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  • 1
    Publication Date: 2020-08-05
    Description: We consider an auction of slots to run trains through a railway network. In contrast to the classical setting for combinatorial auctions, there is not only competition for slots, but slots can mutually exclude each other, such that general conflict constraints on bids arise. This turns the winner determination problem associated with such an auction into a complex combinatorial optimization problem. It also raises a number of auction design questions, in particular, on incentive compatibilty. We propose a single-shot second price auction for railway slots, the Vickrey Track Auction (VTA). We show that this auction is incentive compatible, i.e., rational bidders are always motivated to bid their true valuation, and that it produces efficient allocations, even in the presence of constraints on allocations. These properties are, however, lost when rules on the submission of bids such as, e.g., lowest bids, are imposed. Our results carry over to generalized" Vickrey auctions with combinatorial constraints.
    Keywords: ddc:000
    Language: English
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  • 2
    Publication Date: 2020-08-05
    Description: Technical restrictions and challenging details let railway traffic become one of the most complex transportation systems. Routing trains in a conflict-free way through a track network is one of the basic scheduling problems for any railway company. This article focuses on a robust extension of this problem, also known as train timetabling problem (TTP), which consists in finding a schedule, a conflict free set of train routes, of maximum value for a given railway network. However, timetables are not only required to be profitable. Railway companies are also interested in reliable and robust solutions. Intuitively, we expect a more robust track allocation to be one where disruptions arising from delays are less likely to be propagated causing delays of subsequent trains. This trade-off between an efficient use of railway infrastructure and the prospects of recovery leads us to a bi-criteria optimization approach. On the one hand we want to maximize the profit of a schedule, that is more or less to maximize the number of feasible routed trains. On the other hand if two trains are scheduled as tight as possible after each other it is clear that a delay of the first one always affects the subsequent train. We present extensions of the integer programming formulation in [BorndoerferSchlechte2007] for solving (TTP). These models can incorporate both aspects, because of the additional track configuration variables. We discuss how these variables can directly be used to measure a certain type of robustness of a timetable. For these models which can be solved by column generation techniques, we propose so-called scalarization techniques, see [Ehrgott2005], to determine efficient solutions. Here, an efficient solution is one which does not allow any improvement in profit and robustness at the same time. We prove that the LP-relaxation of the (TTP) including an additional $\epsilon$-constraint remains solvable in polynomial time. Finally, we present some preliminary results on macroscopic real-world data of a part of the German long distance railway network.
    Keywords: ddc:000
    Language: English
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  • 3
    Publication Date: 2016-06-30
    Description: The latest machine generation installed at supercomputer centres in Germany offers a peak performance in the tens of Tflop/s range. We study performance and scaling of our quantum chromodynamics simulation programme BQCD that we obtained on two of these machines, an IBM Blue Gene/L and an SGI Altix 4700. We compare the performance of Fortran/MPI code with assembler code. The latter allows to exploit concurrency at more levels, in particular in overlapping communication and computation as well as prefetching data from main memory.
    Keywords: ddc:000
    Language: English
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  • 4
    Publication Date: 2016-06-09
    Description: We study the optimal control of a maximum-norm objective functional subject to an elliptic-type PDE and pointwise state constraints. The problem is transformed into a problem where the non-differentiable L^{\infty}-norm in the functional will be replaced by a scalar variable and additional state constraints. This problem is solved by barrier methods. We will show the existence and convergence of the central path for a class of barrier functions. Numerical experiments complete the presentation.
    Keywords: ddc:000
    Language: English
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  • 5
    Publication Date: 2020-11-16
    Description: Der Artikel gibt einen Einblick in das reiche Feld der Zusammenarbeit zwischen Mathematik und Medizin. Beispielhaft werden drei Erfolgsmodelle dargestellt: Medizinische Bildgebung, mathematische Modellierung und Biosignalverarbeitung im Bereich der Dynamik des Herzens sowie mathematische Modellierung und Simulation in der Krebstherapie Hyperthermie und der Mund-Kiefer-Gesichts-Chirurgie. In allen Fällen existiert ein Gleichklang der Interessen von Medizin und Mathematik: Beide Disziplinen wollen die Resultate schnell und zuverlässig. Für die Klinik heißt das, dass notwendige Rechnungen in möglichst kurzer Zeit, und zwar auf dem PC, ablaufen müssen und dass die Resultate so genau und belastbar sein müssen, dass medizinische Entscheidungen darauf aufbauen können. Für die Mathematik folgt daraus, dass höchste Anforderungen an die Effizienz der verwendeten Algorithmen und die darauf aufbauende Software in Numerik und Visualisierung zu stellen sind. Jedes Kapitel endet mit einer Darstellung der Perspektive des jeweiligen Gebietes. Abschließend werden mögliche Handlungsoptionen für Politik und Wirtschaft diskutiert.
    Keywords: ddc:000
    Language: German
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  • 6
    Publication Date: 2022-03-14
    Description: 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 for solving satisfiability problems. SCIP is available in source code and free for noncommercial use. We demonstrate the usefulness of CIP on three 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 demonstrate how to use CIP techniques to compute the number of optimal solutions of integer programs. Third, we employ the CIP framework to solve chip design verification problems, which involve some highly nonlinear 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 nonlinear constraints by employing constraint programming techniques.
    Keywords: ddc:000
    Language: English
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  • 7
    Publication Date: 2022-04-11
    Description: Mit dem Informationsdienst Math&Industry soll ein Prototyp eines dezentralen Informationssystems für Förderprogramme und Forschungsprojekte geschaffen werden, das sich auf andere Programme (bezüglich angewandter Mathematik, aber auch darüber hinaus) übertragen lässt. Das betrifft sowohl die Konzeption (Strukturierung der Informationen) als auch die Werkzeuge, die anderen BMBF-Förderprogrammen zur Verfügung gestellt werden können. Damit sollen diese in die Lage versetzt werden, die in Math&Industry entwickelten Konzepte und Werkzeuge an ihre spezifischen Bedürfnisse anzupassen.
