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  • 2005-2009  (42)
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  • 1
    Publikationsdatum: 2020-08-05
    Beschreibung: Das heutige Leben ist durchdrungen von komplexen Technologien. Ohne Kommunikationsnetze, Internet, Mobilfunk, Logistik, Verkehrstechnik, medizinische Apparate, etc. könnte die moderne Gesellschaft nicht funktionieren. Fast alle dieser Technologien haben einen hohen Mathematikanteil. Der "normale Bürger"' weiss davon nichts, der Schulunterricht könnte dem ein wenig abhelfen. Einige mathematische Aspekte dieser Technologien sind einfach und sogar spielerisch intuitiv zugänglich. Solche Anwendungen, die zusätzlich noch der Lebensumwelt der Schüler zugehören, können dazu genutzt werden, die mathematische Modellierung, also die mathematische Herangehensweise an die Lösung praktischer Fragen, anschaulich zu erläutern. Gerade in der diskreten Mathematik können hier, quasi "nebenbei" mathematische Theorien erarbeitet und Teilaspekte (Definitionen, Fragestellungen, einfache Sachverhalte) durch eigenständiges Entdecken der Schüler entwickelt werden. Wir beginnen mit einigen Beispielen.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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  • 2
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    Publikationsdatum: 2020-08-05
    Beschreibung: Den kürzesten Weg in einem Graphen zu finden ist ein klassisches Problem der Graphentheorie. Über einen Vortrag zu diesem Thema beim Tag der Mathematik 2007 von R. Borndörfer kam ich in Kontakt mit dem Konrad-Zuse-Zentrum (ZIB), das sich u.a. mit Wegeoptimierung beschäftigt. Ein Forschungsschwerpunkt dort ist im Rahmen eines Projekts zur Chipverifikation das Zählen von Lösungen, das, wie wir sehen werden, eng mit dem Zählen von Wegen zusammenhängt. Anhand von zwei Fragen aus der Graphentheorie soll diese Facharbeit unterschiedliche Lösungsmethoden untersuchen. Wie bestimmt man den kürzesten Weg zwischen zwei Knoten in einem Graphen und wie findet man alle möglichen Wege? Nach einer Einführung in die Graphentheorie und einer Konkretisierung der Probleme wird zunächst für beide eine Lösung mit auf Graphen basierenden Algorithmen vorgestellt. Während der Algorithmus von Dijkstra sehr bekannt ist, habe ich für das Zählen von Wegen einen eigenen Algorithmus auf der Basis der Tiefensuche entwickelt. Im zweiten Teil der Arbeit wird das Konzept der ganzzahligen Programmierung vorgestellt und die Lösungsmöglichkeiten für Wegeprobleme, die sich darüber ergeben. Schließlich wurden die vorgestellten Algorithmen am Beispiel des S- und U-Bahnnetzes von Berlin implementiert und mit Programmen, die die gleichen Fragen über ganzzahlige Programmierung lösen, verglichen.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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  • 3
    Publikationsdatum: 2016-06-09
    Beschreibung: This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 4
    Publikationsdatum: 2020-08-05
    Beschreibung: Most data networks nowadays use shortest path protocols to route the traffic. Given administrative routing lengths for the links of the network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. In this paper, we present an integer programming algorithm for the minimum congestion unsplittable shortest path routing problem, which arises in the operational planning of such networks. Given a capacitated directed graph and a set of communication demands, the goal is to find routing lengths that define a unique shortest path for each demand and minimize the maximum congestion over all links in the resulting routing. We illustrate the general decomposition approach our algorithm is based on, present the integer and linear programming models used to solve the master and the client problem, and discuss the most important implementational aspects. Finally, we report computational results for various benchmark problems, which demonstrate the efficiency of our algorithm.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 5
    Publikationsdatum: 2020-12-15
    Beschreibung: This paper introduces the "line connectivity problem", a generalization of the Steiner tree problem and a special case of the line planning problem. We study its complexity and give an IP formulation in terms of an exponential number of constraints associated with "line cut constraints". These inequalities can be separated in polynomial time. We also generalize the Steiner partition inequalities.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 6
    Publikationsdatum: 2020-08-05
    Beschreibung: Testing is the process of stimulating a system with inputs in order to reveal hidden parts of the system state. In the case of non-deterministic systems, the difficulty arises that an input pattern can generate several possible outcomes. Some of these outcomes allow to distinguish between different hypotheses about the system state, while others do~not. In this paper, we present a novel approach to find, for non-deterministic systems modeled as constraints over variables, tests that allow to distinguish among the hypotheses as good as possible. The idea is to assess the quality of a test by determining the ratio of distinguishing (good) and not distinguishing (bad) outcomes. This measure refines previous notions proposed in the literature on model-based testing and can be computed using model counting techniques. We propose and analyze a greedy-type algorithm to solve this test optimization problem, using existing model counters as a building block. We give preliminary experimental results of our method, and discuss possible improvements.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 7
    Publikationsdatum: 2021-08-05
    Beschreibung: Starting with the description of the Traveling Salesmen Problem formulation as given by van Vyve and Wolsey in the article Approximate extended formulations'', we investigate the effects of small variations onto the performance of contemporary mixed integer programming solvers. We will show that even minor changes in the formulation of the model can result in performance difference of more than a factor of 1000. As the results show it is not obvious which changes will result in performance improvements and which not.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 8
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    Publikationsdatum: 2022-03-14
    Beschreibung: Orbitopes can be used to handle symmetries which arise in integer programming formulations with an inherent assignment structure. We investigate the detection of symmetries appearing in this approach. We show that detecting so-called orbitopal symmetries is graph-isomorphism hard in general, but can be performed in linear time if the assignment structure is known.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 9
    Publikationsdatum: 2019-01-29
    Beschreibung: Regional hyperthermia is a cancer therapy aiming at heating tumors using phased array applicators. This article provides an overview over current mathematical challenges of delivering individually optimal treatments. The focus is on therapy planning and identification of technical as well as physiological quantities from MR thermometry measurements.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 10
    Publikationsdatum: 2019-05-10
    Beschreibung: Reasons for the failure of adaptive methods to deliver improved efficiency when integrating monodomain models for myocardiac excitation are discussed. Two closely related techniques for reducing the computational complexity of linearly implicit integrators, deliberate sparsing and splitting, are investigated with respect to their impact on computing time and accuracy.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 11
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    Publikationsdatum: 2020-08-05
    Beschreibung: We investigate the computation of periodic timetables for public transport by mixed integer programming. After introducing the problem, we describe two mathematical models for periodic timetabling, the PERIODIC EVENT SCHEDULING PROBLEM (PESP) and the QUADRATIC SEMI-ASSIGNMENT PROBLEM. Specifically, we give an overview of existing integer programming (IP) formulations for both models. An important contribution of our work are new IP formulations for the PESP based on time discretization. We provide an analytical comparison of these formulations and describe different techniques that allow a more efficient solution by mixed integer programming. In a preliminary computational study, on the basis of standard IP solvers, we compare different formulations for computing periodic timetables. Our results justify a further investigation of the time discretization approach. Typically the timetable is optimized for the current traffic situation. The main difficulty with this approach is that after introducing the new timetable the passengers’ travel behavior may differ from that assumed for the computation. Motivated by this problem, we examine an iterative timetabling procedure that is a combination of timetable computation and passenger routing. We discuss the algorithmic issues of the passenger routing and study properties of the computed timetables. Finally, we confirm our theoretical results on the basis of an own implementation.
