Optimal Control of the Primary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

The problem of operating freeze drying of pharmaceutical products in vials placed in trays of a freeze dryer to remove free water (in frozen state) at a minimum time was formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In type I freeze dryer design, upper and lower plate temperatures were controlled together, while in type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Constraints were placed on the system state variables by the melting and scorch temperatures during primary drying stage. Necessary conditions of optimality for the primary drying stage of freeze drying process in vials are derived and presented. Furthermore, an approach for constructing the optimal control policies that would minimize the drying time for the primary drying stage was given. In order to analyze optimal control policy for the primary drying stage of the freeze-drying process in vials, a rigorous multi-dimensional unsteady state mathematical model was used. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in the drying times of primary drying stage of freeze drying process in vials were obtained, as compared to the drying times obtained from conventional operational policies.     

Chemische Zusammensetzung und Mikrostruktur polymerabgeleiteter Gläser und Keramiken im System Si–C–O. Teil 2: Charakterisierung der Gefügeausbildung mittels hochauflösender Durchstrahlungselektronenmikroskopie und Feinbereichsbeugung

Chemical Composition and Microstructure of Polymer‐Derived Glasses and Ceramics in the Si–C–O System. Part 2: Characterization of microstructure formation by means of high‐resolution transmission electron microscopy and selected area diffraction Liquid or solid silicone resins represent the economically most interesting class of organic precursors for the pyrolytic production of glass and ceramics materials on silicon basis. As dense, dimensionally stable components can be cost‐effectively achieved by admixing reactive filler powders, chemical composition and microstructure development of the polymer‐derived residues must be exactly known during thermal decomposition. Thus, in the present work, glasses and ceramics produced by pyrolysis of the model precursor polymethylsiloxane at temperatures from 525 to 1550 °C are investigated. In part 1, by means of analytical electron microscopy, the bonding state of silicon was determined on a nanometre scale and the phase separation of the metastable Si–C–O matrix into SiO₂, C and SiC was proved. The in‐situ crystallization could be considerably accelerated by adding fine‐grained powder of inert fillers, such as Al₂O₃ or SiC, which permits effective process control. In part 2, the microstructure is characterized by high‐resolution transmission electron microscopy and selected area diffraction. Turbostratic carbon and cubic β‐SiC precipitate as crystallization products. Theses phases are embedded in an amorphous matrix. Inert fillers reduce the crystallization temperature by several hundred °C. In this case, the polymer‐derived Si–C–O material acts as a binding agent between the powder particles. Reaction layer formation does not occur. On the investigated pyrolysis conditions, no crystallization of SiO₂ was observed.     

Kinetics of two-step anionic polymerization

This article deals with the kinetics of two-step anionic polymerization by way of a non-steady state method. Several molecular parameters can be evaluated using the formulae developed. A bimodal molecular weight distribution function for the resulting polymer is derived from the set of kinetic differential equations, which is in agreement with the experimental data reported.     

新型实用布线算法──L─M算法

本文提出新型布线算法，集李氏迷宫法与线搜索法的长处为一体，以饱和带法进行动态排序，以线搜索法确定借孔位置，然后用李氏法进行单层布线，获得最佳路径，从而达到线型好，布通率高的效果。     

一种自动布线方法：多级线探索法

本文介绍了一种在微机上实现的印制板自动布线方法──多级线探索法及其编程方法。这种方法是基于完备布线算法的概念，通过分析李氏算法和传统线探索法的不足之处而得到的。虽然它也是一种线探索法，但有较传统线探索法更强的探索能力，不需要结合李氏算法而能单独完成布线任务，是一种较理想的算法，通过实验获得了较为满意的效果。     

A method of identifying latent human errors in work systems

Work system improvements are implemented in various manufacturing processes to prevent problems caused by human errors. However, they are almost always applied to problems which have already occurred. This paper examines a method of identifying latent human errors existing within the work systems beforehand. A procedure for applying failure mode and effect analysis to this identification problem was defined based on over 1000 empirical errors: a work system decomposition criterion and fundamental error modes for listing latent human errors, and then applied to three practical manufacturing processes in order to evaluate its effectiveness.     

Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Influence of Edible Films upon the Moisture Loss and Microstructure of Dietetic Sucrose-Free Sponge Cakes during Storage

The kinetics of changes in the bound water content in dietetic sucrose-free sponge cakes (DC) during storage was investigated. The effect of edible films of polymyxan, pectin, xanthan, and carboxymethylcellulose upon this kinetics was also investigated. The quantitative changes in both states of water (slightly bound water and strongly bound water) were registered by combined dynamic analysis (thermogravimetry analysis, TGA, and differential thermal analysis, DTA). The moisture changes in DC crumb were analyzed by drying out to constant mass. The rate constants were determined according the equation q = q_oe^-kt. The values of rate constants 'k', in day^-1, concerning the different edible films were as follows: for crumb moisture is (8.00 ≤ k ≤ 12.47) × 10^-3, for bound water is (3.07 ≤ k_w ≤ 6.26) × 10^-2, for slightly bound water is (4.22 ≤ k₁ ≤ 8.49) × 10^-2 and for strongly bound water is (2.02 ≤ k₂ ≤ 5.62) × 10^-2 as compared to 18.53 × 10^-3, 7.16 × 10^-2, 9.04 × 10^-2, and 5.36 × 10^-2 in the uncovered DC, respectively. The best water-retaining effect in respect to crumb moisture during storage was ascertained in the use of polymyxan and xanthan films. The lowest rate constant values for bound water and its two states were measured for DC covered with pectin. The relation between the kinetics of both bound water states during storage and ageing of the crumb of DC covered with different edible films and the crumb microstructure was represented. By means of scanning electron microscope was read the smallest change in crumb microstructure of pectin-covered DC on the sixth day of storage.