Autocatalytic reactions in the isothermal,continuous stirred tank reactor: Isolas and other forms of multistability

Autocatalytic reactions are often complicated, and analyses of their behaviour in open systems can seem too particular to permit useful generalisation. We study here the simplest of circumstances (uniform temperatures and concentrations in the isothermal CSTR) and the simplest of reaction schemes: (i) quadratic autocatalysis (A + B→2B); and (ii) cubic autocatalysis (A + 2B→3B). The catalyst B may be stable or have a finite lifetime (B→ inert products). Allowing for this finite lifetime adds another dimension to the interest.The phenomena encountered include multistability, hysteresis, critical extinctions, critical ignitions, and anomalous relaxation times (though infinite values do not arise). Patterns of stationary states as function of residence time can show isolas and mushrooms. All these aspects yield to simple algebraic analysis. The presence of the catalyst B in the inflow can make qualitative differences of a kind parallelled by an additional, non-catalytic reaction of the same stoichiometry (e.g. A→B). Invoking the reversibility of the reactions neither increases nor diminishes their variety, and thermodynamic considerations have little to do with the many different patterns of reactivity displayed.The local stability of the various stationary states has also been characterized. Quadratic autocatalysis shows limited variety (stable node, stable focus); cubic autocatalysis generates all the kinds of stationary state possible in a two-variable system. Again all the algebra is straightforward if not always simple. Sustained oscillatory behavior (limit cycles) also occur.All these remarks relate to isothermal systems, but there are the most striking parallels between isothermal autocatalysis and the exothermic, first-order reaction in the CSTR. Behaviour with an autocatalyst of complete stability corresponds to perfect heat insulation (adiabatic operation) in the non-isothermal, exothermic system.     

Effect of 2-oleodipalmitin and 2-elaidodipalmitin on polymorphic behavior of cocoa butter

The polymorphic behavior of cocoa butter mixed with 2-oleodipalmitin (POP) or 2-elaidodipalmitin (PEP) was investigated with a differential scanning calorimeter. Six mixtures of cocoa butter containing 10, 25, and 50% POP and 10, 25, and 50% PEP were used. Each of the three cocoa butter-POP mixtures exhibited at least four polymorphic forms. The lowmelting form was obtained by quick chilling; the intermediate, by tempering for several hours just below the melting range; and the high-melting, by raising the temperature slowly to 25 C then holding there overnight or longer. In the cocoa butter-POP mixtures, only the low-melting form appeared to be more stable than the corresponding form for pure POP or cocoa butter. In addition to increased stability of the unstable low form, the rate of conversion from the intermediate to the high form, normally quite slow, increased in the cocoa butter-POP mixtures. Typical melting point lowering occurred when POP was added. POP was quite compatible with cocoa butter, the tempered mixture melting as a single compound; and the melting curves were fairly sharp. The three cocoa butter-PEP mixtures appeared to be incompatible. The cocoa butter and PEP behaved like a mixture of two fats, each of which melted independently. Presented at the AOCS Meeting, Chicago, Sept. 1973.     

ON GENERALIZED FRACTIONAL PROCESSES

Abstract. A class of stationary long-memory processes is proposed which is an extension of the fractional autoregressive moving-average (FARMA) model. The FARMA model is limited by the fact that it does not allow data with persistent cyclic (or seasonal) behavior to be considered. Our extension, which includes the FARMA model as a special case, makes use of the properties of the generating function of the Gegenbauer polynomials, and we refer to these models as Gegenbauer autoregressive moving-average (GARMA) models. While the FARMA model has a peak in the spectrum at f = 0, the GARMA process can model long-term periodic behavior for any frequency 0 f 0.5. Properties of the GARMA process are examined and techniques for generation of realizations, model identification and parameter estimation are proposed. The use of the GARMA model is illustrated through simulated examples as well as with classical sunspot data.     

