Simulation of a 2-site Langmuir model for characterizing the sorption capacity of Cs and Se in crushed mudrock under various ionic strength effects

The sorption capacity of cesium (Cs) and selenium (Se) in crushed mudrock was demonstrated in this study through a 2-site Langmuir model. To employ such a numerical analysis, batch tests were applied in this study in synthetic seawater and groundwater with sorption/desorption kinetic experiments (time-dependent) and different concentrations (10^?2–10^?7 M). The 2-site sorption models, which correspond to two rate constants (λ ₁ and λ ₂), might be more adequate than 1-site sorption models in characterizing Cs and Se sorption/desorption according to the least square errors between the numerical analysis and the results of the batch tests. The fitting results showed that a 2-site Langmuir model is capable of appropriately describing Cs and Se sorption in mudrock. Consequently, the sorption capacity was calculated at about 0.06 mol/kg for Cs and at 0.015 mol/kg for Se.     

Blue laser lithography for making antireflective submicron structures on silicon

The application of blue laser lithography for creating antireflective submicron structures on a crystalline silicon substrate was evaluated. The assembled blue laser lithography system was obtained by modifying a commercial blue laser optical pickup head and consisting of a 405-nm-wavelength blue laser and a 0.85-numerical-aperture objective lens. Si substrates were patterned with submicron column patterns of various periods and aspect ratios by blue laser lithography using a sputtered Ge-Sb-Sn-O layer as a resist. The reflectance of the patterned Si substrate decreased to 3% on average in the 300–1000 nm wavelength range, with a low sensitivity to the angle of incident light. Such patterned substrates showed potential for application in crystalline Si solar cells.     

The synthesis,structure, magnetic and luminescent properties of a new tetranuclear dysprosium (III) cluster

The synthesis and characterization of [Dy₄(dhampH₃)₄(NO₃)₂](NO₃)₂ (1), a new tetranuclear dysprosium (III) complex, is described. The compound was characterized by its X-ray structure, magnetic properties as well as the luminescent spectra. The compound crystallizes in a P1? space group with a zig-zag linear form of geometry. The ac magnetic susceptibilities of the molecule indicate that it is a magnetic molecule with a slow magnetization relaxation. The molecule also exhibits an emission spectrum that was confirmed to be ligand based. These results indicate that this molecule has both a slow magnetization relaxation (that could be potentially a SMM) and luminescent properties.     

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.     

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.     

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.

     

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.

     

Molecular dynamical study of the energy relaxation processes after heating the vibrational degree of freedom in a diatomic molecular crystal

Energy relaxation processes initiated by sudden heating of the vibrational degree of freedom were studied with molecular dynamical method. A unit cell of bee structure containing 128 diatomic molecules with periodic boundary conditions was considered. Compound Morse potential was assumed as the atom-atom interactions. It was found that the logarithra of the equilibration time depends linearly upon a factorf ₂₁ which is proportional to the frequency ratio of the intra- and inter-molecular vibrations. The project is supported by the National Natural Science Foundation of China.     

Free Molecular Flow with Boundary Effect

We study the dissipative effect of the boundary condition in the kinetic theory. We focus our study on the simplest situation of the free molecular flow with diffuse reflection boundary condition and constant boundary temperature, T _*. The geometry is also chosen to be the simplest ones, a bounded symmetric domain in ${\mathbb{R}^d}$ : an interval for d = 1, a disk for d = 2, and a ball for d = 3. It is shown that the solution converges to the global Maxwellian with the given boundary temperature T _*. We obtain the optimal convergence rates of (t + 1)^?d . The stochastic formulation of Shih-Hsien Yu is refined and generalized for our analysis.