    Keywords: ddc:000
    Language: German
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  • 8
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    Publication Date: 2019-10-24
    Keywords: ddc:000
    Language: German
    Type: annualzib , doc-type:report
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  • 9
    Publication Date: 2014-02-26
    Description: We propose a variant of the control reduced interior point method for the solution of state constrained problems. We show convergence of the corresponding interior point pathfollowing algorithm in function space. Morever, we provide error bounds for the iterates.
    Keywords: ddc:000
    Language: English
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  • 10
    Publication Date: 2014-02-26
    Description: This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper.
    Keywords: ddc:000
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  • 11
    Publication Date: 2014-02-26
    Description: This work explores two applications of a classical result on the continuity of Nemyckii operators to optimal control with PDEs. First, we present an alternative approach to the analysis of Newton's method for function space problems involving semi-smooth Nemyckii operators. A concise proof for superlinear convergence is presented, and sharpened bounds on the rate of convergence are derived. Second, we derive second order sufficient conditions for problems, where the underlying PDE has poor regularity properties. We point out that the analytical structure in both topics is essentially the same.
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    Language: English
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  • 12
    Publication Date: 2014-02-26
    Description: In this paper, we study the efficiency of Nash equilibria for a sequence of nonatomic routing games. We assume that the games are played consecutively in time in an online fashion: by the time of playing game $i$, future games $i+1,\dots,n$ are not known, and, once players of game $i$ are in equilibrium, their corresponding strategies and costs remain fixed. Given a sequence of games, the cost for the sequence of Nash equilibria is defined as the sum of the cost of each game. We analyze the efficiency of a sequence of Nash equilibria in terms of competitive analysis arising in the online optimization field. Our main result states that the online algorithm $\sl {SeqNash}$ consisting of the sequence of Nash equilibria is $\frac{4n}{2+n}$-competitive for affine linear latency functions. For $n=1$, this result contains the bound on the price of anarchy of $\frac{4}{3}$ for affine linear latency functions of Roughgarden and Tardos [2002] as a special case. Furthermore, we analyze a problem variant with a modified cost function that reflects the total congestion cost, when all games have been played. In this case, we prove an upper bound of $\frac{4n}{2+n}$ on the competitive ratio of $\sl {SeqNash}$. We further prove a lower bound of $\frac{3n-2}{n}$ of $\sl {SeqNash}$ showing that for $n=2$ our upper bound is tight.
    Keywords: ddc:000
    Language: English
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  • 13
    Publication Date: 2016-06-09
    Description: To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing $N$ steps requires only $O(N\log N)$ operations and $O(\log N)$ active memory, in place of $O(N^2)$ operations and $O(N)$ memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differential equations which are solved numerically with adaptive step sizes. Rather than the kernel itself, its Laplace transform is used in the algorithm. The algorithm is illustrated on three examples: a blow-up example originating from a Schrödinger equation with concentrated nonlinearity, chemical reactions with inhibited diffusion, and viscoelasticity with a fractional order constitutive law.
    Keywords: ddc:000
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  • 14
    Publication Date: 2020-11-13
    Description: This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.
    Keywords: ddc:000
    Language: English
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  • 15
    Publication Date: 2019-05-10
    Description: The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle).
    Keywords: ddc:000
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  • 16
    Publication Date: 2020-12-15
    Description: The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branch-and-cut tree. We present a general tool, called orbitopal fixing, for enhancing the capabilities of branch-and-cut algorithms in solving this kind of symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the branch-and-cut tree, removes redundant parts of the tree produced by the above mentioned permutations. The method relies on certain polyhedra, called orbitopes, which have been investigated in (Kaibel and Pfetsch (2006)). However, it does not add inequalities to the model, and thus, it does not increase the difficulty of solving the linear programming relaxations. We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem motivated from frequency planning in mobile telecommunication networks.
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    Language: English
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  • 17
    Publication Date: 2014-11-10
    Description: In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph $D=(V,A)$ and a set $K$ of directed commodities, an USPR is a set of flow paths $\Phi_{(s,t)}$, $(s,t)\in K$, such that there exists a metric $\lambda=(\lambda_a)\in \mathbb{Z}^A_+$ with respect to which each $\Phi_{(s,t)}$ is the unique shortest $(s,t)$-path. In the \textsc{Min-Con-USPR} problem, we seek for an USPR that minimizes the maximum congestion over all arcs. We show that this problem is hard to approximate within a factor of $\mathcal{O}(|V|^{1-\epsilon})$, but easily approximable within min$(|A|,|K|)$ in general and within $\mathcal{O}(1)$ if the underlying graph is an undirected cycle or a bidirected ring. We also construct examples where the minimum congestion that can be obtained by USPR is a factor of $\Omega(|V|^2)$ larger than that achievable by unsplittable flow routing or by shortest multi-path routing, and a factor of $\Omega(|V|)$ larger than by unsplittable source-invariant routing. In the CAP-USPR problem, we seek for a minimum cost installation of integer arc capacities that admit an USPR of the given commodities. We prove that this problem is $\mathcal{NP}$-hard to approximate within $2-\epsilon$ (even in the undirected case), and we devise approximation algorithms for various special cases. The fixed charge network design problem \textsc{Cap-USPR}, where the task is to find a minimum cost subgraph of $D$ whose fixed arc capacities admit an USPR of the commodities, is shown to be $\mathcal{NPO}$-complete. All three problems are of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Our results indicate that they are harder than the corresponding unsplittable flow or shortest multi-path routing problems.
