Feasibility analysis of membrane reactors – discovery of reactive arheotropes

A feasibility analysis methodology adopted from reactive distillation is applied to membrane reactors. A model is formulated to depict the reactive liquid phase composition on the retentate side of a continuous type membrane reactor. The effects of both the chemical reaction kinetics and the membrane mass transfer kinetics on the feasible products are elucidated by means of retentate phase diagrams and bifurcation analysis. The proposed method can be applied to various membrane processes, independent of the specific structure of the membrane. Two quaternary reaction systems are considered to illustrate the methodology. In the first hypothetical system, it is shown how selective membranes can influence the sequence of effective volatilities which in turn affects the feasible products of the system. In the second example of practical importance, i.e. the heterogeneously catalysed synthesis of propyl acetate coupled with permeation through a porous polycarbonate membrane, the dusty gas model is applied to describe the component fluxes through the membrane. For the latter reaction system, the existence of reactive arheotrope is demonstrated. Arheotropes represent mass transfer controlled feasible products of membrane separation process.     

Feedback tuning of bifurcations

The present paper studies a feedback regulation problem that arises in at least two different biological applications. The feedback regulation problem under consideration may be interpreted as an adaptive control problem for tuning bifurcation parameters, and it has not been studied in the control literature. The goal of the paper is to formulate this problem and to present some preliminary results.     

Midplane-symmetry breaking in the flow between two counter-rotating disks

This paper considers the axisymmetric steady flow driven by exact counter rotation of two co-axial disks of finite radius. At the edges of the rotating disks one of three conditions is (typically) imposed: (i) zero velocity, corresponding to a stationary, impermeable, cylindrical shroud (ii) zero normal velocity and zero tangential fluid traction, corresponding to a (confined) free surface and (iii) an edge constraint that is consistent with a similarity solution of von Kármán form. The similarity solution is valid in an infinite geometry and possesses a pitchfork bifurcation that breaks the midplane symmetry at a critical Reynolds number. In this paper, similar bifurcations of the global (finite-domain) flow are sought and comparisons are made between the resulting bifurcation structure and that found for the similarity solution. The aim is to assess the validity of the nonlinear similarity solutions in finite domains and to explore the sensitivity of the solution structure to edge conditions that are implicitly neglected when assuming a self-similar flow. It is found that, whilst the symmetric similarity solution can be quantitatively useful for a range of boundary conditions, the bifurcated structure of the finite-domain flow is rather different for each boundary condition and bears little resemblance to the self-similar flow.     

离散动态系统及其应用（Ⅲ）─市场价格模型的数学分析

本文应用动力系统的定性分析方法，对离散市场价格模型作出全局分析，给出了关于离散市场价格系统的稳定性和分支结构的若干定理及其经济意义．     

Residue curve maps for reactive distillation systems with liquid-phase splitting

A model has been developed to study the effects of chemical kinetics on the residue curve maps (RCM) for reactive distillation systems with liquid phase splitting. In the model, chemical reaction can occur in both or only one of the two liquid phases. The heating policy V/V₀=H/H₀ is applied so that the kinetic effect can be described by a single parameter, the Damköhler number Da. The effects of reaction kinetics on pseudohomogeneous and heterogeneous mixtures have been compared. The properties of their RCMs are the same outside, but are fully different inside the liquid-liquid (L-L) region if they have different chemical equilibrium curves. Inside the L-L region, the chemical equilibrium curve coincides to a unique reactive liquid-liquid tie line in case that the pseudohomogeneous chemical equilibrium curve intersects with the L-L envelope. When the reaction occurs in only one of the two liquid phases, the residue curves inside the L-L region are strongly affected by the L-L envelope, especially at high Da. In the present paper, first an illustrative arbitrary reaction system, and then the reaction of cyclohexene with water to cyclohexanol are analysed with respect to their RCMs.     

Dynamic analysis of a novel time‐lag four‐dimensional fractional‐order financial system

In this paper, a novel four‐dimensional fractional‐order financial system (FFS) with time delay is presented. Unlike traditional bifurcation analysis of financial systems, the selection rules of two bifurcation points within the system are discussed. In addition, the motion state of the system in the vicinity of two bifurcation points are analyzed separately, such that the dynamic analysis of this novel nonlinear fourth‐dimensional FFS is more comprehensive. The detailed dynamical behaviors of this financial system, such as oscillation, stability, and bifurcation points, are deduced via rigorous mathematical analysis. Finally, some simulations are performed to verify the dynamic characteristics of the FFS around the two bifurcation points which satisfy the selection conditions of the bifurcation point.     

Runout effects in milling: Surface finish, surface location error, and stability

This paper investigates the effect of milling cutter teeth runout on surface topography, surface location error, and stability in end milling. Runout remains an important issue in machining because commercially-available cutter bodies often exhibit significant variation in the teeth/insert radial locations; therefore, the chip load on the individual cutting teeth varies periodically. This varying chip load influences the machining process and can lead to premature failure of the cutting edges. The effect of runout on cutting force and surface finish for proportional and non-proportional tooth spacing is isolated here by completing experiments on a precision milling machine with 0.1 μm positioning repeatability and 0.02 μm spindle error motion. Experimental tests are completed with different amounts of radial runout and the results are compared with a comprehensive time-domain simulation. After verification, the simulation is used to explore the relationships between runout, surface finish, stability, and surface location error. A new instability that occurs when harmonics of the runout frequency coincide with the dominant system natural frequency is identified.     

A numerical algorithm coupling a bifurcating indicator and a direct method for the computation of Hopf bifurcation points in fluid mechanics

This paper deals with the computation of Hopf bifurcation points in fluid mechanics. This computation is done by coupling a bifurcation indicator proposed recently (Cadou et al., 2006) [1] and a direct method (Jackson, 1987; Jepson, 1981) [2] and [3] which consists in solving an augmented system whose solutions are Hopf bifurcation points. The bifurcation indicator gives initial critical values (Reynolds number, Strouhal frequency) for the direct method iterations. Some classical numerical examples from fluid mechanics, in two dimensions, are studied to demonstrate the efficiency and the reliability of such an algorithm.     

一种自反馈细胞神经网络稳定性分析及在函数优化中的应用

提出一种具有暂态混沌的细胞神经网络,该网络是利用欧拉算法将模型的状态方程转化为离散形式并引入一项负的自反馈而形成的.由对单个神经元的仿真发现,该模型具有分叉和混沌的特性.在函数优化中,该网络首先经过一个倍周期倒分叉过程进行混沌搜索;然后进行类似Hopfield网络的梯度搜索.由于该网络利用了混沌搜索固有的随机性和轨道遍历性,因而具有较强的全局寻优的能力.最后通过2个函数优化的例子验证了该网络的有效性.     

Influence of Implicit Integration Scheme on Prediction of Shear Band Formation

Implicit integration schemes for elastoplastic constitutive equations have been developed in recent years as an alternative to explicit schemes. The consistent tangent constitutive matrix Dcon that results from implicit schemes makes the global stiffness matrix consistent with the implicit integration procedure and differs from the traditional continuum tangent constitutive matrix Dep that results from explicit schemes. Onset of strain localization and shear banding has been traditionally predicted using the continuum tangent constitutive matrix. It is shown that different criteria for onset of shear-band formation are obtained depending on whether Dcon or Dep is used. It is shown that shear band prediction using Dcon is step-size dependent, and that the use of Dcon influences the predicted onset of strain localization in frictional materials. An analytical equation for prediction of the onset of shear-band formation using Dcon for the Mohr–Coulomb model is developed, and a numerical example is presented.