Mathematical and experimental investigation of the self-propagating high-temperature synthesis (SHS) of TiAl3 and Ni3Al intermetallic compounds

One-dimensional mathematical modeling was used to describe the self-propagating high-temperature synthesis (SHS) process for preparing TiAl₃ and Ni₃Al intermetallics. The kinetic parameters (activation energies and pre-exponential factors) for the two compounds were obtained by matching experimental measurement and the numerical solution. The results thus obtained were compared with rate parameters obtained using different methods. The activation energy was 483 and 283 kJ mol^?1 for the formation of TiAl₃ and Ni₃Al, respectively. The temperature profiles calculated using the mathematical model were compared with experimental measurements for both aluminides which indicated reasonable agreement. Fine particle size and moderate preheating increase the SHS rates.     

Numerical fluorescence correlation spectroscopy for the analysis of molecular dynamics under nonstandard conditions

The suitability of mathematical models used to extract kinetic information from correlated data constitutes a significant issue in fluorescence correlation spectroscopy (FCS). Standard FCS equations are derived from a simple Gaussian approximation of the optical detection volume, but some investigations have suggested this traditional practice can lead to inaccurate and misleading conclusions under many experimental circumstances, particularly those encountered in one-photon confocal measurements. Furthermore, analytical models cannot be derived for all measurement scenarios. We describe a novel numerical approach to FCS that circumvents conventional analytical models, enabling meaningful analyses even under extraordinarily unusual measurement conditions. Numerical fluorescence correlation spectroscopy (NFCS) involves quantitatively matching experimental correlation curves with synthetic curves generated via diffusion simulation or direct calculation based on an experimentally determined 3D map of the detection volume. Model parameters are adjusted iteratively to minimize the residual differences between synthetic and experimental correlation curves. In order to reduce analysis time, we distribute calculations across a network of processors. As an example of this new approach, we demonstrate that synthetic autocorrelation curves correspond well with experimental data and that NFCS diffusion measurements of Rhodamine B remain constant, regardless of the distortion present in a confocal detection volume.     

Composite load models based on field measurements and their applications in dynamic analysis

The composite load model with an induction motor in parallel with a static load has been studied and applied in analysis of dynamics of power systems for a long time. However, the load parameters from field tests are still very limited. Based on the theoretical results of identifiability and estimation methodology of load parameters that have been achieved in the previous work, a project of load modelling based on field measurements is described. Eight sets of equipment for load modelling were installed in HeNan Electric Power Grid (HNEPG) Corporation, and the dynamics of the load were recorded and a dynamic index is proposed to evaluate the dynamic characteristics of the data measured. The load models derived from the field measurements are applied to stability analysis of HNEPG. The critical clearing time and power transfer capability analyses illustrate the enhancement of the stability analysis of the power grid using the load parameters derived from the field measurements and show the benefits of application of such model parameters in power system dynamic analysis.     

Identification of Geological and Geophysical Parameters for Mathematical Models

A neuro-fuzzy network technology (soft computing) for identification of the geological and geophysical parameters for mathematical models of natural reservoirs in the exploitation of oil and gas deposits is proposed and verified. The effectiveness of the technology is demonstrated, especially in the early stage of prospecting, when information is uncertain and limited. With sufficient information, it is proposed that a recursion algorithm be used to identify the coefficients from measurements of the input and output coordinates of this generalized model in the presence of measurement noise.     

Computational procedures for optimal experimental design in biological systems

Mathematical models of complex biological systems, such as metabolic or cell-signalling pathways, usually consist of sets of nonlinear ordinary differential equations which depend on several non-measurable parameters that can be hopefully estimated by fitting the model to experimental data. However, the success of this fitting is largely conditioned by the quantity and quality of data. Optimal experimental design (OED) aims to design the scheme of actuations and measurements which will result in data sets with the maximum amount and/or quality of information for the subsequent model calibration. New methods and computational procedures for OED in the context of biological systems are presented. The OED problem is formulated as a general dynamic optimisation problem where the time-dependent stimuli profiles, the location of sampling times, the duration of the experiments and the initial conditions are regarded as design variables. Its solution is approached using the control vector parameterisation method. Since the resultant nonlinear optimisation problem is in most of the cases non-convex, the use of a robust global nonlinear programming solver is proposed. For the sake of comparing among different experimental schemes, a Monte-Carlo-based identifiability analysis is then suggested. The applicability and advantages of the proposed techniques are illustrated by considering an example related to a cell-signalling pathway.     