    Keywords: ddc:000
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  • 18
    Publication Date: 2014-11-11
    Description: In this paper, we investigate the connection availabilities for the new protection scheme Demand-wise Shared Protection (DSP) and describe an appropriate approach for their computation. The exemplary case study on two realistic network scenarios shows that in most cases the availabilities for DSP are comparable with that for 1+1 path protection and better than in case of shared path protection.
    Keywords: ddc:000
    Language: English
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  • 19
    Publication Date: 2016-06-30
    Description: THESEUS, the ZIB threading environment, is a parallel implementation of a protein threading based on a multi-queued branch-and-bound optimal search algorithm to find the best sequence-to-structure alignment through a library of template structures. THESEUS uses a template core model based on secondary structure definition and a scoring function based on knowledge-based potentials reflecting pairwise interactions and the chemical environment, as well as pseudo energies for homology detection, loop alignment, and secondary structure matching. The threading core is implemented in C++ as a SPMD parallization architecture using MPI for communication. The environment is designed for generic testing of different scoring functions, e.g. different secondary structure prediction terms, different scoring matrices and information derived from multiple sequence alignments. A validaton of the structure prediction results has been done on the basis of standard threading benchmark sets. THESEUS successfully participated in the 6th Critical Assessment of Techniques for Protein Structure Prediction (CASP) 2004.
    Keywords: ddc:000
    Language: English
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  • 20
    Publication Date: 2014-02-26
    Description: We consider a multi-queue multi-server system with $n$ servers (processors) and $m$ queues. At the system there arrives a stationary and ergodic stream of $m$ different types of requests with service requirements which are served according to the following $k$-limited head of the line processor sharing discipline: The first $k$ requests at the head of the $m$ queues are served in processor sharing by the $n$ processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes' monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the $m$ separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of $n$=$k$=1.
    Keywords: ddc:000
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  • 21
    Publication Date: 2014-02-26
    Description: In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled.
    Keywords: ddc:000
    Language: English
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  • 22
    Publication Date: 2020-02-11
    Description: "`Volkssport Sudoku"' titelt der Stern in seiner Ausgabe vom 24. Mai2006. In der Tat traut sich derzeit kaum noch eine Zeitung, ohne Sudoku zu erscheinen. Die Begeisterung am Lösen dieser Zahlenrätsel offenbart eine unvermutete Freude am algorithmischen Arbeiten. Mathematisch kann man Sudokus als lineare diophantische Gleichungssysteme mit Nichtnegativitätsbedingungen formulieren. Solche ganzzahligen linearen Programme sind die wichtigsten Modellierungswerkzeuge in zahlreichen Anwendungsgebieten wie z.B. der Optimierung von Telekommunikations- und Verkehrsnetzen. Moderne Verfahren zur Lösung dieser Optimierungsprobleme sind durch Sudokus allerdings deutlich weniger zu beeindrucken als Zeitungsleser.
    Keywords: ddc:000
    Language: German
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  • 23
    Publication Date: 2020-02-11
    Description: This article surveys mathematical models and methods used for physical PCB layout, i.e., component placement and wire routing. The main concepts are briefly described together with relevant references.
    Keywords: ddc:000
    Language: English
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  • 24
    Publication Date: 2020-12-15
    Description: We study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. Arcs are equipped with load dependent price functions defining the routing weights. We discuss an online algorithm that routes each commodity by minimizing a convex cost function that depends on the demands that are previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is $4K/2+K$-competitive, where $K$ is the number of commodities. For the parallel arc case this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.
    Keywords: ddc:000
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  • 25
    Publication Date: 2021-03-16
    Description: Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations w.r.t different concepts. Perfect graphs are, e.g., characterized as precisely those graphs $G$ where the stable set polytope STAB$(G)$ coincides with the clique constraint stable set polytope QSTAB$(G)$. For all imperfect graphs STAB$(G) \subset$ QSTAB$(G)$ holds and, therefore, it is natural to measure imperfection in terms of the difference between STAB$(G)$ and QSTAB$(G)$. Several concepts have been developed in this direction, for instance the dilation ratio of STAB$(G)$ and QSTAB$(G)$ which is equivalent to the imperfection ratio imp$(G)$ of $G$. To determine imp$(G)$, both knowledge on the facets of STAB$(G)$ and the extreme points of QSTAB$(G)$ is required. The anti-blocking theory of polyhedra yields all {\em dominating} extreme points of QSTAB$(G)$, provided a complete description of the facets of STAB$(\overline G)$ is known. As this is typically not the case, we extend the result on anti-blocking polyhedra to a {\em complete} characterization of the extreme points of QSTAB$(G)$ by establishing a 1-1 correspondence to the facet-defining subgraphs of $\overline G$. We discuss several consequences, in particular, we give alternative proofs of several famous results.
    Keywords: ddc:000
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  • 26
    Publication Date: 2014-11-10
    Description: We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time $O^\ast(2^n)$. This algorithm is based on the old dynamic programming method introduced by Held and Karp for the {\sc Tra veling Salesman} problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. However, our experiments show that the space use d by the algorithm is an important factor to what input sizes the algorithm is effective. For this purpose, we settle the problem of computing treewidth under the restriction that the space used is only polynomial. In this direction we give a simple $O^\ast(4^n)$ al gorithm that requires {\em polynomial} space. We also show that with a more complicated algorithm, using balanced separators, {\sc Treewidth} can be computed in $O^\ast(2.9512^n)$ time and polynomial space.
    Keywords: ddc:000
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  • 27
    Publication Date: 2014-03-10
    Description: The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.
