Role of self-assembled surfactant structure on the spreading of oil on flat solid surfaces

Uniform spreading of oil on solid surfaces is important in many processes where proper lubrication is required and this can be controlled using surfactants. The role of oil–solid interfacial self-assembled surfactant structure (SASS) in oil spreading is examined in this study for the case of hexadecane-surfactant droplet spreading on a flat horizontal copper surface, with triphenyl phosphorothionate surfactants having varying chain lengths (0 to 9). It is shown that the frictional forces (F_SASS) as determined by the SASS regulate droplet spreading rate according to surfactant chain length; surfactants with longer chains led to higher reduction in the spreading rate. The extent of such forces, F_SASS, depends on the surfactant density of the evolving SASS, and specific configuration the evolving SASS exhibit as per the orientations of the surfactant chains therein. Thus, F_SASS = [k₁ + k_2(t)] Γ_δ(t), where Γ_δ(t) is the surfactant adsorption density of SASS at time ‘t’ during evolution, and, k₁ and k_2(t) are the force coefficients for Γ_δ(t) and orientations (as a function of spreading time) of the surfactant chains respectively. As a SASS evolves/grows along with adsorption of surfactants at the spreading induced fresh interface, the k₁Γ_δ(t) component of F_SASS increases and contributes to reduction in the net spreading force (S). With a decrease in the net spreading force, the existence of a cross-over period, during which the transition of the spatial dynamics of the chains from disordered to realignment/packing induced ordered orientation occurs, has been inferred from the F_SASS vs. chain length relationships. Such relationships also suggested that the rate of realignment/packing is increased progressively particularly due the realignment/packing induced decrease in the net spreading force. Therefore, the realignment process is a self-induced process, which spans a measurable period of time (several minutes), the cross-over period, during which the net spreading force decreases essentially due to such self-induced process.     

Properties of ε-value functions for a two person differential game

We consider the problem of approximate minimax for the Bolza problem of optimal control. Starting from the method of dynamic programming (Bellman) we define the ?-value function to be the approximation for the value function being a solution to the Hamilton–Jacobi equation.     

The duality property of the Discrete Fourier Transform based on Simpson's rule

The classical Discrete Fourier Transform (DFT) satisfies a duality property that transforms a discrete time signal to the frequency domain and back to the original domain. In doing so, the original signal is reversed to within a multiplicative factor, namely the dimension of the transformation matrix. In this paper, we prove that the DFT based on Simpson's method satisfies a similar property and illustrate its effect on a real discrete signal. The duality property is particularly useful in determining the components of the transformation matrix as well as components of its positive integral powers. Copyright © 2012 John Wiley & Sons, Ltd.     

变形谐振子势的能谱方程

讨论了3种变形谐振子势:左右两边不同参数的谐振子势、左边方形势加右边谐振子势和谐振子势中间加δ势中的能量本征态函数.这些函数都可以由厄米函数表示.由波函数及其一次导数在原点的衔接条件,得到了能谱方程.     

Liouville–Green (WKB) asymptotics for almost-diagonal linear second-order matrix difference equations

A Liouville–Green (or WKB) asymptotic approximation theory is developed for a class of almost-diagonal (‘asymptotically diagonal’) linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration.     

Generalized vector variational-like inequalities and nonsmooth vector optimization problems

In this article, we establish some relationships between a solution of generalized vector variational-like inequalities and an efficient solution or a weakly efficient solution to the nonsmooth vector optimization problem under the assumptions of pseudoinvexity or invariant pseudomonotonicity. Our results extend and improve the corresponding results in the literature.     

Separation and Analysis of o.p'-DDD and its Lipophilic Metabolite,O.P'-DDE,in Tissue,Faeces and Plasma

Abstract

An analytical procedure based on electron capture gas chromatography for the determination of o,p′-DDD, a drug used for the treatment of Cushing′s syndrome, is presented. Detection of a metabolite, identified as o,p′-DDE, is also described.     

Analysis of the multiple roots of the Lundberg fundamental equation in the PH (n) risk model

In the study of the Sparre Andersen risk model with phase‐type (n) inter‐claim times (PH (n) risk model), the distinct roots of the Lundberg fundamental equation in the right half of the complex plane and the linear independence of the eigenvectors related to the Lundberg matrix L_δ(s) play important roles. In this paper, we study the case where the Lundberg fundamental equation has multiple roots or the corresponding eigenvectors are linearly dependent in the PH (n) risk model. We show that the multiple roots of the Lundberg fundamental equation det[L_δ(s)] = 0 can be approximated by the distinct roots of the generalized Lundberg equation introduced in this paper and that the linearly dependent eigenvectors can be approximated by the corresponding linearly independent ones as well. Using this result we derive the expressions for the Gerber–Shiu penalty function. Two special cases of the generalized Erlang(n) risk model and a Coxian(3) risk model are discussed in detail, which illustrate the applicability of main results. Finally, we consider the PH(2) risk model and conclude that the roots of the Lundberg fundamental equation in the right half of the complex plane are distinct and that the corresponding eigenvectors are linearly independent. Copyright © 2011 John Wiley & Sons, Ltd.     

一类非光滑Chua’s电路的同步控制

本文研究两个带x|x|非线性项的Chua’s电路的全局指数同步和全局同步的控制问题.证明这两个系统在未加控制时不可能同步,但设计不同的控制器可以实现这两个系统的全局指数同步和全局同步.