Modeling of the mechanical properties of bone tissue in the jaw and calculation of the stress-strain state of maxillary teeth systems with artificial implants

Techniques and methods for the design of tooth and jaw systems with artificial implants are analyzed. The mathematical model is based on data of precision measurements of the entire complement of biometric characteristics that determines the properties of a biomechanical system. The calculations presented here make it possible to predict complications that may arise in the process of implanting dentures.     

Parameter Identification Method of Large Macro-Micro Coupled Constitutive Models Based on Identifiability Analysis

Large and complex macro-micro coupled constitutive models, which describe metal flow and microstructure evolution during metal forming, are sometimes overparameterized with respect to given sets of experimental datum. This results in poorly identifiable or non-identifiable model parameters. In this paper, a systemic parameter identification method for the large macro-micro coupled constitutive models is proposed. This method is based on the global and local identifiability analysis, in which two identifiability measures are adopted. The first measure accounts for the sensitivity of model results with respect to single parameters, and the second measure accounts for the degree of near-linear dependence of sensitivity functions of parameter subsets. The global identifiability analysis adopts a sampling strategy with only a limited number of model evaluations, and the strategy is a combination of Latin-hypercube sampling, one-factor-at-a-time sampling and elitism preservation strategy. The global identifiability index is the integration of the corresponding local index. A hybrid global optimization method is designed to identify the parameter. Firstly, the genetic algorithm is adopted to identify the model parameter rudely, and then the obtained parameter is further refined through the improved Levenberg-Marquardt algorithm. The niching method is used to maintain the population diversity and to choose the initial value for the Levenberg-Marquardt algorithm. A transition criterion between the genetic algorithm and the Levenberg-Marquardt algorithm is proposed, through the improvement on the average objective function value of the chromosomes and the objective function value of the best chromosome. During optimization by the Levenberg-Marquardt algorithm, the local identifiability analysis is taken at the beginning stage of each iteration, and then the variable with poor identifiability remains unchanged in this iteration; the problem of violation constraint for some solution is solved through adjusting the search step length. At last, taking Ti-6Al-4V as an example, a set of satisfactory material parameters is obtained. The calculated results agree with the experimental results well. The identified results show that some parameters involved in the model are poorly identifiable; at the same time, the identifiability analysis method can provide a guide to experiment design.     

Life Testing in Variably Scaled Environments

Typically, accelerated life-testing models postulate a specific functional relationship between the stress level at which an experiment is performed and the parameters of the assumed family of lifetime distributions. These models, and the statistical analyses that accompany them, are often criticized on the basis of the dubious validity of the assumed functional relationship and of the uncertainty involved in the extrapolation of experimental results to low stress levels at which little or no data have been obtained. This study focuses on an exponential factorial model for accelerated life tests that postulates that the lifetime distributions of different component types tested under varying environmental conditions are linked via environmental or component-related scale changes. Necessary and sufficient conditions are given for the identifiability of model parameters. For both censored and complete data, the derivation and properties of maximum likelihood estimates of these parameters are discussed in detail. Under the conditions that guarantee identifiability, the existence and the uniqueness of the maximum likelihood estimators are demonstrated, and their computation and large-sample behavior are discussed. In the final section, the model is fitted to published data from an accelerated life-testing experiment.     

覆铜箔层压板专用低溴环氧树脂/双氰胺体系的固化反应动力学

采用程序升温DSC法研究了覆铜箔层压板专用的低溴环氧树脂／双氰胺体系的非等温固化反应动力学。分别用Kissinger方程和Ozawa—F1ynn—Wall方程推导了该固化体系的固化动力学方程，并计算了固化反应活化能。结果显示Kissinger方程能够较好地反映该体系非等温固化过程中放热峰顶温度的动力学参数，而Ozawa—F1ynn—Wall方程则可在较大固化度范围内计算该固化体系的动力学参数。本研究为环氧树脂／破纤布基覆铜箔层压板及多层印刷电路板的制作工艺提供了理论指导。     

Critical perspective on the consequences of the limited availability of kinetic data in metabolic dynamic modelling

Detailed kinetic models at the network reaction level are usually constructed using enzymatic mechanistic rate equations and the associated kinetic parameters. However, during the cellular life cycle thousands of different reactions occur, which makes it very difficult to build a detailed large-scale ldnetic model. In this work, we provide a critical overview of specific limitations found during the reconstruction of the central carbon metabolism dynamic model from E. coli (based on kinetic data available). In addition, we provide clues that will hopefully allow the systems biology community to more accurately construct metabolic dynamic models in the future. The difficulties faced during the construction of dynamic models are due not only to the lack of kinetic information but also to the fact that some data are still not curated. We hope that in the future, with the standardization of the in vitro enzyme protocols the approximation of in vitro conditions to the in vivo ones, it will be possible to integrate the available kinetic data into a complete large scale model. We also expect that collaborative projects between modellers and biologists will provide valuable kinetic data and permit the exchange of important information to solve most of these issues.     

