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Numerical simulation of the efficiency of mixing in heterogeneous microchannels with patterned surface potentials

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Progress in Natural Science:Materials International 2006年第12期16卷 1322-1328页

作者： ZHANG Kai~1, LIN Jianzhong~ 1,2.** and LI Huijun~1(1. state key {2. of {2. power transmission and control, Zhejiang University, hangzhou 31002., china 2. china Jiliang University, hangzhou 310018, china) [a]state key {2. of {2. power transmission and control Zhejiang University Hanghou China [b]china Jiliang University Hangzhou China

The mixing of samples in heterogeneous microchannels with a periodically stepwise surface potential was analyzed numerically using the control volume method. The equations describing the wall potential and external potential were solved first to get the distribution of wall potential and external potential, respectively, then the momentum equation was solved to get the developed flow field. Finally, the mass transport equation was solved to get the concentration field. The simulation results show that the distribution of samples at the inlet of the microchannel determines its theoretical value of concentration, therefore, the pattern of the distribution of samples at the inlet and its corresponding velocity can be changed to get the desirable concentration of solute. The heterogeneous wall potential almost has no effect on the mixing of samples in two-inlet microfluidic devices. For three-inlet microfluidic devices, the comprehensive ability of transportation and mixing has an optimization when the ratio of periodic length of wall potential to the height of the microchannel is about 4.88. The above conclusions are helpful to the optimization of the design of microfluidic devices.

关键词： microchannel mixing efficiency electroosmosis numerical simulation.

Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems

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Acta Mechanica Sinica 2007年第4期23卷 437-444页

作者： Maolin Deng Weiqiu Zhu Department of Mechanics,state key {2. of {2. power transmission and control,Zhejiang University,hangzhou 31002.,china Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

Abstract A nonlinear stochastic optimal control strategy for minimizing the first-passage failure of quasi integrable Hamiltonian systems （multi-degree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations） is proposed. The equations of motion for a controlled quasi integrable Hamiltonian system are reduced to a set of averaged It6 stochastic differential equations by using the stochastic averaging method. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximization of reliability and mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The final dynamical programming equations for these control problems are determined and their relationships to the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are separately established. The conditional reliability function and the mean first-passage time of the controlled system are obtained by solving the final dynamical programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illustrate the application and effectiveness of the proposed control strategy.

关键词： Nonlinear stochastic system First-passage time Reliability Stochastic control Dynamical programming

Stochastic stability of quasi-integrable Hamiltonian systems with time delay by using Lyapunov function method

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Science china(Technological Sciences) 2010年第3期53卷 703-712页

作者： LING Quan 1,JIN XiaoLing 1 &HUANG ZhiLong 2.1 Department of Mechanics,Zhejiang University,hangzhou 31002.,{2. 2.state key laboratory of fluid power transmission and control,Zhejiang University,hangzhou 31002.,{2. 1. Department of Mechanics Zhejiang University Hangzhou 310027 China2. State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The asymptotic Lyapunov stability of one quasi-integrable Hamiltonian system with time-delayed feedback control is studied by using Lyapunov functions and stochastic averaging ***,a quasi-integrable Hamiltonian system with time-delayed feedback control subjected to Gaussian white noise excitation is approximated by a quasi-integrable Hamiltonian system without time ***,stochastic averaging method for quasi-integrable Hamiltonian system is used to reduce the dimension of the original system,and after that the Lyapunov function of the averaged It equation is taken as the optimal linear combination of the corresponding independent first integrals in ***,the stability of the system is determined by using the largest eigenvalue of the linearized *** examples are used to illustrate the proposed procedure and the effects of delayed time on the Lyapunov stability are discussed as well.

关键词： Lyapunov stability Lyapunov function time delay stochastic averaging

Exact stationary solutions independent of energy for strongly nonlinear stochastic systems of multiple degrees of freedom

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Science china(Technological Sciences) 2009年第8期52卷 2424-2431页

作者： HUANG ZhiLong1,2.& JIN XiaoLing1 1 Department of Mechanics, Zhejiang University, hangzhou 31002., china {2., Zhejiang University, hangzhou 31002., china Department of Mechanics Zhejiang University Hangzhou 310027 China The state key {2. of {2. power transmission and control Zhejiang University Hangzhou 310027 China

A new procedure is proposed to construct strongly nonlinear systems of multiple degrees of freedom subjected to parametric and/or external Gaussian white noises, whose exact stationary solutions are independent of energy. Firstly, the equivalent Fokker-Planck-Kolmogorov (FPK) equations are derived by using exterior differentiation. The main difference between the equivalent FPK equation and the original FPK equation lies in the additional arbitrary antisymmetric diffusion matrix. Then the exact stationary solutions and the structures of the original systems can be obtained by using the coefficients of antisymmetric diffusion matrix. The obtained exact stationary solutions, which are generally independent of energy, are for the most general class of strongly nonlinear stochastic systems multiple degrees of freedom (MDOF) so far, and some classes of the known ones dependent on energy belong to the special cases of them.