    Beschreibung: Wir untersuchen die Berechnung von Taktfahrplänen für den öffentlichen Verkehr mit gemischt-ganzzahliger Programmierung (MIP). Im Anschluss an die Problembeschreibung, stellen wir zwei mathematische Modellierungen vor, das PERIODIC EVENT SCHEDULING PROBLEM (PESP) und das QUADRATIC SEMI-ASSIGNMENT PROBLEM. Wichtiger Bestandteil ist ein Überblick über existierende ganzzahlige Formulierungen beider Modelle. Wir entwickeln neue ganzzahlige Formulierungen für das PESP auf der Basis von Zeitdiskretisierung. Diese werden analytisch miteinander verglichen und wir beschreiben verschiedene Techniken, die eine effizientere Lösung der Formulierungen mit gemischt-ganzzahliger Programmierung ermöglichen. In einer ersten Rechenstudie, unter Verwendung gängiger MIP-Löser, vergleichen wir verschiedene ganzzahlige Formulierungen zur Berechnung von Taktfahrplänen. Unsere Ergebnisse rechtfertigen eine weitere Untersuchung des Zeitdiskretisierungsansatzes. In der Regel werden Fahrpläne mit Bezug auf die gegenwärtige Verkehrssituation optimiert. Dies birgt jedoch folgendes Problem. Wenn der neue Fahrplan eingeführt wird, ist es möglich, dass die Passagiere ein anderes Fahrverhalten zu Tage legen, als für die Berechnung des Fahrplans angenommen wurde. Vor diesem Hintergrund behandeln wir ein iteratives Verfahren zur Berechnung von Taktfahrplänen. Dieses ist eine Kombination aus Fahrplanberechnung und Passagierrouting. Neben den algorithmischen Details des Passagierroutings untersuchen wir Eigenschaften der berechneten Fahrpläne. Abschließend bestätigen wir unsere theoretischen Ergebnisse auf Grundlage einer eigenen Implementierung des Verfahrens.
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: masterthesis , doc-type:masterThesis
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  • 12
    Publikationsdatum: 2020-08-05
    Beschreibung: This paper describes several experiments to explore the options for solving a class of mixed integer nonlinear programming problems that stem from a real-world mine production planning project. The only type of nonlinear constraints in these problems are bilinear equalities involving continuous variables, which enforce the ratios between elements in mixed material streams. A branch-and-bound algorithm to handle the integer variables has been tried in another project. However, this branch-and-bound algorithm is not effective for handling the nonlinear constraints. Therefore state-of-the-art nonlinear solvers are utilized to solve the resulting nonlinear subproblems in this work. The experiments were carried out using the NEOS server for optimization. After finding that current nonlinear programming solvers seem to lack suitable preprocessing capabilities, we preprocess the instances beforehand and use an heuristic approach to solve the nonlinear subproblems. In the appendix, we explain how to add a polynomial constraint handler that uses IPOPT as embedded nonlinear programming solver for the constraint programming framework SCIP. This is one of the crucial steps for implementing our algorithm in SCIP. We briefly described our approach and give an idea of the work involved.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 13
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    Publikationsdatum: 2020-08-05
    Beschreibung: Dieser kurze Aufsatz zur Algorithmengeschichte ist Eberhard Knobloch, meinem Lieblings-Mathematikhistoriker, zum 65. Geburtstag gewidmet. Eberhard Knobloch hat immer, wenn ich ihm eine historische Frage zur Mathematik stellte, eine Antwort gewusst – fast immer auch sofort. Erst als ich mich selbst ein wenig und dazu amateurhaft mit Mathematikgeschichte beschäftigte, wurde mir bewusst, wie schwierig dieses „Geschäft“ ist. Man muss nicht nur mehrere (alte) Sprachen beherrschen, sondern auch die wissenschaftliche Bedeutung von Begriffen und Symbolen in früheren Zeiten kennen. Man muss zusätzlich herausfinden, was zur Zeit der Entstehung der Texte „allgemeines Wissen“ war, insbesondere, was seinerzeit gültige Beweisideen und -schritte waren, und daher damals keiner präzisen Definition oder Einführung bedurfte. Es gibt aber noch eine Steigerung des historischen Schwierigkeitsgrades: Algorithmengeschichte. Dies möchte ich in diesem Artikel kurz darlegen in der Hoffnung, dass sich Wissenschaftshistoriker dieses Themas noch intensiver annehmen, als sie das bisher tun. Der Grund ist, dass heute Algorithmen viele Bereiche unserer Alltagswelt steuern und unser tägliches Leben oft von funktionierenden Algorithmen abhängt. Daher wäre eine bessere Kenntnis der Algorithmengeschichte von großem Interesse.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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  • 14
    Publikationsdatum: 2016-06-09
    Beschreibung: We consider first order optimality conditions for state constrained optimal control problems. In particular we study the case where the state equation has not enough regularity to admit existence of a Slater point in function space. We overcome this difficulty by a special transformation. Under a density condition we show existence of Lagrange multipliers, which have a representation via measures and additional regularity properties.
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    Sprache: Englisch
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  • 15
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    Publikationsdatum: 2016-06-09
    Beschreibung: The enormous time lag between fast atomic motion and complex pro- tein folding events makes it almost impossible to compute molecular dy- namics on a high resolution. A common way to tackle this problem is to model the system dynamics as a Markov process. Yet for large molec- ular systems the resulting Markov chains can hardly be handled due to the curse of dimensionality. Coarse graining methods can be used to re- duce the dimension of a Markov chain, but it is still unclear how far the coarse grained Markov chain resembles the original system. In order to answer this question, two different coarse-graining methods were analysed and compared: a classical set-based reduction method and an alternative subspace-based approach, which is based on membership vectors instead of sets. On the basis of a small toy system, it could be shown, that in con- trast to the subset-based approach, the subspace-based reduction method preserves the Markov property as well as the essential dynamics of the original system.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 16
    Publikationsdatum: 2021-02-19
    Beschreibung: Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 17
    Publikationsdatum: 2020-08-05
    Beschreibung: It is well known that competitive analysis yields too pessimistic results when applied to the paging problem and it also cannot make a distinction between many paging strategies. Many deterministic paging algorithms achieve the same competitive ratio, ranging from inefficient strategies as flush-when-full to the good performing least-recently-used (LRU). In this paper, we study this fundamental online problem from the viewpoint of stochastic dominance. We show that when sequences are drawn from distributions modelling locality of reference, LRU is stochastically better than any other online paging algorithm.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 18
    Publikationsdatum: 2020-12-15
    Beschreibung: Die Angebotsplanung im öffentlichen Nahverkehr umfasst die Aufgaben der Netz-, Linien-,Fahr- und Preisplanung. Wir stellen zwei mathematische Optimierungsmodelle zur Linien- und Preisplanung vor. Wir zeigen anhand von Berechnungen für die Verkehrsbetriebe in Potsdam(ViP), dass sich damit komplexe Zusammenhänge quantitativ analysieren lassen. Auf diese Weise untersuchen wir die Auswirkungen von Freiheitsgraden auf die Konstruktion von Linien und die Wahl von Reisewegen der Passagiere, Abhängigkeiten zwischen Kosten und Reisezeiten sowie den Einfluss verschiedener Preissysteme auf Nachfrage und Kostendeckung.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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  • 19
    Publikationsdatum: 2022-03-14
    Beschreibung: This article introduces constraint integer programming (CIP), which is a novel way to combine constraint programming (CP) and mixed integer programming (MIP) methodologies. CIP is a generalization of MIP that supports the notion of general constraints as in CP. This approach is supported by the CIP framework SCIP, which also integrates techniques from SAT solving. SCIP is available in source code and free for non-commercial use. We demonstrate the usefulness of CIP on two tasks. First, we apply the constraint integer programming approach to pure mixed integer programs. Computational experiments show that SCIP is almost competitive to current state-of-the-art commercial MIP solvers. Second, we employ the CIP framework to solve chip design verification problems, which involve some highly non-linear constraint types that are very hard to handle by pure MIP solvers. The CIP approach is very effective here: it can apply the full sophisticated MIP machinery to the linear part of the problem, while dealing with the non-linear constraints by employing constraint programming techniques.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 20
    Publikationsdatum: 2016-06-09
    Beschreibung: An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control.
