Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C

Fast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

A new subspace iteration method for the algebraic Riccati equation

We consider the numerical solution of the continuous algebraic Riccati equation A*X + XA ? XFX + G = 0, with F = F*,G = G* of low rank and A large and sparse. We develop an algorithm for the low‐rank approximation of X by means of an invariant subspace iteration on a function of the associated Hamiltonian matrix. We show that the sought‐after approximation can be obtained by a low‐rank update, in the style of the well known Alternating Direction Implicit (ADI) iteration for the linear equation, from which the new method inherits many algebraic properties. Moreover, we establish new insightful matrix relations with emerging projection‐type methods, which will help increase our understanding of this latter class of solution strategies. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model

We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.     

有机半导体非平衡态HOMO和LUMO能量位移规律与OLED中“热激子”形成的唯象理解

以能斯特方程为基础, 通过分析电流密度与氧化还原物种活度变化, 即载流子浓度变化的关系, 计算出有机半导体材料电极电势的变化, 从而建立起有机半导体前线轨道, 即最高占据分子轨道(HOMO)能级和最低未被占据分子轨道(LUMO)能级相对于热力学平衡态的能量位移随电流密度变化的数学关系. 进而依据能级能量位移引起的能隙变化, 提出了有机电致发光显示器（OLED）中“热激子”的产生机制.     

Mixed Quantum Classical Reaction Rates based on the Phase Space Formulation of the Hierarchical Equations of Motion

In a previous work [J. Chem. Phys. 140 , 174105 (2014)], we have shown that a mixed quantum classical (MQC) rate theory can be derived to investigate the quantum tunneling effects in the proton transfer reactions. However, the method is based on the high temperature approximation of the hierarchical equation of motion (HEOM) with the Debye-Drude spectral density, and results in a multi-state Zusman type of equation. We now extend this theory to include quantum effects of the bath degrees of freedom. By writing the full HEOM into a multidimensional partial differential equation in phase space, we can define a new reaction coordinate, and the previous method can be generalized to the full quantum regime. The validity of the new method is demonstrated by using numerical examples, including the spin-Boson model, and the double well model for proton transfer reaction. The new method is found to resolve some key problems of the previous theory based on high temperature approximation, including possible numerical instability in long time simulation and wrong rate constant at low temperatures.     

Photo-Induced Ultrafast Electron Dynamics in Anatase and Rutile TiO2: Effects of Electron-Phonon Interaction

The photo-induced ultrafast electron dynamics in both anatase and rutile TiO\begin{document}$_{2}$\end{document} are investigated by using the Boltzmann transport equation with the explicit incorporation of electron-phonon scattering rates. All structural parameters required for dynamic simulations are obtained from ab initio calculations. The results show that although the longitudinal optical modes significantly affect the electron energy relaxation dynamics in both phases due to strong Fr?hlich-type couplings, the detailed relaxation mechanisms have obvious differences. In the case of a single band, the energy relaxation time in anatase is 24.0 fs, twice longer than 11.8 fs in rutile. This discrepancy is explained by the different diffusion distributions over the electronic Bloch states and different scattering contributions from acoustic modes in the two phases. As for the multiple-band situation involving the lowest six conduction bands, the predicted overall relaxation times are about 47 fs and 57 fs in anatase and rutile, respectively, very different from the case of the single band. The slower relaxation in rutile is attributed to the existence of multiple rate-controlled steps during the dynamic process. The present findings may be helpful to control the electron dynamics for designing efficient TiO\begin{document}$_{2}$\end{document}-based devices.     

Measurement and modeling of metoclopramide hydrochloride (anti-emetic drug) solubility in supercritical carbon dioxide

Knowledge of drug solubility data in supercritical carbon dioxide (SC-CO₂) is a fundamental step in producing nano and microparticles through supercritical fluid technology. In this work, for the first time, the solubility of metoclopramide hydrochloride (MCP) in SC-CO₂ was measured in pressure and temperature range of 12 to 27 MPa and 308 to 338 K, respectively. The results represented a range mole fractions of 0.15 × 10^-5 to 5.56 × 10^-5. To expand the application of the obtained data, six semi-empirical models and three models based on the Peng-Robinson equation of state (PR + VDW, PR + WS + Wilson and PR + MHV1 + COSMOSAC) with different mixing rules and various ways to describe intermolecular interactions were investigated. Furthermore, total enthalpy, sublimation enthalpy and solvation enthalpy relevant to MCP solvating in SC-CO₂ were estimated.     

An Easy Synthesis of Monofluorinated Derivatives of Pyrroles from β-Fluoro-β-Nitrostyrenes

The catalyst-free conjugate addition of pyrroles to β-Fluoro-β-nitrostyrenes was investigated. The reaction was found to proceed under solvent-free conditions to form 2-(2-Fluoro-2-nitro-1-arylethyl)-1H-pyrroles. The effectiveness of this approach was demonstrated through the preparation of a series of the target products in a quantitative yield. The kinetics of a conjugate addition of pyrrole was studied in detail to reveal the substituent effect and activation parameters of the reaction. The subsequent base-induced elimination of nitrous acid afforded a series of novel 2-(2-Fluoro-1-arylvinyl)-1H-pyrroles prepared in up to an 85% isolated yield. The two-step sequence herein proposed is an indispensable alternative to a direct reaction with elusive and unstable 1-Fluoroacetylenes.     

一种计算液接电势的新方法*

依据液接电势达稳态时通过边界层的净电荷为零这一思想,提出了一种计算液接电势的新方法。对于3类液接电势的计算,特别是Lewis-Sargent公式与Henderson方程的推导,思路清晰易懂,避免了过往液接电势计算方法存在的一些问题。本文所提出的方法能够为液接电势相关内容的教学提供借鉴。