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.     

Prediction of Experimental Methanol Decomposition Rates on Platinum from First Principles

A microkinetic model for methanol decomposition on platinum is presented. The model incorporates competitive decomposition pathways, beginning with both O–H and C–H bond scission in methanol, and uses results from density functional theory (DFT) calculations [Greeley and Mavrikakis, J. Am. Chem. Soc. 124 (2002) 7193, Greeley and Mavrikakis, J. Am. Chem. Soc. 126 (2004) 3910]. Results from reaction kinetics experiments show that the rate of H₂ production increases with increasing temperature and methanol concentration in the feed and is only nominally affected by the presence of CO or H₂ with methanol. The model, based on the values of binding energies, pre-exponential factors and activation energy barriers derived from first principles calculations, accurately predicts experimental reaction rates and orders. The model also gives insight into the most favorable reaction pathway, the rate-limiting step, the apparent activation energy, coverages, and the effects of pressure. It is found that the pathway beginning with the C–H bond scission (CH₃OH→H₂COH→HCOH→CO) is dominant compared with the path beginning with O–H bond scission. The cleavage of the first C–H bond in methanol is the rate-controlling step. The surface is highly poisoned by CO, whereas COH appears to be a spectator species.     

Interactive Simulation of Rigid Body Dynamics in Computer Graphics

Interactive rigid body simulation is an important part of many modern computer tools, which no authoring tool nor game engine can do without. Such high‐performance computer tools open up new possibilities for changing how designers, engineers, modelers and animators work with their design problems. This paper is a self contained state‐of‐the‐art report on the physics, the models, the numerical methods and the algorithms used in interactive rigid body simulation all of which have evolved and matured over the past 20 years. Furthermore, the paper communicates the mathematical and theoretical details in a pedagogical manner. This paper is not only a stake in the sand on what has been done, it also seeks to give the reader deeper insights to help guide their future research.     

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.     

Influence of Amorphous Grain Boundary Phases on the Superplastic Behavior of 3-mol%-Yttria-Stabilized Tetragonal Zirconia Polycrystals (3Y-TZP)

Amorphous silicate grain boundary phases of varying chemistry and amounts were added to 3Y-TZP in order to determine their influence on the superplastic behavior between 1200° and 1300°C and on the room-temperature mechanical properties. Strain rate enhancement at high temperatures was observed in 3Y-TZP containing a glassy grain boundary phase, even with as little as 0.1 wt% glass. Strain rate enhancement was greatest in 3Y-TZP with 5 wt% glass, but the room-temperature hardness, elastic modulus, and fracture toughness were degraded. The addition of glassy grain boundary phases did not significantly affect the stress exponent of 3Y-TZP, but did lower the activation energy for superplastic flow. Strain rate enhancement was highest in samples containing the grain boundary phase with the highest solubility for Y₂O₃ and ZrO₂, but the strain rate did not scale inversely with the viscosity of the silicate phases. Grain boundary sliding accommodated by diffusional creep controlled by an interface reaction is proposed as the mechanism for superplastic deformation in 3Y-TZP with and without glassy grain boundary phases.     

An industrial study of applying input space partitioning to test financial calculation engines

This paper presents results from an industrial study that applied input space partitioning and semi-automated requirements modeling to large-scale industrial software, specifically financial calculation engines. Calculation engines are used in financial service applications such as banking, mortgage, insurance, and trading to compute complex, multi-conditional formulas to make high risk financial decisions. They form the heart of financial applications, and can cause severe economic harm if incorrect. Controllability and observability of these calculation engines are low, so robust and sophisticated test methods are needed to ensure the results are valid. However, the industry norm is to use pure human-based, requirements-driven test design, usually with very little automation. The Federal Home Loan Mortgage Corporation (FHLMC), commonly known as Freddie Mac, concerned that these test design techniques may lead to ineffective and inefficient testing, partnered with a university to use high quality, sophisticated test design on several ongoing projects. The goal was to determine if such test design can be cost-effective on this type of critical software. In this study, input space partitioning, along with automation, were applied with the help of several special-purpose tools to validate the effectiveness of input space partitioning. Results showed that these techniques were far more effective (finding more software faults) and more efficient (requiring fewer tests and less labor), and the managers reported that the testing cycle was reduced from five human days to 0.5. This study convinced upper management to begin infusing this approach into other software development projects.     

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.     

Microstructure and properties of TiB/Ti-6Al-4V coatings produced with laser treatments

TiB/Ti-6Al-4V metal-matrix composite (MMC) layers were produced on Ti-6Al-4V substrates by laser cladding. A TiB₂/Ti powder mixture was used as a precursor to obtain a dispersion of TiB needles in the Ti alloy matrix, with the aid of an exothermic reaction between TiB₂ and Ti. A eutectic microstructure was obtained that consisted of an extremely homogeneous dispersion of TiB eutectic needles in the Ti alloy matrix, having a volume fraction as high as 0.33. Also, an equilibrium-like microstructure was found, consisting of a dispersion of both primary and eutectic TiB needles inside the Ti alloy matrix. An analysis of the geometry of the layers was performed and proved successful in determining the percentage of B. Further, it correctly predicted the variation of atomic B content as a function of laser power. The relative wear resistance coefficient, defined as the wear coefficient of the uncoated matrix divided by that of coating, shows an improvement by a factor as high as 1500 for the eutectic microstructure. This paper was presented at the 2nd International Surface Engineering Congress sponsored by ASM International, on September 15–17, 2003, in Indianapolis, Indiana, and appeared on pp. 411–18 of the Proceedings.