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    Sprache: Englisch
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  • 21
    Publikationsdatum: 2021-08-05
    Beschreibung: In the recent years there has been tremendous progress in the development of algorithms to find optimal solutions for integer programs. In many applications it is, however, desirable (or even necessary) to generate all feasible solutions. Examples arise in the areas of hardware and software verification and discrete geometry. In this paper, we investigate how to extend branch-and-cut integer programming frameworks to support the generation of all solutions. We propose a method to detect so-called unrestricted subtrees, which allows us to prune the integer program search tree and to collect several solutions simultaneously. We present computational results of this branch-and-count paradigm which show the potential of the unrestricted subtree detection.
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    Sprache: Englisch
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  • 22
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    Publikationsdatum: 2020-08-05
    Beschreibung: Edmonds showed that the so-called rank inequalities and the nonnegativity constraints provide a complete linear description of the matroid polytope. By essentially adding Grötschel's cardinality forcing inequalities, we obtain a complete linear description of the cardinality constrained matroid polytope which is the convex hull of the incidence vectors of those independent sets that have a feasible cardinality. Moreover, we show how the separation problem for the cardinality forcing inequalities can be reduced to that for the rank inequalities. We also give necessary and sufficient conditions for a cardinality forcing inequality to be facet defining.
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    Sprache: Englisch
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  • 23
    Publikationsdatum: 2020-08-05
    Beschreibung: The paper describes a method for solution of very large overdetermined algebraic polynomial systems on an example that appears from a classification of all integrable 3-dimensional scalar discrete quasilinear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. The overdetermined polynomial algebraic system that has to be solved is far too large to be formulated. A probing' technique which replaces independent variables by random integers or zero allows to formulate subsets of this system. An automatic alteration of equation formulating steps and equation solving steps leads to an iteration process that solves the computational problem.
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    Sprache: Englisch
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  • 24
    Publikationsdatum: 2020-08-05
    Beschreibung: An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.
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    Sprache: Englisch
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  • 25
    Publikationsdatum: 2021-02-26
    Beschreibung: We classify all integrable 3-dimensional scalar discrete affine linear equations $Q_3=0$ on an elementary cubic cell of the lattice ${\mathbb Z}^3$. An equation $Q_3=0$ %of such form is called integrable if it may be consistently imposed on all $3$-dimensional elementary faces of the lattice ${\mathbb Z}^4$. Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only ontrivial(non-linearizable) integrable equation from this class is the well-known dBKP-system.
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    Sprache: Englisch
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  • 26
    Publikationsdatum: 2020-12-11
    Beschreibung: The article describes the online mathematics test {\tt http://lie.math.brocku.ca/mathtest}, its typical applications and experiences gathered.
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    Sprache: Englisch
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  • 27
    Publikationsdatum: 2020-08-05
    Beschreibung: We introduce (TTPlib), a data library for train timetabling problems that can be accessed at http://ttplib.zib.de. In version 1.0, the library contains data related to 50 scenarios. Most instances result from the combination of macroscopic railway networks and several train request sets for the German long distance area containing Hannover, Kassel and Fulda, short denoted by Ha-Ka-Fu. In this paper, we introduce the data concepts of TTPlib, describe the scenarios included in the library and provide a free visualization tool TraVis.
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 28
    facet.materialart.
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    Publikationsdatum: 2020-08-05
    Beschreibung: The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. A second conceptual aim is to present an algorithm that is in some sense dual to the fundamental Euclids algorithm, and thus an alternative to the special case of a Gr\"{o}bner basis algorithm as it is used for solving linear ODE-systems. In the paper Euclids algorithm and the new dual version' are compared and their complementary strengths are analysed on the task of solving underdetermined ODEs. An implementation of the described algorithm is interactively accessible at http://lie.math.brocku.ca/crack/uode.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 29
    Publikationsdatum: 2020-08-05
    Beschreibung: This paper proposes a new method for probabilistic analysis of online algorithms that is based on the notion of stochastic dominance. We develop the method for the Online Bin Coloring problem introduced by Krumke et al. Using methods for the stochastic comparison of Markov chains we establish the strong result that the performance of the online algorithm GreedyFit is stochastically dominated by the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 30
    Publikationsdatum: 2020-12-15
    Beschreibung: The optimization of fare systems in public transit allows to pursue objectives such as the maximization of demand, revenue, profit, or social welfare. We propose a non-linear optimization approach to fare planning that is based on a detailed discrete choice model of user behavior. The approach allows to analyze different fare structures, optimization objectives, and operational scenarios involving, e.g., subsidies. We use the resulting models to compute optimized fare systems for the city of Potsdam, Germany.
    Schlagwort(e): ddc:510
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
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  • 31
    Publikationsdatum: 2022-03-14
    Beschreibung: Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 32
    Publikationsdatum: 2020-08-05
    Beschreibung: Millionen von Menschen werden allein in Deutschland täglich von Bussen, Bahnen und Flugzeugen transportiert. Der öffentliche Personenverkehr (ÖV) ist von großer Bedeutung für die Lebensqualität einzelner aber auch für die Leistungsfähigkeit ganzer Regionen. Qualität und Effizienz von ÖV-Systemen hängen ab von politischen Rahmenbedingungen (staatlich geplant, wettbewerblich organisiert) und der Eignung der Infrastruktur (Schienensysteme, Flughafenstandorte), vom vorhandenen Verkehrsangebot (Fahr- und Flugplan), von der Verwendung angemessener Technologien (Informations-, Kontroll- und Buchungssysteme) und dem bestmöglichen Einsatz der Betriebsmittel (Energie, Fahrzeuge und Personal). Die hierbei auftretenden Entscheidungs-, Planungs- und Optimierungsprobleme sind z.T. gigantisch und "schreien" aufgrund ihrer hohen Komplexität nach Unterstützung durch Mathematik. Dieser Artikel skizziert den Stand und die Bedeutung des Einsatzes von Mathematik bei der Planung und Durchführung von öffentlichem Personenverkehr, beschreibt die bestehenden Herausforderungen und regt zukunftsweisende Maßnahmen an.
