反演在骨生长方程参数识别中的应用

基于BFGS算法,根据自行设计的动物实验,得到在不同应力环境中,快速生长期大鼠股骨生 长与重建过程中骨密度实测数据,采用反演数值方法,获取了骨生长方程中随时间变化的 生物参数B和K. 通过正演验证,表明所建立的基于BFGS算法的参数识别方法具有较好的 稳定性和较高的识别精度,能够反演出比较切合实际的生物参数数值. 研究表明,反问 题方法是解决生命现象不可测性和未知性问题的有效手段,把反演方法应用到骨生长与重建 等生命现象的研究中,可确定、修正预设的数学模式,为数值量化骨适应生物模型的建立提 供了一条可行的途径.     

蒙脱石细微结构对其水体系ζ电势的影响

The zeta-potential of montmorillonite-water colloid systems of different districts and distinct types are different. In this study the zeta-potentials were determined for montmorillonitewater colloid system of different districts and types. The relationship of octahedral(Fe~(3+)+Mg~(2+)) and the cell parameter b0 dimension of montmorillonites with the zeta-potential of montmo rillonite-water colloid systems were discussed.     

基于改进无迹卡尔曼滤波器算法的滞回模型参数识别研究

地震产生的周期荷载作用下,钢混桥墩结构表现出滞回行为。为描述滞回行为,研究者提出各类滞回模型,其中BWBN(Bouc-Wen-Baber-Noori)模型可以描述结构滞回行为的强度退化、刚度退化和捏拢效应等典型特征。此外,无迹卡尔曼滤波器UKF(unscented Kalman filter)算法是识别BWBN模型参数的高效方法,但当参数初始值与真实值的偏差过大及缺乏对系统的整体估计时,UKF算法识别过程受到局限。本文改进生成样本点规则,提出改进UKF算法。数值模拟结果表明,在无噪声条件下,改进UKF算法识别得到的参数估计值与准确值的误差平均为1.51%,最大误差为4%;在2%均方根RMS(root mean square)高斯白噪声条件下,误差平均为5.43%,最大误差为18%;在5%RMS高斯白噪声条件下,误差平均为8.9%,最大误差为26%和22%。改进UKF算法识别非线性滞回系统状态估计和BWBN模型参数更加准确和稳定。     

A three‐dimensional finite element model for the control of certain non‐linear bioreactors

This paper deals with the dynamics of non‐linear distributed parameter fixed‐bed bioreactors. The model consists of a pair of non‐linear partial differential (evolution) equations. The true spatially three‐dimensional situation is considered instead of the usual one‐dimensional approximation. This enables one to take into account the effects of flow profiles and the true location of the measurement transducer. The (output) evolution of the corresponding open‐loop control system is simulated. Furthermore, the associated closed‐loop system with respect to the relevant output function is considered. Especially, the asymptotic output tracking is found to be successful by applying the usual process based on the state feedback linearization. Copyright © 2000 John Wiley & Sons, Ltd.     

Preparation and properties of polyesters from diphenylmethane-4,4′-di(methylthiopropionic acid) and aliphatic diols

The new linear polyesters containing sulfur in the main chain were obtained by melt polycondensation of diphenylmethane-4,4′-di(methylthiopropionic acid) with ethanediol, 1,3-propanediol, 1,4-butanediol, 1,5-pentanediol, 1,6-hexanediol, 1,2-propanediol, 1,3-butanediol, and 2,2′-oxydiethanol. Low-molecular weights, low-softening temperatures and, very good solubility in organic solvents are their characteristics. The structure of all polyesters was determined by elemental analysis, FT-IR and ¹H-NMR spectroscopy, and x-ray diffraction analysis. The thermal behavior of these polymers was examined by differential thermal analysis (DTA), thermogravimetric analysis (TGA), and differential scanning calorimetry (DSC). The kinetics of polyesters formation by uncatalyzed melt polycondensation was studied in a model system: diphenylmethane-4,4′-di(methylthiopropionic acid) and 1,4-butanediol or 2,2′-oxydiethanol at 150, 160, and 170°C. Reaction rate constants (k₃) and activation parameters (ΔG^≠, ΔH^≠, ΔS^≠) from carboxyl group loss were determined using classical kinetic methods. © 1997 John Wiley & Sons, Inc.     

Study on ketalization reaction of poly(vinyl alcohol) by ketones. IX. Kinetic study on acetalization and ketalization reaction of 1,3-butanediol as a model compound for poly(vinyl alcohol)

