Initial stages of soot formation in thermal pyrolysis of acetylene. II. A model for the incipience and growth of soot particles

A model is developed which describes simultaneously occurring processes of the initial hydrocarbon pyrolysis, nucleation, surface growth, and coagulation of soot particles. The model permits one to find the size distribution of the primary soot particles up to size 30–40 nm using a relatively small set of equations. The computed time dependence of soot particle concentration agrees satisfactorily with available experimental data. The existence of two limiting stages of the soot formation is revealed.     

Die Anwendung von Kaliummanganat in der quantitativen Analyse

Zusammenfassung Die oxydimetrische Analyse einer großen Anzahl von organischen und anorganischen Verbindungen mit Kaliummanganat bei 60°C in 1–3 m Lauge wurde untersucht. In vielen Fällen ergaben sich stöchiometrische Reaktionen, die eine genaue quantitative Bestimmung ermöglichen, z. B. bei Ameisensäure, Milchsäure, Glykolsäure, Äpfelsäure, Brenztraubensäure, verschiedenen Zuckern, Alkoholen, Formaldehyd, Cyanid und einigen schwefelhaltigen anorganischen Verbindungen. Bei Weinsäure, Fumarsäure und Maleinsäure wurden um einige Prozent zu niedrige Ergebnisse erhalten, während die Analyse von Äthanol und Citronensäure überhaupt nicht möglich war.Bei den schwer oxydierbaren Verbindungen erwies sich die Stabilität der Manganatlösungen in Lauge während längerer Zeit bei erhöhter Temperatur als ein großer Vorteil. Insbesondere bei der Bestimmung kleiner Mengen solcher Stoffe ist Manganat in alkalischer Lösung dem Permanganat in saurer Lösung weit überlegen.     

Outer approximation algorithm for nondifferentiable optimization problems

It is known that the problem of minimizing a convex functionf(x) over a compact subsetX of ⁿ can be expressed as minimizing max{g(x, y)|y X}, whereg is a support function forf[f(x) g(x, y), for ally X andf(x)=g(x, x)]. Standard outer-approximation theory can then be employed to obtain outer-approximation algorithms with procedures for dropping previous cuts. It is shown here how this methodology can be extended to nonconvex nondifferentiable functions.This research was supported by the Science and Engineering Research Council, UK, and by the National Science Foundation under Grant No. ECS-79-13148.     

A new radiometric titration method based on separation by means of ion-exchange

The determination of thallium with potassium chlorate is chosen as an example for the earlier suggested new radio-oxidimetric titration procedure, in which phase separation is achieved by means of a strongly basic anion exchanger in the solution. Concentrations of thallium down to 2·10⁻⁶ M have been determined. Special care has to be taken for concentrations lower than 10⁻⁵ M as UV radiation is a disturbing factor. Other oxidizing agents have also been tested.     

Unified steerable phase I-phase II method of feasible directions for semi-infinite optimization

In this paper, we complete a cycle in the construction of methods of feasible directions for solving semi-infinite constrained optimization problems. Earlier phase I-phase II methods of feasible directions used one search direction rule in all of ⁿ with two stepsize rules, one for feasible points and one for infeasible points. The algorithm presented in this paper uses both a single search direction rule and a single stepsize rule in all of ⁿ . In addition, the new algorithm incorporates a steering parameter which can be used to control the speed with which feasibility is achieved. The new algorithm is simpler to analyze and performs somewhat better than existing, first order, phase I-phase II methods. The new algorithm is globally convergent, with linear rate.The research reported herein was sponsored in part by the National Science Foundation Grant ECS-8713334, the Air Force Office of Scientific Research Contract AFOSR-86-0116, and the State of California MICRO Program Grant 532410-19900.The authors would like to thank Dr. J. Higgins for providing the C-code of Algorithm 3.1.     

Correlation method for comparison of selectivity and retention on different chiral stationary phases

Summary The main chromatographic properties: selectivity and retention of two chiral stationary phases: (R)-3,5-dinitrobenzoylphenylglycine (CSP I) and (S)-3,5-dinitro-benzoylleucine (CSP II) have been compared on the basis of correlation of retention factors of derivatized esters of amino acids and derivatized aminoalcohols. The differences in retention and selectivity for the two CSPs can be easily estimated from the correlation equation. It is shown that in the case of the correlation for two sets of retention factors obtained on two different CSPs, it is mainly the intercept that decides which CSP has the better selectivity. It is demonstrated that the correlation method provides more informations on the selectivity and retention than comparison of the chromatographic data of single pairs of enantiomers. Additionally, the possible influence of the polar modifier mixed with n-hexane as diluent on the constants in the correlation equation is demonstrated.     

An exact penalty function algorithm for optimal control problems with control and terminal equality constraints,part 2

In Part 1 of this paper, implementable and conceptual versions of an algorithm for optimal control problems with control constraints and terminal equality constraints were presented. It was shown that anyL accumulation points of control sequences generated by the algorithms satisfy necessary conditions of optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithms always have accumulation points in the sense of control measure, and these accumulation points satisfy optimality conditions for the corresponding relaxed control problem.This work was supported by the United Kingdom Science Research Council, by the US Army Research Office, Contract No. DAA-29-73-C-0025, and by the National Science Foundation, Grant No. ENG-73-08214-A01.     

A stable matching model with an entrance criterion applied to the assignment of students to dormitories at the technion

This paper reports on a case study of the assignment of students to dormitories at the Technion–Israel Institute of Technology. Two criteria are used in considering applicants. The first criterion, determined by personal socio-economic characteristics, is used to make decisions about the privilege of getting on-campus housing. The second criterion is used for the actual assignment of the students who were found eligible for on-campus housing to specific dormitories—here the priority is determined by academic seniority and academic excellence. A modification of the classic stable matching model that allows for an “entrance criterion” is developed and analyzed. In particular, a new concept of quasi-stable outcomes is introduced and an algorithm that produces such an outcome with desirable properties is described. The algorithm was implemented successfully for the assignment of students to dormitories at the Technion toward the 2004/2005 academic year.     

On the use of corrected cohesion energies in model computations of transition metal properties: The case of Pt–Rh cluster compositional structures

Experimental cohesive energies were quite often used as bulk energies in semi-empirical or empirical modeling of transition metal and alloy properties (e.g. in TB-SMA, the EAM, the bond order simulation (BOS) model, etc.), thus ignoring the free-atom spin-polarizations and promotion energy contributions. The importance of employing corrected cohesion energy in avoiding erroneous results is emphasized, especially for alloys with similar cohesion energies of the constituents. We demonstrate the effect of the correction in the prediction of equilibrium compositional structures and thermodynamical properties of cuboctahedral 55 atom Pt–Rh nanoclusters.     

Extensions of Stochastic Optimization Results to Problems with System Failure Probability Functions

We derive an implementable algorithm for solving nonlinear stochastic optimization problems with failure probability constraints using sample average approximations. The paper extends prior results dealing with a failure probability expressed by a single measure to the case of failure probability expressed in terms of multiple performance measures. We also present a new formula for the failure probability gradient. A numerical example addressing the optimal design of a reinforced concrete highway bridge illustrates the algorithm. This work was sponsored by the Research Associateship Program, National Research Council. The authors are grateful for the valuable insight from Professors Alexander Shapiro, Evarist Gine, and Jon A. Wellner. The authors also thank Professor Tito Homem-de-Mello for commenting on an early draft of this paper.