    Schlagwort(e): ddc:510
    Sprache: Deutsch
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  • 33
    Publikationsdatum: 2019-05-10
    Beschreibung: Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 34
    Publikationsdatum: 2016-06-09
    Beschreibung: In this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems, governed by partial differential equations. We will derive existence of solutions together with first order optimality conditions. Afterwards we show continuity of the central path, together with convergence rates depending on the interior point parameter.
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    Sprache: Englisch
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  • 35
    Publikationsdatum: 2016-06-09
    Beschreibung: We consider an interior point method in function space for PDE constrained optimal control problems with state constraints. Our emphasis is on the construction and analysis of an algorithm that integrates a Newton path-following method with adaptive grid refinement. This is done in the framework of inexact Newton methods in function space, where the discretization error of each Newton step is controlled by adaptive grid refinement in the innermost loop. This allows to perform most of the required Newton steps on coarse grids, such that the overall computational time is dominated by the last few steps. For this purpose we propose an a-posteriori error estimator for a problem suited norm.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 36
    Publikationsdatum: 2020-08-05
    Beschreibung: Ticket pricing in public transport usually takes a welfare or mnemonics maximization point of view. These approaches do not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and integer programming. An application to pricing railway tickets for the intercity network of the Netherlands demonstrates that, in this sense, prices that are much fairer than standard ones can be computed in this way.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 37
    Publikationsdatum: 2014-02-26
    Beschreibung: We present a second order sharp interface finite volume method for the solution of the three-dimensional poisson equation with variable coefficients on Cartesian grids. In particular, we focus on interface problems with discontinuities in the coefficient, the source term, the solution, and the fluxes across the interface. The method uses standard piecewiese trilinear finite elements for normal cells and a double piecewise trilinear ansatz for the solution on cells intersected by the interface resulting always in a compact 27-point stencil. Singularities associated with vanishing partial volumes of intersected grid cells are removed by a two-term asymptotic approach. In contrast to the 2D method presented by two of the authors in [M.~Oevermann, R.~Klein: A Cartesian grid finite volume method for elliptic equations with variable coefficients and embedded interfaces, J.~Comp.~Phys.~219 (2006)] we use a minimization technique to determine the unknown coefficients of the double trilinear ansatz. This simplifies the treatment of the different cut-cell types and avoids additional special operations for degenerated interface topologies. The resulting set of linear equations has been solved with a BiCGSTAB solver preconditioned with an algebraic multigrid. In various testcases -- including large coefficient ratios and non-smooth interfaces -- the method achieves second order of accuracy in the L_inf and L_2 norm.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 38
    Publikationsdatum: 2020-08-05
    Beschreibung: Given a combinatorial optimization problem and a subset $N$ of natural numbers, we obtain a cardinality constrained version of this problem by permitting only those feasible solutions whose cardinalities are elements of $N$. In this paper we briefly touch on questions that addresses common grounds and differences of the complexity of a combinatorial optimization problem and its cardinality constrained version. Afterwards we focus on polytopes associated with cardinality constrained combinatorial optimization problems. Given an integer programming formulation for a combinatorial optimization problem, by essentially adding Grötschel's cardinality forcing inequalities, we obtain an integer programming formulation for its cardinality restricted version. Since the cardinality forcing inequalities in their original form are mostly not facet defining for the associated polyhedra, we discuss possibilities to strengthen them.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 39
    Publikationsdatum: 2020-08-05
    Beschreibung: This survey concerns optimization problems arising in the design of survivable communication networks. It turns out that such problems can be modeled in a natural way as non-compact linear programming formulations based on multicommodity flow network models. These non-compact formulations involve an exponential number of path flow variables, and therefore require column generation to be solved to optimality. We consider several path-based survivability mechanisms and present results, both known and new, on the complexity of the corresponding column generation problems (called the pricing problems). We discuss results for the case of the single link (or node) failures scenarios, and extend the considerations to multiple link failures. Further, we classify the design problems corresponding to different survivability mechanisms according to the structure of their pricing problem. Finally, we show that almost all encountered pricing problems are hard to solve for scenarios admitting multiple failures.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 40
    Publikationsdatum: 2021-02-19
    Beschreibung: We introduce an optimization model for the line planning problem in a public transportation system that aims at minimizing operational costs while ensuring a given level of quality of service in terms of available transport capacity. We discuss the computational complexity of the model for tree network topologies and line structures that arise in a real-world application at the Trolebus Integrated System in Quito. Computational results for this system are reported.
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    Sprache: Englisch
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  • 41
    Publikationsdatum: 2021-02-19
    Beschreibung: Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated.
    Schlagwort(e): ddc:510
    Sprache: Englisch
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  • 42
    Titel: Recht verstehen /; Bd. 19
    Beteiligte Person(en): Klein, Wolfgang , Becker, Angelika , Parádi, Zsuzsa , Witzmann, Franziska
    Verlag: Berlin :Akademie Verl.,
    Erscheinungsjahr: 2008
    Seiten: IX, 242 S. : , graph. Darst. ; , 240 mm x 170 mm
    Serie: Forschungsberichte der Interdisziplinären Arbeitsgruppen der Berlin-Brandenburgischen Akademie der Wissenschaften Bd. 19
    ISBN: 978-3-05-004484-2
    Materialart: Buch
    Sprache: Deutsch
    Schlagwort(e): Private Altersversorgung ; Vertragsbedingung ; Verständlichkeit ; Umfrage ; Private Altersversorgung ; Vertragsbedingung ; Verständlichkeit ; Umfrage
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  • 43
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 13-17 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Graphical correlations of binary gas diffusion coefficients are developed based on the Hirschfelder-Bird-Spotz diffusion equation and the theorem of corresponding states. A critical diffusion coefficient is defined and is used in turn for a definition of a “reduced” coefficient. The reduced diffusion coefficient is correlated graphically in generalized form in terms of the reduced properties of the diffusing gas. Using air as a reference “barrier” gas, the authors compared critical diffusion coefficients for various gases diffusing through a single barrier gas with the critical coefficients for these gases through air. This ratio, termed the barrier gas ratio, was found to be independent of the properties of the diffusing gas. A graphical correlation of the barrier gas ratio enables rapid estimation of a binary diffusion coefficient with a minimum of information.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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  • 44
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 26-33 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The rates of nitration of benzene by nitric acid in mixed acid to produce mononitrobenzene have been measured in well-emulsified reaction mixtures in the temperature range from 34° to 54°C. The acid-phase compositions ranged from 1.6 mole % nitric acid and 27 mole % sulfuric acid to 35 mole % nitric acid and zero % sulfuric acid; the organicphase composition ranged from 4 to 95 mole % benzene, and the relative extent of the acid and organic phases was varied from 25 to 80 volume % acid phase.The reaction rate based on the total volume of the reacting mixture is shown to be a function of the phase compositions, temperature, and volume % of acid phase.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
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  • 45
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 18-25 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A method of estimating the true conditions of operation of a bubble-cap tray is presented. Intermediate between the Murphree and the Lewis methods, which represent the extremes of actual operation, this method involves the use of a correlation to determine the degree of liquid mixing on the tray and the use of new relations between the Murphree vapor efficiency, the Lewis case I efficiency, and the true local efficiency. For the last, partial liquid mixing is taken into account.Data were obtained on an 18-in. O.D. three-tray bubble-cap tower containing ten 3-in. bubble caps a tray. Partial liquid mixing was correlated for changes in vapor and liquid rates, pressure, temperature, and weir height for the system ethylene dichloride-toluene.Efficiency data on acetone-water, ethanol-water, and ethylene dichloride-toluene showed the following effects: (1) low concentration of lwo boiler usually, but not always, resulted in low true local efficiencies, always with high Murphree efficiencies; (2) vapor velocity effects are more intimately connected with slot velocity than superficial velocity (and hence entrainment); (3) raising the pressure gives higher efficiencies; (4) an increase in liquid depth increases the true local efficiency but may have no effect on the Murphree efficiency.