关键词： exact stationary solution nonlinear stochastic system equivalent system independent of energy

STRUCTURAL PARAMETERS CALIBRATION BY POSTURE MEASUREMENT ON PARALLEL 6-DOF PLATFORM

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Chinese Journal of Mechanical Engineering 2002年第4期15卷 334-338,343页

作者： Wu Jiangning Li Shilunstate key {2. of {2. power transmission and control, Zhejiang University,hangzhou 31002., china state key {2. of {2. power transmission and control Zhejiang University Hangzhou 310027 China

Some approaches to measure parallel 6-degree of freedom platform's posturestatically and to calibrate the platform's actual structural parameters by measuring a series of theplatform's varying postures are studied. In the case where high posture accuracy is requiredrelatively, to obtain the platform's actual structural parameters is very important. Threedimensions measurement with 2.theodolites are used to obtain the platform's postures statically andNewton iterative method is adopted to calibrate structural parameters. Some measures taken in themeasurement and the calibration are discussed in detail. And the experiment results of theplatform's posture control before and after the calibration are given. The results show that theplatform's posture control accuracy after the calibration is improved notably.

关键词： parallel 6-DOF platform theodolite posture measurement nonlinearequation group structural parameters calibration

STABILITY IN THE CIRCULAR PIPE FLOW OF FIBER SUSPENSIONS

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Journal of Hydrodynamics 2003年第2期15卷 12-18页

作者： You Zhen jiang, Lin Jian zhong Department of Mechanics, state key {2. of {2. power transmission and control, Zhejiang University, hangzhou 31002., china DepartmentofMechanics StateKeyLaboratoryofFluidPowerTransmissionandControlZhejiangUniversityHangzhou310027China

A linear stability analysis on the circular pipe flow of fiber suspensions ispresented. The fiber orientation tensors are used to describe the characteristics of theorientation dislribution of fibers. The constitutive equation for the fiber suspensions is set upand the modified Orr-Sommerfeld stability equation is derived. An improved finite difference methodwith high order accuracy is employed to solve the e-quation. The Newtonian pipe Poiseuille flowcorresponding to H = 0 is also analyzed for comparison. The results reveal that the fiber additiveswill enhance the flow stability, the degree of enhancement becomes high with the increases of theparameter H which accounts for the fiber resistance to the stretching along its axis. Fibersuspensions with large H can suppress the influence of high Reynolds number on the flow ***, fibers give a higher attenuation of the short waves of disturbance.

关键词： flow stability circular pipe flow fiber suspensions numerical simulation

Transport and deposition of nanoparticles in bend tube with circular cross-section

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Progress in Natural Science:Materials International 2009年第1期19卷 33-39页

作者： Peifeng Lin a,Jianzhong Lin a,b,a state key {2. of {2. power transmission and control,Zhejiang University,hangzhou 31002.,china b china Jiliang University,hangzhou 310018,china [a]state key {2. of {2. power transmission and control Zhejiang University Hangzhou 310027 China [b]China Jiliang University Hangzhou 310018 China

Transport and deposition of nanoparticles in bend tube with circular cross-section were simulated numerically for different Reynolds numbers and Dean numbers.A finite-volume code and the SIMPLE scheme were used to solve the *** results show that the distribution of nanoparticle concentration is symmetrical with respect to the top and bottom sides of the *** diameter of the nanoparticles has a weak effect on the distribution of nanoparticle *** maximum and minimum of the deposition enhancement factor occur near the outside and inside walls of the bend tube,*** higher the Reynolds number is,the shorter is the time for nanoparticle *** bend curvature radius has a slight effect on the deposition enhancement factor.

关键词： Nanoparticles Transport Deposition Numerical simulation

Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems

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Science china(Physics,Mechanics & Astronomy) 2010年第1期53卷 147-154页

作者： FENG Ju, ZHU WeiQiu & YING ZuGuang Department of Mechanics, state key {2. of {2. power transmission and control, Zhejiang University, hangzhou 31002., china 1. Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.

关键词： quasi-integrable Hamiltonian system partial observation stochastic optimal control

First passage failure of dynamical power systems under random perturbations

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Science china(Technological Sciences) 2010年第9期53卷 2495-2500页

作者： CHEN LinCong1 & ZHU WeiQiu2.1 College of Civil Engineering,Huaqiao University,Xiamen 36102.,china 2.Department of Mechanics,state {2. {2. of fluid power transmission and control,Zhejiang University,hangzhou 31002.,china 1. College of Civil Engineering Huaqiao University Xiamen 361021 China2. Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The first-passage problem of dynamical power system of a single-machine-infinite-bus (SMIB) system under random perturbations is ***,the stochastic averaging method for quasi non-integrable generalized Hamiltonian systems is applied to reduce the equations of the SMIB system under random perturbations to a set of averaged It ***,the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first passage time are established and solved numerically,***,the proposed method is verified by using the Monte Carlo simulation of the original system.

关键词： dynamical power system random perturbation stochastic averaging first passage failure