    Keywords: ddc:000
    Language: English
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  • 28
    Publication Date: 2014-02-26
    Description: Das deutschsprachige Bibliothekswesen verfügt mit den \glqq Regeln für den Schlagwortkatalog \grqq (RSWK) unter Verwendung der \glqq Schlagwortnormdatei \grqq (SWD) über ein Instrumentarium, welches zusammen mit einem \glqq Faceted Browsing \grqq das bisher bestehende Angebot für ein Information Retrieval optimal ergänzen kann. Die Verbindung zwischen Standardvokabular (SWD) und Kettenbildung (RSWK) einerseits und eine nach Facetten-Eigenschaften gegliederte Navigation andererseits unterstützt bestmöglich eine inhaltlich bezogene Recherche. Die Stärken und Schwächen der RSWK/SWD werden erörtert und auch Klassifikationen (DDC und RVK) als mögliche Facetten diskutiert.
    Keywords: ddc:000
    Language: German
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  • 29
    Publication Date: 2016-06-09
    Keywords: ddc:000
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 30
    Publication Date: 2022-03-14
    Description: A lot of problems arising in Combinatorial Optimization and Operations Research can be formulated as Mixed Integer Programs (MIP). Although MIP-solving is an NP-hard optimization problem, many practically relevant instances can be solved in reasonable time. In modern MIP-solvers like the branch-cut-and-price-framework SCIP, primal heuristics play a major role in finding and improving feasible solutions at the early steps of the solution process. This helps to reduce the overall computational effort, guides the remaining search process, and proves the feasibility of the MIP model. Furthermore, a heuristic solution with a small gap to optimality often is sufficient in practice. We investigate 16 different heuristics, all of which are available in SCIP. Four of them arise from the literature of the last decade, nine are specific implementations of general heuristic ideas, three have been newly developed. We present an improved version of the feasibility pump heuristic by Fischetti et al., which in experiments produced solutions with only a third of the optimality gap compared to the original version. Furthermore, we introduce two new Large Neighborhood Search (LNS) heuristics. Crossover is an LNS improvement heuristic making use of similarities of diverse MIP solutions to generate new incumbent solutions. RENS is an LNS rounding heuristic which evaluates the space of all possible roundings of a fractional LP-solution. This heuristic makes it possible to determine whether a point can be rounded to an integer solution and which is the best possible rounding. We conclude with a computational comparison of all described heuristics. It points out that a single heuristic on its own has only a slight impact on the overall performance of SCIP, but the combination of all of them reduces the running time by a factor of two compared to a version without any heuristics.
    Keywords: ddc:000
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 31
    Publication Date: 2014-02-26
    Description: We present a finite volume method for the solution of the two-dimensional Poisson equation $ \nabla\cdot( \beta( {\mbox{\boldmath $x$}}) \nabla u({\mbox{\boldmath $x$}})) = f(\mbox{\boldmath $x$}) $ with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution $u({\mbox{\boldmath $x$})$ resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the $L^\infty$ and $L^2$ norm.
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    Language: English
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  • 32
    Publication Date: 2014-11-11
    Description: In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.
    Keywords: ddc:000
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  • 33
    Publication Date: 2014-02-26
    Description: The concept of jump system, introduced by Buchet and Cunningham (1995), is a set of integer points with a certain exchange property. In this paper, we discuss several linear and convex optimization problems on jump systems and show that these problems can be solved in polynomial time under the assumption that a membership oracle for a jump system is available. We firstly present a polynomial-time implementation of the greedy algorithm for the minimization of a linear function. We then consider the minimization of a separable-convex function on a jump system, and propose the first polynomial-time algorithm for this problem. The algorithm is based on the domain reduction approach developed in Shioura (1998). We finally consider the concept of M-convex functions on constant-parity jump systems which has been recently proposed by Murota (2006). It is shown that the minimization of an M-convex function can be solved in polynomial time by the domain reduction approach.
    Keywords: ddc:000
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  • 34
    Publication Date: 2020-12-15
    Description: We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a well-known formulation of the graph coloring problem. We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group. Our main results are complete linear inequality descriptions of these polytopes by facet-defining inequalities. For the cyclic group case, the descriptions turn out to be totally unimodular, while for the symmetric group case, both the description and the proof are more involved. The associated separation problems can be solved in linear time.
    Keywords: ddc:000
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  • 35
    Publication Date: 2014-11-21
    Description: The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an $\varepsilon$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.
    Keywords: ddc:000
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  • 36
    Publication Date: 2014-11-21
    Description: Wir beschäftigen uns mit dem Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißnähten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden müssen. Die Schweißnähte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, für jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißnähte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie möglich eingesetzt werden. Dabei müssen einige Nebenbedingungen berücksichtigt werden. Für dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich für die untersuchten praktischen Fälle sehr schnell lösen lässt.
    Keywords: ddc:000
    Language: German
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  • 37
    Publication Date: 2021-08-05
    Description: Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.
    Keywords: ddc:000
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  • 38
    Publication Date: 2014-11-21
    Description: The Bottleneck Shortest Path Problem is a basic problem in network optimization. The goal is to determine the limiting capacity of any path between two specified vertices of the network. This is equivalent to determining the unsplittable maximum flow between the two vertices. In this note we analyze the complexity of the problem, its relation to the Shortest Path Problem, and the impact of the underlying machine/computation model.
    Keywords: ddc:000
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  • 39
    Publication Date: 2014-02-26
    Description: We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lov\´{a}sz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of highly connected, highly symmetric manifolds.
    Keywords: ddc:000
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  • 40
    Publication Date: 2014-02-26
    Description: We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.
    Keywords: ddc:000
    Language: English
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  • 41
    Publication Date: 2014-02-26
    Description: Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort.
    Keywords: ddc:000
    Language: English
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  • 42
    Publication Date: 2014-02-26
    Description: We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of this inverse problem. For relatively moderate assumptions on the constraint we can always prove weak convergence of the iterative scheme. In certain cases, i.e. for special families of convex constraints, weak convergence implies norm convergence. The presented approach covers a wide range of problems, e.g. Besov- or BV-restoration for which we present also numerical experiments in the context of image processing.