    Zusätzliches Material: 15 Ill.
    Materialart: Digitale Medien
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  • 46
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 38-41 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A procedure for obtaining equilibrium data and predicting ideal-stage requirements in a complex liquid-liquid extraction system is presented. Preliminary equilibrium data are obtained from a simulated column run involving a series of batch contacts operated in such a manner as to approach steady state countercurrent conditions. The flow ratios and stage requirements for continuous operation are then estimated by trial-and-error by use of a modified McCabe-Thiele method.The procedure lends itself particularly well to those systems with interdependent distribution of the two components. Data for the separation of hafnium from zirconium are presented to show the utility of the method.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
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  • 47
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 42-45 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Because of the large scale of the motion responsible for mixing in turbulent fields, turbulent transport processes differ from molecular transport processes in that the mixing depends on the previous history of the diffusing material and turbulent fields are generally nonhomogeneous.The effect of the time dependency of the diffusion process is examined for the case of heat transfer from a hot wall to a cold wall through a turbulently flowing fluid. The fluid is assumed to have a uniform velocity and the turbulence is assumed to be homogeneous and isotropic. The calculations are carried out by assuming a distribution of heat sources along the hot wall and of heat sinks along the cold wall. G. I. Taylor's theory of turbulent diffusion for a homogeneous isotropic field is used to describe the properties of these sources and sinks. These calculations are compared with temperature profiles obtained as a solution to Fick's Law using a constant diffusion coefficient. A marked difference between the two sets of curves is obtained in the vicinity of the wall and in the beginning of the heat exchange section.A calculated profile on the basis of an idealized model of heat transfer in channel flow is compared with actual measurements made by Page, Corcoran, Schlinger, and Sage (7) at a distance far enough downstream so that the temperature profile had reached a steady condition.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 48
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 46-54 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The hydrogenation of carbon monoxide and carbon dioxide on various steel catalysts was studied in the temperature range of 800° to 1,300°F. and at pressures from 5 to 30 atm. The feed gases (3.75 to 20 SCFH) were passed over a catalyst bed of 1/8-in. steel balls supported in a brass-lined reactor 0.81 in. in diam. The percentage of carbon oxides in the feed was 30% in the runs using a H2—CO2 feed and varied from 15 to 38% in the runs with a H2—CO feed. The effects of temperature, pressure, feed composition, space velocity, and mass velocity were studied. Carbon deposition did not affect the activity of the catalyst and could be removed readily.
    Zusätzliches Material: 18 Ill.
    Materialart: Digitale Medien
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  • 49
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 34-37 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: In the usual method of calculating the solvent extraction of complex mixtures it is assumed that the complex mixture behaves like a binary mixture. However, the hypothetical binary composition of the mixture is never explicitly used; rather, an additive property of the mixture is used as an indication of its composition. The calculation must be done graphically on a triangular diagram or its equivalent.On the assumption that the complex mixture consists of only two hypothetical components, empirical equations have been arrived at relating the distribution coefficients of these two components and of the solvent to the phase compositions. These equations contain three arbitrary constants. By use of the data from a minimum of three simple laboratory batch extractions of a given complex mixture, the three constants, plus the hypothetical binary composition of the original complex mixture, can be determined.With the equations for the distribution coefficients, the equilibrium curve and tie lines for the system can be calculated. Properties of the raffinates and extracts can be measured and related to the hypothetical binary compositions of these mixtures.The use of the method is demonstrated by comparing calculated results with laboratory yields and properties. The calculated results show good agreement with the experimental results. Calculations can be carried out not only on the triangular diagram, but by any of the other graphical methods that have been developed for the solvent extraction of binary mixtures. Equally important, calculations can be done analytically, and therefore the use of automatic computers is feasible.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
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  • 50
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 55-58 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The physical processes are discussed by which a fluid is displaced from a porous medium during steady state viscous flow by another fluid of the same density and viscosity under conditions of complete miscibility of the two fluids. The displacement occurs on a microscopic scale as a result of combined convective and diffusional mixing. The length of the zone of mixing which comprises the displacement front is predicted to be dependent upon the rate of flow, the diffusion coefficient for the two-fluid system, the characteristics of the pore geometry, and the distance the front has traversed at the time of its observation.Experimental data are presented for the displacement of benzene by ethyl n-butyrate at several rates of flow from packed sand columns. These data show that the length of the frontal mixing zone after a prescribed distance of flow is greater at the higher rates of flow. The postulated dependence of the length of the front upon the diffusion coefficient and the pore geometry has not yet been investigated.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 51
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Fluid flow data are presnted for beds of uniformly sized spheres consolidated with resin over a porosity range from 36.4 to 12.3%. The data are analyzed in terms of an effective pore volume and equations are given for predicting pressure drop by use of a friction-factor-Reynolds-number plot.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 52
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 71-74 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: An equation for correlating regeneration process variables in fluid-catalytic cracking has been developed from pilot plant data. This equation takes into account not only the chemical-reaction rate for burning coke deposited on the catalyst but also the diffusional resistance to oxygen transfer. The resistance presumably occurs between the bubbles within the fluidized bed and the void spaces in the relatively denser mass of particles. The coefficient of mass transfer was found to be inversely proportional to the 1.5 power of the average particle diameter and directly proportional to the square of the gas mass velocity. The specific reaction-verlocity constant was found to be a function to temperature and catalyst activity as well as the nature of the feed from which the coke was deposited. Comparison of pilot plant data with commercial data suggests that nonuniform gas distribution in larger beds makes some of the catalyst ineffective.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 53
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 88-93 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A theoretical equation is presented for predicting the specific heat at constant volume and constant pressure of organic liquids as a function of temperature from data on the velocity of sound, infrared and Raman spectra. By use of this equation, the average deviation of the calculated from the experimental values of specific heat for 100 organic liquids at 68°F. is ±1.5%.An alternate correlation for hydrocarbon liquids based on a modified statement of the theory of corresponding states is also presented. Based on it, the average deviation of the calculated from the experimental values for 100 points representing the entire temperature range is ±0.9%.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 54
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 101-106 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The object of this study has been the measurement of concentration profiles of water vapor in a wetted-wall column with fully developed turbulent pipe flow of air for several positions downstream of the inlet. The air Reynolds number was 25,000. The mathematical formulation of this problem involves the Navier-Stokes equations and the mass transfer equation with a boundary condition of constant concentration at the wall. No attempt has been made toward an analytical solution of this problem, as the exact solution of the turbulence problem has not been developed. Instead, values of the mass and momentum transfer correlation, urh, and urux, have been computed as a function of the radius. The eddy diffusivity for momentum and mass and the local mass transfer rates are shown for engineering purposes.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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  • 55
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 94-100 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: An apparatus for the determination of relative permeability under simulated reservoir conditions has been designed, constructed, and operated successfully. Complete water-oil relative-permeability data, with kerosene and simulated reservoir brine have been taken on four natural-sandstone cores at fluid pressures to 5,000 1b./sq. in. and overburden pressures to 10,000 1b./sq. in. One run was made at low pressure at a temperature of 160°F. for comparison with the results at low temperature. The apparatus is now being expanded so that gas-oil relative-permeability data may be taken, and crude oil containing gas in solution may be employed as the oil phase.The results indicate that essentially the same water-oil relative-permeability data are obtained at fluid pressures of 5,000 1b./sq. in. as at 30 1b./sq. in. gauge. The application of overburden pressure causes a reduction in both water and oil effective permeability in about the same proportion as it affects the single-phase permeability. Consequently the calculated relative permeabilities are affected to only a moderate extent. The results of the one run at 160°F. were in good agreement with the values obtained at room temperature.