中碳高合金高强度钢线膨胀测量中奥氏体-铁素体相变过程分析

线膨胀测量是获取钢铁材料固态相变动力学信息的一种重要手段,而从线膨胀测量结果提取相变动力学信息的杠杆法则,不适用于两相或者多相连续析出的过程,因而在计算相变体积分数时会产生很大的系统误差.以中碳高合金高强度钢(MCHAHS)的奥氏体一铁素体相变过程为主要研究对象,通过确定冷却过程中各生成相的晶格常数随温度的变化关系,发展了一种新的由线膨胀量信息提取相变动力学信息的计算方法,从而得到了MCHAHS钢转变过程中铁素体和珠光体体积分数随温度的变化关系,计算结果与验证性实验结果吻合良好.     

Back analysis of model parameters in geotechnical engineering by means of soft computing

In this paper, a parameter identification (PI) method for determination of unknown model parameters in geotechnical engineering is proposed. It is based on measurement data provided by the construction site. Model parameters for finite element (FE) analyses are identified such that the results of these calculations agree with the available measurement data as well as possible. For determination of the unknown model parameters, use of an artificial neural network (ANN) is proposed. The network is trained to approximate the results of FE simulations. A genetic algorithm (GA) uses the trained ANN to provide an estimate of optimal model parameters which, finally, has to be assessed by an additional FE analysis. The presented mode of PI renders back analysis of model parameters feasible even for large‐scale models as used in geotechnical engineering. The advantages of theoretical developments concerning both the structure and the training of the ANN are illustrated by the identification of material properties from experimental data. Finally, the performance of the proposed PI method is demonstrated by two problems taken from geotechnical engineering. The impact of back analysis on the actual construction process is outlined. Copyright © 2003 John Wiley & Sons, Ltd.     

The characterization and polymorphism of α-Glycine in the presence of butyric acid

The present study aims to investigate the effect of butyric acid used as an additive and its concentration ranging between 50?ppm and 250?ppm during the polymorphic phase transformation of β-glycine to α-glycine. Analysis includes a continuous measurement of the ultrasonic velocity and periodically the X-ray diffraction (XRD) pattern. Morphological characterization shows that the α-glycine crystals obtained in pure media are smooth, prismatic shapes, and that butyric acid plays a major role in crystal shape change. SEM imaging and morphology analysis indicates that the presence of butyric acid to media results in shorter, rounded and aggregated crystals. Further analyses of Fourier Transform Infrared Spectroscopy (FTIR), zeta potential measurements, and elemental analysis reveals that butyric acid adsorbs on the crystals’ surface and changes both the surface charge and the elemental composition of the crystals obtained. In addition, thermal decomposition behaviors of the crystals are investigated and the obtained data is modeled using the thermal decomposition kinetic models of FWO, KAS, and Tang. Based on the data of the FWO kinetic model, the average activation energy of the crystals obtained in butyric acid media is calculated as 118.8?±?17.0?kJ/mol, which is higher than that of crystals obtained in pure media.     

结构影响线识别：反问题可识别性分析与降维贝叶斯不确定性量化

结构影响线识别是移动荷载下既有结构评估的理论基础,其本质上是基于系统输入-输出含噪数据反向对静力系统指定截面的响应函数进行识别。已有研究虽然取得了进展,但它们在以下两个方面存在局限性：缺乏反问题可识别性分析;缺乏不确定性量化。反问题可识别性分析是为了厘清系统识别的参数的解的情况。不确定性量化是基于测量输入-输出含噪数据估计影响线参数的后验概率密度函数。针对上述两个局限性,该文在贝叶斯概率框架的基础上开展关于影响线识别的反问题可识别性分析与贝叶斯不确定性量化。该文进行基于直接参数化的影响线识别,包括系统输入与输出、反问题可识别性分析、参数最优值。经分析得出：一方面,直接参数化无法保证全局模型可识别;另一方面,现有方法即使是全局模型可识别的情况下也无法进行不确定性量化。为保证反问题是全局模型可识别且同时获取参数后验概率密度函数,该文提出基于降维贝叶斯不确定性量化的影响线后验识别,包括系统输入与输出重构、反问题可识别性分析、后验概率密度函数。该文进行模拟数据下新光大桥吊杆拉力影响线识别,与实测及模拟数据下简支梁桥应变影响线识别,验证提出方法的有效性。     