    Keywords: ddc:000
    Language: English
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  • 43
    Publication Date: 2014-03-10
    Description: Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.
    Keywords: ddc:000
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  • 44
    Publication Date: 2016-02-29
    Description: \noindent We give a partial description of the $(s,t)-p$-path polytope of a directed graph $D$ which is the convex hull of the incidence vectors of simple directed $(s,t)$-paths in $D$ of length $p$. First, we point out how the $(s,t)-p$-path polytope is located in the family of path and cycle polyhedra. Next, we give some classes of valid inequalities which are very similar to inequalities which are valid for the $p$-cycle polytope, that is, the convex hull of the incidence vectors of simple cycles of length $p$ in $D$. We give necessary and sufficient conditions for these inequalities to be facet defining. Furthermore, we consider a class of inequalities that has been identifie d to be valid for $(s,t)$-paths of cardinality at most $p$. Finally, we transfer the results to related polytopes, in particular, the undirected counterpart of the $(s,t)-p$-path polytope.
    Keywords: ddc:000
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  • 45
    Publication Date: 2020-11-13
    Description: The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional $L^2$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact).
    Keywords: ddc:000
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  • 46
    Publication Date: 2016-06-30
    Keywords: ddc:000
    Language: German
    Type: masterthesis , doc-type:masterThesis
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  • 47
    Publication Date: 2014-02-26
    Description: We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.
    Keywords: ddc:000
    Language: English
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  • 48
    Publication Date: 2014-02-26
    Description: The concept of L##-convexity is introduced by Fujishige--Murota (2000) as a discrete convexity for functions defined over the integer lattice. The main aim of this note is to understand the difference of the two algorithms for L##-convex function minimization: Murota's steepest descent algorithm (2003) and Kolmogorov's primal algorithm (2005).
    Keywords: ddc:000
    Language: English
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  • 49
    Publication Date: 2014-02-26
    Description: In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.
    Keywords: ddc:000
    Language: English
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  • 50
    Publication Date: 2020-02-11
    Description: This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most~8\% above a lower bound on optimal RMG utilization.
    Keywords: ddc:000
    Language: English
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  • 51
    Publication Date: 2014-02-26
    Description: We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices.
    Keywords: ddc:000
    Language: English
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  • 52
    Publication Date: 2014-02-26
    Description: We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.
    Keywords: ddc:000
    Language: English
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  • 53
    Publication Date: 2014-02-26
    Description: We give a complete enumeration of combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2 x S^1$ and 615 triangulations of the twisted sphere product $S^2 \underline{x} S^1$. An analysis of the 3-spheres with up to 10 vertices shows that all these spheres are shellable, but that there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.
    Keywords: ddc:000
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  • 54
    Publication Date: 2019-05-10
    Description: Adaptive numerical methods in time and space are introduced and studied for linear poroelastic models in two and three space dimensions. We present equivalent models for linear poroelasticity and choose both the {\em displacement--pressure} and the {\em stress--pressure} formulation for our computations. Their discretizations are provided by means of linearly implicit schemes in time and linear finite elements in space. Our concept of adaptivity opens a way to a fast and reliable simulation of different loading cases defined by corresponding boundary conditions. We present some examples using our code {\sf Kardos} and show that the method works efficiently. In particular, it could be used in the simulation of some bone healing models.
    Keywords: ddc:000
    Language: English
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  • 55
    Publication Date: 2016-06-30
    Description: During the last few years more and more functionalities of RNA have been discovered that were previously thought of being carried out by proteins alone. One of the most striking discoveries was the de tection of microRNAs, a class of noncoding RNAs that play an important role in post-transcriptional gene regulation. Large-scale analyses are needed for the still increasingly growing amount of sequen ce data derived from new experimental technologies. In this paper we present a framework for the detection of the distinctive precursor structure of microRNAS that is based on the well-known Smith-Wat erman algorithm and various filtering steps. We conducted experiments on real genomic data and we found several new putative hits for microRNA precursor structures.
    Keywords: ddc:000
    Language: English
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  • 56
    Publication Date: 2014-02-26
    Description: Wir erleben zu Beginn des aufkommenden Informationszeitalters mit dem Siegeszug von Google und anderen Internet-Technologien einen Wandel im Verhalten von Wissenschaftlern und Studenten, der mit dem Einsatz von {\sl Google Scholar} und {\sl Google Book Search} einen Paradigmenwechsel für Bibliotheken und Informationsversorger gleichkommt. Der Artikel untersucht die technischen Hintergründe für den Erfolg dieser besonderen Art des Information Retrievals: Fulltext Indexing und Citation Ranking als besondere Form des Information Minig. Er diskutiert Stärken und auch Schwächen des Google-Ansatzes. Der Autor stellt sich auch der Frage, unter welchen Bedingungen es möglich ist, ein zu {\sl Google Scholar} und der {\sl Google Book Search} konkurrenzfähiges Retrieval in der Landschaft der Bibliotheken und Bibliotheksverbünde zu entrichten. Die These ist, dass dieses unter Einsatz des {\sl Open Source} Indexierers {\sl Lucene} und des Web-Robots {\sl Nutch} möglich ist. Bibliotheken können durch gezielten Einsatz solcher Internet-Technologien dem Nutzer die Leistungen, welche Google uns mit seinen Tools im {\sl Visible Web} und mit Referenzen auf {\sl Citations} in der Welt der Literatur zur Verfügung stellt, in vergleichbarer Art auch für ihre eigenen durch Lizenzen geschützten digitalen Journale und ihre speziellen lokal verfügbaren Ressourcen, auf die Internet-Suchmaschinen keine Zugriff haben, anbieten. Es besteht die Hoffnung, dass Nutzer dann nicht - wie in einer kürzlichen Studie des OCLC konstatiert - überwiegend im Internet verbleiben, sondern bei ihrer Suche auch den Weg zu den Angeboten der örtlichen Bibliothek attraktiv finden.