    Zusätzliches Material: 15 Ill.
    Materialart: Digitale Medien
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  • 56
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 107-112 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Although vacuum crystallizers are used widely, crystal-size-control methods have not been adequately analyzed. This paper supplies in part the deficiency of technical information on this problem. Industrial crystallizers may have inherent nucleation rates in excess of or below the seed-crystal requirement for the desired product-crystal size. This paper deals specifically with means of crystal-size control by removal of excess nuclei from mixed circulating suspensions as encountered in vacuum crystallizers. It is shown that under certain conditions the cumulative size distribution in the suspension varies as the fourth power of the size. Therefore, it may also be shown that the key to effective size-control procedures is the segregation time of nuclei in the fines-removal system. Procedures based mainly on crystal-size classification by hydraulic elutriation can hardly be effective unless they are also designed to meet the segregation-time requirements.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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  • 57
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 127-138 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 20 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 58
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 113-117 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Extension of the understanding of properties of films of metals produced on glass surfaces by vacuum evaporation has permitted the fabrication of film-resistance thermometers that with simple instrumentation accurately measure surface or average surface temperatures without altering the geography of that surface. Formerly unknown and unstabled related properties of such films have been classified and may be anticipated or eliminated by recommended experimental procedures. Films of several of the most chemically inert and refractory metals 300 to 3,000 Å. thick have been shown to attain accuracies as high as 0.01°C. for practical periods of time. Their use, which is described, is developing satisfactorily, and the technique and equipment for their preparation are relatively simple.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 59
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 139-139 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 60
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956) 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 61
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 139-140 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 62
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: In this paper extensive calculations on the quasi isothermal tubular reactor are presented. Temperature and concentration profiles were obtained on an analogue computer (R.E.A.C.). The calculations tend to show that there are regions of operation in which the reactor effluent is very sensitive to operating conditions. For example, it is shown that in some regions of operation a small change in the heat transfer coefficient at the reactor wall or a small dilution of the feed will produce large changes in the effluent. In such cases the reactor is said to exhibit parametric sensitivity. It is shown analytically that this sensitivity may be predicted by analyzing the frequency response or transient response of the reactor approximated by a local linearization. This linearization requires complete solutions of the steady state problem. Semiquantitative results are then obtained for the regulation required from a given specification of product limits. The frequency-response analysis should be useful in connection with the control problem.If the reactor is fed partially with a recycle stream, then experience with electrical systems indicates that the possibility of instability exists. It is shown that at least theoretically these instabilities do exist, and a method based on the transfer function is developed for derivation of criteria of stability or instability.
    Zusätzliches Material: 14 Ill.
    Materialart: Digitale Medien
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  • 63
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 64
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 141-141 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 65
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 163-168 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The liquid-metal-fuel reactor under development at the Brookhaven National Laboratory uses a fuel which is a solution of U233, Mg, and Zr in liquid bismuth. For a power breeder thermal reactor, high neutron economy is essential, and this calls for low concentrations of those fission products in the fuel which are high neutron capturers. Roughly 45% by weight of the fission products can be continuously removed from the fuel by salt extraction with alkali and alkaline-earth fused-salt mixtures. These fission products contain the highly “poisonous” rare earths. This paper will present a discussion of processdesign considerations and proposed flow sheets.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 66
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 177-183 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Knowledge of local heating rates is needed for estimation of operating temperatures, thermal stresses, and cooling requirements in nuclear reactor components. Heat is liberated by the dissipation of the energy of fission fragments, beta particles, fast neutrons, and gamma photons. Heating rates are formulated in terms of either neutron or gamma flux densities, the corresponding collision probabilities, and appropriate energy transfer coefficients, the forms of which are given. Special methods of estimating the flux densities are discussed. The data on the magnitudes of the various energy sources are reviewed.
    Zusätzliches Material: 2 Tab.
    Materialart: Digitale Medien
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  • 67
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 184-189 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The rate of mass transfer was measured for solid metal shapes dissolving into mercury at room temperature. Sherwood numbers for horizontal tin, cadmium, zinc, and lead cylinders dissolving by natural convection agreed with Nusselt numbers for heat transfer in nonmetallic liquids at the same Rayleigh (Grashof × Prandtl) numbers. Dissolving of zinc tubes by mercury flowing turbulently within them agreed with heat transfer to nonmetals in tubes. Dissolving of random beds of lead spheres by mercury flowing through the bed agreed with similar nonmetal systems. It is concluded that mass transfer processes in liquid metals follow substantially the correlations for other fluids in heat or mass transfer, which with moderate safey factors may thus be used for at least preliminary design purposes.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
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  • 68
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 190-194 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Extensive pilot plant studies of the continuous, mercury-catalyzed nitric acid dissolution of uranium-aluminum alloy materials similar to possible reactor fuel elements were carried out. Marked differences were observed in the dissolution rates of cast and wrought alloys. Optimum feed-acid concentrations varied with the type of alloy. At constant acid feed conditions dissolving rates varied approximately with the cube root of catalyst concentration up to a limiting concentration. The metal dissolving rate was proportional to the 0.8 power of the nitric acid feed rate. A general empirical correlation was developed.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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  • 69
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 195-198 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Diffusion rates of uranium through graphite were determined in the temperature range of 3,000° to 4,350°F. The diffusion couples consisted of sintered UC2 disks in contact with graphite rods. The observations indicated two distinct types of uranium transport which could be associated with volume diffusion and with migration along pores respectively.Volume diffusion was characterized by steep concentration gradients and shallow penetration. The diffusion coefficient Dv, in sq. cm./sec. between 3,300° and 4,250°F., is given by an equation. Above 4,250°F. incipient melting of the UC2 was evident and the diffusion coefficients were much higher than those given by the equation.As an example of the penetration resulting from volume diffusion, calculations show that, after 1,000 hr. at 4,200°F. the uranium concentration at 0.1 cm. from the interface will be 1,000 mg./cc., compared with 10,000 mg./cc. for pure UC2.Pore migration resulted in uranium penetration far beyond that arising from volume diffusion at equivalent temperatures and diffusion times. However, uranium concentrations were very small compared with those corresponding to volume diffusion. Pore migration is strongly temperature dependent.To estimate the practical importance of pore migration, the uranium flow through a graphite wall at 3,000°F. was measured. With a wall thickness of 0.32 cm., the average flow per unit area was 0.015 mg./ (sq. cm.)/ (hr.) for a 40-hr. test.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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  • 70
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 199-205 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The coolant flow distribution among parallel tubes in a nuclear reactor (or boiler or heat exchanger) can be very sensitive to variations in heat input, dimensions, etc. Analytical expressions are given for partial derivatives which measure flow variations for several situations. The utility of orifices and valves in reducing flow sensitivity is discussed. Numerical results are reported for a system using water at supercritical pressurs with an eightfold expansion from inlet to outlet.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
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  • 71
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 271-272 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A method, based upon the pertinent flat-plate heat transfer equation, is presented for computing the local heat transfer coefficients for a boundary layer subjected to streamwise velocity and pressure gradients. No extensive mathematical background is required as the complexity of a rigorous solution for this type of problem is avoided. The validity of the method for gases is demonstrated by comparison of the predicted coeffcients with the experimental data for two widely different problems.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
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  • 72