飞行器周边气体折射率变化对激光测量影响的模拟研究

在利用激光测量飞行器姿态参数的实验中,当测量光线穿过飞行器所产生的射流场时,场内气体光折射率不同而使光路发生弯曲,从而对测量结果造成影响.本文根据空气射流动力学原理,对飞行器周围射流场内气体的光折射率分布规律进行分析,建立简化模型,并以此得出影响测量误差的相应因素,估算出测量光束弯曲的角度偏差,从而对测量结果进行修正;同时可以提高系统的测量精确性,对测量系统的设计有所帮助.模拟试验结果表明,该计算方法可以有效的计算出测量结果的误差.     

一种基于数学模型的自动测量方法

为适应航天产品批量化及高效化的研制需求,提出一种基于产品数学模型的自动测量方法,在对产品数学模型进行数理分析的基础上,在装配组件上预置标定实物并标定其位置信息,装配过程以标定物为测量对象,利用仪器自动采样、自动评价,实现对组件装配状态的快速测量及判定。经试验证明:该方法自动化程度高、应用面广、适应性强,可以降低现场数据差错率,显著提升测量效率。     

Selecting creep models using Bayesian methods

The development of creep prediction models has been a field of extensive research and many different models have already been proposed. This paper presents an evaluation method of the prediction quality of creep models for specific experimental data. Within the scope of this paper, the model according to Bockhold and the model according to Heidolf are examined. First, the parameters of the models are identified with respect to existing experimental data. This is done using a sampling based approach of Bayesian updating developed by Ba?ant and Chern. In extension to the method by Ba?ant and Chern, the uncertainty coming from inaccurate measurement data is taken into account in the definition of the likelihood function within the updating algorithm. The more inaccurate the measurements are, the more uncertain the estimated model parameters and model prognoses become. The identification is performed for different short- and long-term creep tests. The intension is not to validate these models intensively, but to evaluate their prognoses for the individually tested creep behavior. The results show that the identifiability of the models?? parameters is different for both models and consequently the models prognoses differ in their uncertainties. Second, the models are evaluated using two different strategies: the stochastic model selection according to MacKay, Beck and Yuen based on the Ockham factor, and a comparison of the uncertainties taking into account parameter and model uncertainties. The results of the evaluation of the creep models differ for various experimental tests. Model Heidolf is more flexible and gives a better fit to the data, however, it fails to predict reliable long-term creep deformations using only short-term measurements compared to model Bockhold. Comparing the evaluation methods, the analysis of uncertainties of the creep prognosis proofs to be more stable than the evaluation using the stochastic model selection.     

Conjugated polymer-based real-time fluorescence caspase assays

We have developed conjugated polyelectrolyte-based fluorescence turn-on assays for caspase 3 and 8. These assays are composed of a cationic polyphenylene ethynylene polymer PPE4+ and p-nitroaniline modified caspase peptide substrate. The fluorescence of the assay is initially turned-off because of the efficient quenching of the polymer by p-nitroaniline moiety on anionic peptide substrates. A turn-on effect is observed due to the cleavage of the peptide by the enzyme and formation of the neutral p-nitroaniline unit which has no quenching on the polymer. We validated this assay design and obtained kinetic parameters of caspase 3 and caspase 8. These assays demonstrated good sensitivity as in pmol/L (0.1 units/mL) for caspase 3 and nmol/L (0.2 units/mL) for caspase 8. This method also showed high specificity by using caspase 3 assay as a model system and the results demonstrated that other proteases including caspase 8, papain, pepsin, and trypsin did not show observable fluorescence turn-on effect. The dose-response curve of a caspase inhibitor Z-VAD-FMK was evaluated by caspase 3 assay, by which the IC(50) value was determined to be 0.73 μM and was in a good agreement with the literature reported value at 0.62 μM. This design could be applied into the in vitro screening of small molecular inhibitors for drug discovery.