    Keywords: ddc:000
    Language: German
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  • 57
    Publication Date: 2014-02-26
    Description: We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system. We derive systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a stable and fast recursive algorithm for the LST of the second moment of the conditional waiting time, which in particular yields the second moment of the unconditional waiting time. Moreover, asymptotically tight upper bounds for the moments of the conditional waiting time are given. The presented numerical results for the first two moments of the sojourn times in the $M/M/m-PS$ system show that the proposed algorithms work well.
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  • 58
    Publication Date: 2022-07-07
    Description: We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.
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  • 59
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 7 (1961), S. 174-174 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 60
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 7 (1961), S. 26-28 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This study deals with boundary-layer flow on continuous solid surfaces. Flow of this type represents a new class of boundary-layer problems, with solutions substantially different from those for boundary-layer flow on surfaces of finite length. In this paper the boundary-layer behavior on continuous surfaces is examined, and the basic differential and integral momentum equations of boundary-layer theory are derived for such surfaces. In subsequent papers these equations will be solved for the boundary layer on a moving continuous flat surface and a moving continuous cylindrical surface, for both laminar and turbulent flow in the boundary layer.
    Additional Material: 3 Ill.
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  • 61
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 7 (1961), S. 38-41 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An experimental study of superposed free and forced convection for air in a horizontal tube is reported. The laminar Nusselt number, based on the log mean temperature difference, ranged from 29.9 to 15.2; the laminar flow Graetz number, based on the bulk or average temperature of the air, ranged from 33 to 1,300, the Grashof-Prandtl modulus based on properties of air at the wall temperature ranged from 1.1 × 106 to 2.2 × 106. The Grashof number utilized the log mean temperature difference. An analysis of the system from a macroscopic viewpoint led to the determination of an equation which fits the laminar flow experimental data in the range of Graetz numbers from 60 to 1,300. An equation was also found for the turbulent data.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 62
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 7 (1961), S. 61-63 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A continuous velocity distribution is derived which is based on an arbitrary modification of Prandtl's mixing length expression. The resulting velocity distribution agrees well with experiments for transition and fully developed turbulent flow throughout the entire cross section of the conduit. Furthermore the mixing length expression applies to parallel flow in smooth circular tubes and between infinite parallel plates with the same set of constants.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 63
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 7 (1961), S. 78-80 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The results obtained by the evaporation of water and nitrobenzene in air from celite spheres in conjunction with the prevailing surface temperature have permitted the simultaneous determination of mass and heat transfer factors. The spheres used were 1.42, 1.88, and 2.00 in. in diameter. The experimental results of this study show that an essentially direct correspondence exists for mass and heat transfer in the flow of fluids past single spheres.
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  • 64
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    AIChE Journal 7 (1961), S. 303-307 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The formation of a solid phase as the result of isothermally increasing pressure on a binary solution is analyzed from a thermodynamic point of view. Exact thermodynamic equations are presented for the case in which there are no more than one liquid and one solid phase in equilibrium for the entire range of compositions. Approximate relations incorporating the additional assumption of ideality in both solid and liquid phases are also presented. Experimental data for the system ethylene bromide-ethylene chloride are reported and compared with predicted values. Incomplete data for the system benzene-n-heptane are also reported.
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  • 65
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    AIChE Journal 7 (1961), S. 324-328 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The analytical solution to the equation of motion is given for the steady laminar flow of a uniformly conducting incompressible non-Newtonian fluid between two parallel planes. The fluid is under the influence of a constant pressure gradient and is subjected to a steady magnetic field perpendicular to the direction of motion. Two non-Newtonian models are considered: the Bingham plastic model and the power-law model. Flow rates and the velocity profiles for various values of the Hartmann number and the generalized Hartmann number are presented and compared with those corresponding to Newtonian fluids.
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  • 66
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    AIChE Journal 7 (1961), S. 346-347 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 1 Ill.
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  • 67
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    AIChE Journal 7 (1961), S. 337-342 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The effect of mass transfer resistance in reducing the effectiveness of porous catalysts has been known since the publication of Thiele's classical paper in 1939. The variation in temperature caused by resistance to heat transfer may bring about equally significant changes in effectiveness in some cases. An extension of Thiele's treatment to take exact account of heat transfer resistance leads to a set of nonlinear differential equations that can only be solved numerically.This paper presents an approximate treatment of the simulataneous effects of resistances to mass and heat transfer. With the limitations imposed by linearizing the equations the formulas derived give the activity and selectivity for any combination of reactions. The use of the results is illustrated by three examples. It is shown that the principal effects are associated with the variation of concentration within the pellet of catalyst and with the difference in temperature between the surface of the pellet and the bulk fluid.
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  • 68
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    AIChE Journal 7 (1961), S. 354 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The Chemical Engineering Progress Symposium Series is composed of papers on specific subjects conveniently bound in individual books, which are published at intervals. The books are 8 ½ by 11 inches, paper covered, and cost $4.00 to members, $6.00 to nonmembers for “Heat Transfer - Storrs,” No. 30, and $3.75 to members, $5.75 to nonmembers for “Advances in Computational and Mathematical Techniques in Chemical Engineering,” No. 31. They may be ordered from the Secretary's Office, the American Institute of Chemical Engieers, 25 West 45 Street, New York 36, New York.The A. I. Ch. E. Journal will publish, from time to time, abstracts of the articles appearing in the Symposium Series volumes. Recently published volumes are abstracted below.