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 264-270 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The effect of chemical reaction on plate efficiency has been given little attention in the determination of bubble-plate efficiencies, although it is of importance in many operations. A typical example is the absorption of carbon dioxide in monoetnanolamine solutions.The over-all Murphree gas-phase plate efficiency can be shown to be a function of Kg(A/V) where A/V is the interfacial surface area formed per tray per unit volume of gas. In order to evaluate variations in tray efficiency due to factors influencing Kg, data available in the literature for the absorption of carbon dioxide in monoethanolamine were considered. These showed that the liquid film was controlling and that for a packed column at constant liquid rate the absorption coefficient could be satisfactorily expressed by an equation that resembles somewhat equations which have been developed for the effect of rapid secondorder reactions on kL. However, the observed effect of carbon dioxide partial pressure in the gas is not so great as the theoretical equations would predict.By use of the equation mentioned above to predict Kg, satisfactory correlation of observed plate efficiencies is obtained for a commercial column over a considerable range of conditions. It appears that the correlation can be extended to other pressures, flow rates, and column designs by an evaluation of the effect of these variables on A/V and Kg.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
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  • 73
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 277-279 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The various forms of Bernoulli's equation as customarily written express static pressure energy in terms of absolute pressure, thereby restricting their direct application to systems situated in vacuo. It is shown here that recognition (1) of the universal presence of a fluid outside all systems over which Bernoulli's equation is written, and (2) of the practical necessity of measuring pressure within such systems as gauge pressures relative to the pressure of the exterior fluid leads to a more general set of equations and to a concept of buoyant static pressure and potential energies, as opposed to strictly abslute values.Failure properly to distinguish between these two types of energy quantities may result in error and confusion in the application of the various forms of Bernoulli's equation.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
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  • 74
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 18J 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 75
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 20J 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 76
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956) 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 77
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 21J 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 78
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 20J 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 79
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 281-281 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 80
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 23 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 81
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 290-295 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Three viscosity correlations were tested for liquids at their boiling points. Compounds studied included normal paraffins, branched-chain hydrocarbons, aromatics, halogenated methanes and ethanes, water, and aliphatic alcohols. The correlations were tested for the most part with viscosity and thermodynamic data found in the literature. Some experimental viscosity measurements were made, however, for normal paraffins from pentane to octane at temperatures up to about 300°F., which is higher than has previously been reported.Two correlations are based on Eyring's theory of absolute reaction rates. The third is based on the compressibility factor of the saturated liquid, and this correlation is unique, as all available data for normal paraffins with eight or more carbon atoms are represented by a single curve. The three correlations presented here can be used to extrapolate viscosity data over large temperature ranges up to the critical temperature. Logical predictions of the viscosities of related compounds are possible.
    Zusätzliches Material: 7 Ill.
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  • 82
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 337-342 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Air bubbles were formed in water and in mineral oil by use of single, circular, horizontal, square-edged orifices facing upward. Twenty orifices were tested, ranging from 0.017 to 0.79 cm. (0.0067 to 0.31 in.) in radius. Incieasms the whime, of the gas chamber below the orifice (over the range of 4 to 4,000 cc.) was found to increase the bubble size. The gas-chamber volume was minimized in most of the work in order to confine attention to the effects of orifice size and gas-flow rate. The liquid containers were large enough to eliminate significant wall effects, and operations were conducted at atmospheric pressure.The gas-flow rate was varised from about 0.01 to about 250 cc./sec. over the course of the work. At relatively low rates, the orifices generally formed single “static” bubbles, the volumes of which were proportional to the surface tension and orifice radius and independent of the gas-flow rate. At high flow rates the bubble frequency became high and the bubble volume became proportional to the gas-flow rate and independent of the surface tension. The bubble frequency reached a maximum value for each orifice, this value being a function of the orifice radius. For air bubbles in water, the correlation of the maximum bubble frequency, nm bubbles/sec., with the orifice radius, r cm., and the air-flow rate, q cc./sec., was found to be nm = 9.1q0.13/r0.43. The maximum frequencies ranged from about 25 bubbles/sec. for the largest orifices to about 75 bubbles/sec. for the smallest orifices used.It was found that consecutive bubbles paired or coalesced in definite ways in certain ranges of the gas-flow rate. A description is given of this bubble behavior, based on stroboscopic and photographic observation.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
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  • 83
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 343-347 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A method of estimating enthalpies of mixtures of light hydrocarbons is presented. Enthalpes so obtained are consistent with equilibrium-vaporization constants that have been correlated with the composition characterization factor, the molal average boiling point (M.A.B.P.).Values of the isothermal-pressure corrections to the enthalpy of ideal gas mixtures (H° — H) are presented on three plots with parameters of temperature, pressure, and molal-average boiling point. Pressures range from zero to 1,500 lb./sq. in. abs., temperatures from -200° to 500°F., and M.A.B.P. from -200° to 150°F.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 84
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 347-353 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: A rigorous analysis of the available data presented in the literature for all the saturated aliphatic hydrocarbons from methane through n-eicosane was conducted to establish the constants A, B, C, and D of the vapor-pressure equation developed by Frost and Kalkwarf (21). With all the constants determined, vapor pressures can be calculated accurately from the triple to the critical point. The actual constants A, B, C, and D have been calculated from the available reported vapor-pressure data of eighty-seven saturated aliphatic hydrocarbons and include all the normal paraffins through eicosane and all the isomeric paraffins through the nonanes.In order to ascertain the validity of calculated-vapor-pressure constants, values of A, B, C, and D were produced from the molecular structure and normal boiling point for all the normal paraffins through eicosane and all the thirty-four isomeric nonanes. The normal paraffins were selected to cover the range of the saturated aliphatic hydrocarbons; whereas the nonanes were chosen because they represent the most complex structures for which reported vapor pressures are available.With the calculated constants, vapor pressures were evaluated from the equation at several representative points and were compared with reported values to produce an overall absolute average percentage of deviation of 0.58 for the normal paraffins and 0.73 for the isomeric nonanes, or 0.68 for these fifty-four saturated aliphatic hydrocarbons.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
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  • 85
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 389-392 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: By use of saturated-vapor enthalpies determined by accepted procedures in conjunction with differential latent heats of condensation, the saturated-liquid enthalpies are established for the system methane-ethane at 200, 400, and 600 lb./sq. in. abs. and for the system ethane-n-butane and propane-n-butane at the two lower pressures. Where comparison is possible, the liquid-enthalpy values obtained by this method are in general agreement with those previously determined by Edmister and Canjar. The procedure used is thermodynamically rigorous and may be applied to any binary mixture, provided the Benedict-Rubin-Webb equation of state is valid in the vapor phase and P-V-T-x data are available.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
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  • 86
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 393-403 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 87
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 426-427 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 88
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 11S 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 89
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 90
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 12S 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 91
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 92
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 529-535 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: This investigation was undertaken to show how the efficiency of solute transfer between two immiscible liquids is influenced by the type, size, and submergence and rotational speed of the impeller and the degree of baffling, residence time, and phase ratio. The system water-kerosene-n-butylamine solute was agitated in a continuous-flow 14 3/4-in. -diam. vessel using propellers, spiral turbines, and flat-blade turbines from 4 to 10 in. in diameter. The feed streams were introduced at the wall at the bottom of the vessel and left at the top of the vessel.On the basis of the power required for a given level of stage efficiency, the best agitator design is any impeller that has a diameter about 40% of the vessel diameter and is centered in the unbaffled vessel. Without baffles the impeller type and depth of submergence have little effect on performance. The power increase required by the addition of baffles is small at the highest stage efficiencies, especially with the larger radial-flow impellers, but may be severalfold at efficiency levels of 70 to 90%. This presumably results from the lowered mass transfer driving force caused by the increase in end-to-end mixing due to wall baffles. Whether baffles have such a large adverse effect if the feed is introduced into the impeller rather than at the vessel wall is not fully established, but there is some evidence that baffling is also undesirable in this case. For baffled operation, impeller type and submergence do affect performance.A correlation of stage efficiency is presented in terms of Reynolds number and power number. In addition, energy input per volume of total flow is correlated in terms of residence time and stage efficiency for one size of baffled propeller.Spot samples taken from the vessel showed large, random-concentration fluctuations out to 20 residence times and perhaps indefinitely. Reproducible results were obtained by taking time-averaged samples.