A kinetic study was carried out on the acetalization reaction of 1,3-butanediol, as a model compound for poly(vinyl alcohol) (PVA), in water, under acidic conditions. Since these equilibrium constants of ketalization reaction of 1,3-butanediol and ethylene glycol are so small, the kinetic parameters were estimated from the hydrolysis reactions of the corresponding ketals. It was made clear that these reactions proceed in the reversible bimolecular reaction, and the heat of reaction and activation energy are nearly equal to that of PVA. The rate constants of hydrolysis reaction (k′s) of model compounds were calculated on the basis of value of acetone ketal, Hammett-Taft's equation log k′s/k′so – 0.54(n – 6) = ρ^*σ^* was established, and the value of ρ^* was obtained (3.60), which coincided with the value of PVA. Therefore, it was made clear that the hydrolysis reactions of acetals and ketals are electrophilic reaction (SE II reaction) and the step of rate determination is the formation of hemiacetal and hemiketal. The rate constants of hydrolysis reaction of 1,3-butanediol acetals and ketals were approximately 10–20 larger, and those of ethylene glycol were approximetly 50–80 larger except for ketals, and those of ethanol were roughly 2000–10,000 larger compared with that of high-molecular weight compound (PVA). It can be well explained that these differences in the rate constant depend on their entropy and the mobility of molecules. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 1719–1931, 1997     

Computation of the stabilization parameter for the finite element solution of advective–diffusive problems

In a previous paper a general procedure for deriving stabilized finite element schemes for advective type problems based on invoking higher order balance laws over finite size domains was presented. This provides an expression for the element stabilization parameter in terms of the solution residual and its first derivatives in a kind of iterative or adaptative manner. Details of the application of this procedure to 1D and 2D advective–diffusive problems are given. Some examples of applications showing the potential of the new approach are presented. © 1997 John Wiley & Sons, Ltd.     

Polyesters containing sulfur. VI. Synthesis and characterization of polyesters from naphthalene-1,4- or naphthalene-1,5-bis(methylthioacetic acid) and aliphatic diols

Two series of new linear polyesters containing sulfur in the main chain were obtained by melt polycondensation of naphthalene-1,4-bis(methylthioacetic acid) (N-1,4-BMTAA) or naphthalene-1,5-bis(methylthioacetic acid) (N-1,5-BMTAA) with some aliphatic diols using a 0.05 molar excess of diol. Softening temperatures ranging from 55 to 130°C, reduced viscosities in the range of 0.15–0.39 dL/g, and low-molecular weights were their characteristic. The structure and thermal properties of all polyesters were examined by using elemental analysis, FT-IR and ¹H-NMR spectroscopy, X-ray diffraction analysis, differential thermal analysis (DTA), thermogravimetric analysis (TGA), and differential scanning calorymetry (DSC). The kinetics of polyester formation by uncatalyzed melt polycondensation was studied in a model system: N-1,4-BMTAA or N-1,5-BMTAA and 2,2′-oxydiethanol (ODE) at 150, 160, and 170°C. Reaction rate constants (k₃) and activation parameters (ΔG^‡, ΔH^‡, ΔS^‡) from carboxyl group loss were determined using classical kinetic methods. Hydroxyl-terminated polyesters derived from 1,4-butanediol, 1,5-pentanediol, and 1,6-hexanediol were used for preparation of the polyurethanes by melt polyaddition with hexamethylene diisocyanate (HDI). They were characterized by reduced viscosity, FT-IR spectroscopy, X-ray diffraction analysis, TGA, DSC, polarizing microscope observation, and hardness and tensile properties. The resulting polyurethanes behave like high-elasticity thermoplastic elastomers, except the one derived from N-1,5-BMTAA and 1,6-hexanediol-based polyester. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. A Polym. Chem. 36: 2359–2369, 1998     

Construction of ternary phase diagrams in nonsolvent/solvent/PMMA systems

In this work, the ternary phase diagrams in three nonsolvent/solvent/PMMA systems (n-hexane/n-butyl acetate/PMMA, water/acetone/PMMA, and n-hexane/acetone/PMMA) were constructed by theoretical calculation and experimental measurement. Binodal curves were calculated by using the Flory–Huggins theory for three-component systems and measured by titrating the PMMA solution with nonsolvent until the onset of turbidity. By using concentration-dependent nonsolvent/solvent and solvent/PMMA interaction parameters and constant nonsolvent/PMMA interaction parameters, good agreement has been obtained between the calculation and the measurement. The values of nonsolvent/solvent interaction parameters were taken from the literature sources, and the values of solvent/PMMA and nonsolvent/PMMA interaction parameters were measured by vapor sorption and swelling equilibrium, respectively. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 607–615, 1998     

Swelling of polyacrylamide gels in polyacrylamide solutions

Swelling behavior of polyacrylamide (PAAm) and polyacrylamide-co-polyacrylic acid (PAAm-co-PAAc) gels was investigated in aqueous solutions of monodisperse PAAms with molecular weights (M_w) ranging from 1.5 × 10³ to 5 × 10⁶ g/mol. The volume of the gels decreases as the PAAm concentration in the external solution increases. This decrease becomes more pronounced as the molecular weight of PAAm increases. The classical Flory–Huggins (FH) theory correctly predicts the swelling behavior of nonionic PAAm gels in PAAm solutions. The polymer–polymer interaction parameter χ₂₃ was found to decrease as the molecular weight of PAAm increases. The swelling behavior of PAAm-co-PAAc gels in PAAm solutions deviates from the predictions of the FH theory. This is probably due to the change of the ionization degree of AAc units depending on the polymer concentration in the external solution. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1313–1320, 1998