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  • 69
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    AIChE Journal 7 (1961), S. 260-263 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An experimental investigation of the concurrent cogravity flow of particulate solids and water in a 1-in. diameter vertical column is reported. Measurements were made of the particle concentration, or holdup, existing in the column as a function of the fluid and particle flow rates for two particle sizes, 0.0184- and 0.00396-in. diameter glass spheres. The experimental results form the basis for a prediction of the generalized characteristics of concurrent cogravity fluidization.The data for each particle size are correlated in terms of the slip velocity and the holdup. The slip velocity is demonstrated to be the same unique function of the holdup for concurrent cogravity flow and for batch fluidization. Therefore the holdup and the conditions of limiting operation for concurrent cogravity flow can be accurately predicted from the batch fluidization curve.
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  • 70
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    AIChE Journal 7 (1961), S. 273-276 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Previous investigators have developed general integrations of the Nernst-Planck flux equations to predict the behavior of ion exchange membranes in forced diffusion cells. These results are also applicable to stagnant liquid films, since this latter case can be considered as a membrane with a vanishingly small concentration of fixed charges (1). However these general integrations yield results of considerable complexity, and even the analysis of a specific system becomes a problem of some scope. This paper is based upon a much less general integration which proceeds by a straightforward manipulation of the Nernst-Planck flux equations for the special case of a single one-to-one electrolyte. The results are used to predict the behavior of a system consisting of a membrane with a stagnant film of liquid on either side. To further facilitate understanding the initial results are further simplified by assuming certain specific systems and then constructing plots showing the membrane efficiency in terms of readily interpreted, commonly encountered variables such as thicknesses, currents, and concentrations.
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  • 71
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    Notes: A Burnett type of apparatus for the study of the volumetric behavior of gases at low temperatures and high pressures was constructed. The apparatus was used to study the volumetric behavior of methane and four mixtures of hydrogen and methane from +50° to -200°F. and pressures as high as 7,000 lb./sq. in.The experimental data were used to obtain the second virial coefficients for pure methane and for the mixtures. The results of approximately 600 experimental points were used to obtain a table of compressibility factors for methane and the mixtures at even increments of pressure and temperture.
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  • 72
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    AIChE Journal 7 (1961), S. 288-294 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The growing availability of fast, large memory digital computers has made it practical to consider the physical implementation of control system designs incorporating appropriate strategies for automatic process optimization. The control system is taken to consist of the process to be optimized together with the interconnected digital computer. The control strategy is realized in the program of the digital computer. In the present paper a number of such programs or algorithms are discussed for carrying out a search of the possible settings of the process input (independent) variables in such a way as to locate an extremal of the possible values of a chosen objective function. The magnitude of these variables is determined from measurements taken of the dependent variables in the process. It is shown that for the particular process used as an example it is desirable to alter the search strategy as the optimization proceeds in order to locate the extremal in a minimum amount of time. The emphasis at the beginning of the search is on speed in moving towards the optimum and at the end on accuracy.Further, a computational technique is described whereby the dynamic response of the process to the various search steps (or settings) is under time-optimal control. This procedure is important for the fast execution of the search programs and consequent rapid location of the extremal of the chosen objective function.
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    AIChE Journal 7 (1961), S. 312-318 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 13 Ill.
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  • 74
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    AIChE Journal 7 (1961), S. 329-335 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The principles involved in designing a process for the production of fixed nitrogen by the direct use of fission fragment recoil energy are reviewed. The problems concerned with the radiation chemistry, development of fuel element, reactor design, and chemical process design are pointed out. Possible solutions to these problems incorporated in a complete plant design are presented. An economic evaluation, comparing the chemonuclear process with other conventional processes, is made. The conclusion is reached that at the present state of knowledge there does not seem to be any clear-cut advantage over conventional processes, even based on a nuclear economy. However moderate research efforts should continue for further evaluation of this process.
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    AIChE Journal 7 (1961), S. 347-348 
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    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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    AIChE Journal 7 (1961), S. 350-351 
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    Keywords: Chemistry ; Chemical Engineering
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    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 77
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    AIChE Journal 7 (1961), S. 352-352 
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  • 78
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    AIChE Journal 7 (1961), S. 5J 
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  • 79
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    AIChE Journal 7 (1961), S. 355-355 
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  • 80
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    AIChE Journal 7 (1961), S. 371-375 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A recirculation type of apparatus with a novel liquid-sampling system was used to obtain liquid-vapor equilibrium data for the hydrogen-nitrogen and deuterium-nitrogen systems at 90° and 95°K. and pressures up to 1,000 lb./sq. in. abs. The data obtained show an average scatter in liquid compositions of the order of 0.01%, thus proving the feasibility of the new liquid-sampling system. The vapor samples are shown by thermodynamic analysis to scatter less than 0.1%. Deuterium is slightly more soluble in liquid nitrogen than hydrogen; the relative volatility is 1.198 at 90°K. and about 1.177 at 95°K. The relative volatility is practically independent of pressure; thus at 90°K. the relative volatility decreases from 1.198 at 100 lb./sq. in. abs. to 1.196 at 1,000 lb./sq. in. abs., but this range of values is well within the experimental error.
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  • 81
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    AIChE Journal 7 (1961), S. 6S 
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  • 82
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    AIChE Journal 7 (1961), S. 548-550 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Waves at an interface between a concurrent air-water flow cause an increase in the interfacial stress. This increase in stress is correlated with the root-mean-square displacement of the liquid from its average height. The data are compared with Nikuradse's measurements with sand roughness.