第一批人凝血因子Ⅶ浓制剂国家标准品协作标定

目的 协作标定第一批人凝血因子Ⅶ浓制剂国家标准品。方法 以 WHO 97/592批人凝血因子Ⅶ浓制剂国际标准品为对照,采用一期法标定我国首批人凝血因子Ⅶ因家标准品,并将标准品分别置4℃、22℃、37℃保存5个月,用加速破坏试验进行稳定性考查。结果 该批标准品效价为16.0IU/支,稳定性良好。其他项目均达到国家标准品要求。结论 已成功研制第一批人凝血因子Ⅶ浓制剂国家标准品。     

Fundamentals of bitumen coking processes analogous to granulations: A critical review

A number of coking processes use hot particles to heat liquid bitumen or petroleum residue to cause cracking reactions. These particles may be mineral or coke solids. Interactions of these particles, in fluid beds, moving beds and other types of contactors, are governed by the liquid films on the particle surfaces. This paper explores the analogy between granulation and coking, and suggests that the key relationships that will govern the behavior of wet particles in coking processes are the Stokes number of the particles, the thickness or the liquid films, and the diameter and surface roughness of the particles. The implications for distribution of liquid feed in the reactor, fouling, and defluidization or bogging are discussed. This analysis suggests experiments that can be performed under non‐reactive conditions with scaled variables in order to study phenomena that cannot be observed in situ in high‐temperature cracking processes.     

Two for the General Audience Plus a Survey on BI

Abstract

The research in this paper considers the complex and dynamic arrangements for potential and actual knowledge sharing in interorganizational networks. The essence of this stance is that “knowledge” relates to affirmative managerial action beyond the necessary collection of information facilitated through technology. The issue is to determine the nature and extent of the degree of organizational agreement that may be achieved as competitors either cooperate or continue to compete in the face of challenging and pervasive market conditions. The theory relating to network formulation is reviewed, findings from empirical analyses from the experiences from automobile distributors in a large USA city, and one scientific collaborators network are presented. A framework is proposed identifying the factors necessary to initially construct the network and then to further sustain it over time. A number of lessons learned are developed, which are believed to be of value to researchers and practitioners engaged in these processes.     

Calculus Students' Use and Interpretation of Variables: Algebraic vs. Arithmetic Thinking

Abstract

The ability to use and interpret algebraic variables as generalized numbers and changing quantities is fundamental to the learning of calculus. This study considers the use of variables in these advanced ways as a component of algebraic thinking. College introductory calculus students' (n = 174) written responses to algebra problems requiring the use and interpretation of variables as changing quantities were examined for evidence of algebraic and arithmetic thinking. A framework was developed to describe and categorize examples of algebraic, transitional, and arithmetic thinking reflected in these students' uses of variables. The extent to which students' responses showed evidence of algebraic or arithmetic thinking was quantified and related to their course grades. Only one third of the responses of these entering calculus students were identified as representative of algebraic thinking. This study extends previous research by showing that evidence of algebraic thinking in students' work was positively related to successful performance in calculus.     

Simulation of the S2 state multiline electron paramagnetic resonance signal of photosystem II: a multifrequency approach

The S2 state electron paramagnetic resonance (EPR) multiline signal of Photosystem II has been simulated at Q-band (35 Ghz), X-band (9 GHz) and S-band (4 GHz) frequencies. The model used for the simulation assumes that the signal arises from an essentially magnetically isolated MnIII-MnIV dimer, with a ground state electronic spin ST = 1/2. The spectra are generated from exact numerical solution of a general spin Hamiltonian containing anisotropic hyperfine and quadrupolar interactions at both Mn nuclei. The features that distinguish the multiline from the EPR spectra of model manganese dimer complexes (additional width of the spectrum (195 mT), additional peaks (22), internal "superhyperfine" structure) are plausibly explained assuming an unusual ligand geometry at both Mn nuclei, giving rise to normally forbidden transitions from quadrupole interactions as well as hyperfine anisotropy. The fitted parameters indicate that the hyperfine and quadrupole interactions arise from Mn ions in low symmetry environments, corresponding approximately to the removal of one ligand from an octahedral geometry in both cases. For a quadrupole interaction of the magnitude indicated here to be present, the MnIII ion must be 5-coordinate and the MnIV 5-coordinate or possibly have a sixth, weakly bound ligand. The hyperfine parameters indicate a quasi-axial anisotropy at MnIII, which while consistent with Jahn-Teller distortion as expected for a d4 ion, corresponds here to the unpaired spin being in the ligand deficient, z direction of the molecular reference axis. The fitted parameters for MnIV are very unusual, showing a high degree of anisotropy not expected in a d3 ion. This degree of anisotropy could be qualitatively accounted for by a histidine ligand providing pi backbonding into the metal dxy orbital, together with a weakly bound or absent ligand in the x direction.