Peng. We verify that our numerical solutions approximate the proper viscosity solutions obtained by the second author in a recent Hokkaido University preprint. Finally, since the solution of scalar conservation law equations can be constructed using existing numerical techniques, we use it to verify that our numerical solution approximates the entropy solution.

     

A real options approach for entering the Internet securities trading businesses with start‐up time

This paper uses a real options approach to establish a new evaluation model under uncertainty of both the volume of Internet securities transactions and the total transaction volume of a securities firm. The proposed approach can assist securities firms in evaluating the optimal thresholds for entering the Internet securities trading business and withdrawing from the conventional securities trading business. This paper assumes that the annual number of Internet securities transactions and the total annual number of securities transactions both follow a geometric Brownian motion. Besides, this model considers a start‐up time to complete the entry project's procedure. Accordingly, a decision model based on the real options approach is introduced, and the closed form solutions for the optimal threshold values of the entry or withdrawal models are determined. The conclusions provide some valuable references to help strategic managers of securities firms in making decisions on entering the Internet securities trading business or withdrawing from the conventional trading business. Copyright © 2003 John Wiley & Sons, Ltd.