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.     

Molecular Dynamics in 1- and 2-D Confinement as Studied for the Case of Poly(Cis-1,4-Isoprene)

Broadband Dielectric Spectroscopy (BDS) is used to probe the molecular dynamics of Type A polymer, poly(cis-1,4-isoprene), when confined in the 1-dimensional (1D) exploring space of thin layers and the 2-dimensional (2D) constraining geometry of unidirectional anodic aluminum oxide (AAO) nanopores. For both cases, it was observed that the structural relaxation remains bulk-like in its mean relaxation rate, although the distribution of its relaxation times is broadened in 2D confinement. Furthermore, the fluctuation of the end-to-end vector is interrupted, with the 1D case being relatively less pronounced. By this clear-cut comparison, it is demonstrated that the effects of confinement on molecular dynamics depend, inter alia, on the dimensionality of the restricting space.     

Fluorescence quenching of naphthols by Cu2+ in micelles

Effect of the micelles of anionic, cationic and non-ionic surfactants on the fluorescence quenching of 1- and 2-naphthols has been studied in the presence of copper ion. The excited state lifetime, dynamic and static quenching constants for these systems have been determined. Fluorescence quenching in water and SDS micelle is due to the collision of the fluorophore with the quencher with a small static component. The negatively charged naphtholate ions in the excited state are quenched with significantly higher rates than the neutral naphthol molecules, which are located further inside the mesophase. CTAB micelle is less effective than the SDS micelle for fluorescence quenching. The effect of CTAB on water-assisted excited-state deprotonation has been investigated in the presence of ZnSO₄. For TX-100 micelle there is negligible quenching even at higher concentration of the quencher.     

Evaluation of defect induced surface heterogeneity in Metal-Organic Framework materials with alkali dopants employing adsorption isotherm modelling

In this article, an assessment of surface structural heterogeneity in porous metal organic framework (MOF) structure has been demonstrated by employing the methane and carbon-dioxide adsorption isotherms data. The virgin MIL-101-(Cr) MOF was synthesized by the hydrothermal method and defects were induced in the MOF structure by doping with various alkali (K, Na, Li) cations. The synthesized MOFs were characterized by XRD, SEM, EDX and BET measurement techniques. In order to understand the defect induced surface heterogeneity by alkali cation dopants, the surface energy distributions for CH₄ and CO₂ adsorptions on MOFs were measured by Dubinin – Astakhov model equation. The surface heterogeneity is mainly controlled by the limiting uptakes of adsorbates, the polarizability of adsorbates and the adsorbate-adsorbent interaction energy.     

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.     

Engineering shapes of active colloids for tunable dynamics

Active particles can autonomously propel and have the tendency to organize into high-order ensembles and phases that evolve and reconfigure. They have emerged as a focused subject in contemporary colloid science, holding great promise in advancing fields, such as cargo delivery, sensing, micromachinery and microrobotics, and materials science. Realization of the full potentials of active particles requires delicate control of their dynamics in propulsion and assembly, which is challenging due to the out-of-equilibrium nature of such systems. Recently, systematically engineered colloidal shapes have been exploited as an effective means to tune and even program the dynamic behaviors of active particles. Various anisotropic particles, with controlled geometries and possessing either homogeneous or heterogeneous composition, have been fabricated, regulating how particles actively propel, interact, and assemble under several chemical and physical stimuli. In this paper, we provide an overview of these progresses. We also briefly discuss our view on the future directions and challenges.     

Volatile surfactants: Characterization and areas of application

Amphiphilic aroma molecules, representatives of fragrance molecules, are introduced as dynamic volatile surfactants. Surface tension of their aqueous solutions proves to be a sensitive and revealing quantity, used for assessment of the adsorption-evaporation behavior both under equilibrium conditions and in regimes of no instantaneous equilibrium. Such volatile amphiphiles are characterized by fast adsorption from bulk solution at an air-water interface, on a timescale of tens of microseconds, and exhibit synergetic effect in mixtures with conventional micellar-forming surfactants. Their ability to evaporate from the interface on a time scale of minutes suggests their applications as “temporal” dynamic cosurfactants in technologies involving fast formation of new surfaces. Current challenges concern evaluation of specific material parameters of volatile aroma surfactants in order to enable their selection for targeted applications.