    Zusätzliches Material: 13 Ill.
    Materialart: Digitale Medien
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  • 93
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 545-551 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Liquid-liquid phase separation and mass transfer studies were made in a 4-in.-diam. cyclone of conventional construction. The cyclone was tested with oil-water volume phase ratios ranging from values of 1/3 to 9/1 and for total flows up to 24 gal./min., although most variables were studied at a feed rate of 10 gal./min. Kerosene or a white oil (vis. 9 centipoises at 77°F.) was used as the oil phase. Valve or line premixing was used to disperse the feed. Valve pressure drops were in the range of 0.1 to 1.0 lb./sq.in., and inlet drop sizes, where determined, were about 1 mm. The optimum cyclone geometry (volume, diameter of inlet, overflow and underflow lines) and the optimum split (overflow/underflow) were determined in terms of a phase-separation efficiency Es.At optimum geometry and split a number of mass transfer runs were made in which monobutylamine solute was transferred from the kerosene to the water phase. These runs indicated that Es decreased but mass transfer efficiency increased as the feed rate or pressure drop across the mixing valve was increased.
    Zusätzliches Material: 16 Ill.
    Materialart: Digitale Medien
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  • 94
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 552-554 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: By use of Cp values from the literature and experimentally determined vapor-pressure-temperature and pressure-volume-temperature relationships, a thermodynamic network has been established for tertiary butyl alcohol in the range of 78° to 500°F. and 14.7 to 700 lb./sq. in. abs. The results include tabulated values of p, v, T, H, S, f, and Z, as well as the vapor-pressure-temperature curve, the critical properties, and constants for the Beattie-Bridgeman equation.The original pressure data were accurate to within 0.14% in the high range and to within 4% in the low range. The limits on the experimental volume data were 0.07% for large vapor volumes and 2% for liquid volumes. The temperature was determined to within 0.1 °F., or less than 0.02% of the absolute temperature.Experimentally determined vapor pressures were found to be lower than those reported in the literature in the range above 1 atm. Values previously reported were obtained by extrapolation of a vapor-pressure-temperature relation developed for use at subatmospheric pressures. For pressures below 1 atm. the experimental values agreed with the reported values.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 95
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 555-560 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: This paper describes an investigation of the factors affecting the change in composition with vaporization of a binary-component spray in heated air at atmospheric pressure. The behavior of the system orthodichlorobenzene-tetrachloroethylene was studied in air ranging from 400° to 1,000°F. Initial drop diameters in the sprays were in the 20- to 400-µ range. The experimental data obtained indicated that the rate of change of spray composition during vaporization was affected only by the chamber-air temperature, the initial feed composition, and the nozzle characteristics.Equations are presented which mathematically describe the vaporization process, liquid diffusion being assumed within the drop controls. These equations have been solved by a stepwise procedure for three initial drop sizes. Results of these calculations have been added statistically according to the initial-drop-size distribution in order to predict the vaporization behavior of the spray. Details of this process of statistical combination have been summarized by Culverwell (1).The calculations agreed with the experimental data previously obtained during the first 5 in. of nozzle-to-tray travel. After 5 in. the deviation was great. Future experimental work to determine more precise values of drop-size distribution, initial drop velocity, and liquid diffusion coefficient may result in more complete agreement.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 96
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 560-567 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The production of oil and gas by pressure depletion involves both the formation of bubbles and the diffusion of gas from the liquid phase into these bubbles. Studies were undertaken to outline in detail the process of bubble formation when the driving force is small. This work shows that the formation of bubbles is a random process which can, however, be described by a simple probability distribution function. Also, calculations have been made to determine how fast gas will diffuse into uniformly distributed gas bubbles.These results make it possible to describe the manner in which a gas phase is established during the pressure depletion process. In this process the rate of pressure decline is the most important factor influencing the total number of bubbles produced. Laboratory tests have substantiated the finding that in certain types of porous media the amount of oil recovered is sensitive to the number of bubbles formed.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 97
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 568-571 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: Experimental data are reported for the ignition of single grains of solid propellant in a stream of gas at high temperature. The investigation encompassed gas temperatures from 578° to 1,070°K., gas velocities corresponding to free-stream Reynolds numbers from 156 to 624, a complete range of oxygen-nitrogen mixtures, and a few oxygen-carbon dioxide mixtures. Pyrocellulose and double-base propellants were tested. The grains were approximately 1/8 in. in diameter and extended through the gas stream, so that ignition was forced to take place on the cylindrical surface rather than on the end of the grain. The exposure before ignition was measured for a large number of grains. The data can be represented by an equation that is consistent with the known effect of flow rate on convective heat transfer and the known effect of temperature on chemical reaction rates, an indication that both processes are important in ignition.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 98
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 572-573 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: The reactor-unit concept proposed by Hurt is extended in this paper to include fractional-order reactions and to show the effect of volume change on the system. Equations defining the reactor unit for homogeneous and heterogeneous reactions are derived.The catalytic dehydration of tertiary butanol was chosen as a means of studying the validity of the extended reactor-unit concept. The experimental investigation was conducted over a wide range of flow rates, catalyst bed heights, and temperatures. The result of the application of this modified reactor-unit expression to the correlation of the data was excellent.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 99
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 100
    Digitale Medien
    Digitale Medien
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 2 (1956), S. 577 
    ISSN: 0001-1541
    Schlagwort(e): Chemistry ; Chemical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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