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  • 83
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    AIChE Journal 7 (1961), S. 565-573 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Measurements have been made of the simultaneous rates of transfer of acetone and benzene between a liquid film and a turbulent three component gas mixture. The measurements were made in a wetted-wall column with both mixtures of acetone, benzene and nitrogen, and acetone, benzene and helium.As predicted by the equations of Part I the mass transfer differs qualitatively as well as quantitatively from mass transfer in the corresponding binary system in which one component is stagnant. In several experiments acetone was transferred from low to high concentrations in accord with the predictions.Both the ternary film and Prandtl-Taylor models satisfactorily predict the rates of transfer of acetone and benzene, and, except possibly for very high Reynolds numbers, the simpler film model is recommended.
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  • 84
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    AIChE Journal 7 (1961), S. 467-472 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The behavior of laminar and turbulent boundary layers on a moving continuous cylindrical surface is investigated by the integral method, based on assumed velocity profiles that satisfy the appropriate boundary conditions. Equations for the characteristic boundary-layer parameters are presented for both the laminar and turbulent boundary layers, and comparison is made with the boundary-layer behavior over a cylindrical surface of finite length. The analysis for the laminar boundary layer with a logarithmic velocity profile leads to satisfactory results. The turbulent boundary-layer behavior on continuous cylindrical surfaces, and cylindrical surfaces of finite length, can best be investigated experimentally.
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  • 85
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    AIChE Journal 7 (1961), S. 606-610 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Mechanical and dynamical characteristics of semifluidized beds of single-size particles in solid-liquid system were investigated. A semifluidized bed is a type of fluidized bed in which the bed expansion is partially restricted. The emphasis was placed on the study of packed bed formation and pressure drop increase when the semifluidized beds were formed by the compression of fluidized beds. The data showed good agreement with the theoretical and semiempirical equations based on a simple model of fluidized beds.The results of this investigation would also contribute to the understanding of fluidized beds.
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  • 86
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    AIChE Journal 7 (1961), S. 631-634 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The liquid film coefficient is related to bubble diameter and velocity in pure water and to the physical properties of the liquid. The addition to water of organic substances which influence the surface tension and viscosity will decrease the size of the air bubble released from a diffuser and reduce the transfer of oxygen into the solution. The maximum reduction in oxygen transfer occurs in the region of maximum surface tension change. The effect of the addition of several organic substances on the oxygen transfer characteristics are shown.
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  • 87
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    AIChE Journal 7 (1961), S. 653-657 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: One of the numerous equations needed to define the dynamics of a distillation column has been derived. This equation relates the feed composition to the product composition. Thederivation is accomplished by the reduction of the signal flow diagram. The poles and zeros of the equation are almost entirely determined by the ratio of the tray holdup to the liquid flow rates and the number of trays.
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  • 88
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    AIChE Journal 7 (1961), S. 319-324 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A study has been made of the effect of column geometry and flow condition upon the dispersed-phase holdup in an rotating disk type of extraction column. Variables investigated were stator opening, disk diameter, compartment height, rotor speed, and flow rates of the dispersed and continuous phases. The toluene-water system, with the toluene dispersed, was used throughout the study. The radio-isotope technique was used to measure the dispersed-phase holdup.Results of this study as well as those of earlier investigators have been used to expand upon the design equations proposed by Logsdail, Thornton, and Pratt for estimating flooding rates and dispersed-phase holdup in rotating disk columns. Modifications to increase the accuracy of prediction of these equations have also been suggested, while possible limitations in their application have been indicated.
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    AIChE Journal 7 (1961), S. 343-345 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The P-V-T-x properties of binary gas mixtures and their dependence on reduced temperature and pressure have been reviewed in detail.A modified form of Kay's original method for estimating P-V-T-x properties of mixtures is suggested for purposes of engineering calculations.
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  • 90
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    AIChE Journal 7 (1961), S. 348-349 
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    Keywords: Chemistry ; Chemical Engineering
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  • 91
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    AIChE Journal 7 (1961), S. 5J 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 92
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    AIChE Journal 7 (1961) 
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    AIChE Journal 7 (1961), S. 367-370 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A finite-difference method is presented for solving three-dimensional transient heat conduction problems. The method is a modification of the method of Douglas and Rachford which achieves the higher-order accuracy of a Crank-Nicholson formulation while preserving the advantages of the Douglas-Rachford method: unconditional stability and simplicity of solving the equations at each time level. Although the method has not yet been applied, the analysis in this paper suggests that it will prove to be the most efficient method yet proposed for the numerical integration of three-dimensional transient heat conduction problems.
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    AIChE Journal 7 (1961), S. 5S 
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    AIChE Journal 7 (1961) 
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    AIChE Journal 7 (1961), S. 625-631 
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    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Experimental viscosity, thermal conductivity, and self-diffusivity data available in the literature for carbon dioxide have been critically reviewed and used to develop reduced state correlations of the transport properties for this substance. These correlations should apply to nonpolar compounds having critical compressibility factors approximately equal to that of carbon dioxide, zc = 0.275.In order to establish the dependence of these transport properties in the high pressure and liquid state regions, use has been made of relationships between the residual properties, μ-μ*, k-k*, and (PD)*-(PD) and density. These residual quantities represent the differences between the values of the properties at any pressure and temperature and those at atmospheric pressure and the same temperature. These relationships also allow the determination of the values of the transport properties at the critical point. The resulting critical values along with the residual relationships enabled the construction of reduced state correlations for viscosity, thermal conductivity, and the product of self-diffusivity and pressure for carbon dioxide.These correlations extend from the saturated vapor and liquid states to reduced temperatures of TR = 10 and reduced pressures of PR = 50. Comparisons made between values resulting from these correlations and corresponding experimental values, including the region of high pressure for both the gaseous and liquid states and the vicinity of the critical point, produced an average deviation of 2.0% for viscosity, 1.4% for thermal conductivity, and 5.9% for self-diffusivity.
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    AIChE Journal 7 (1961), S. 3D-3D 
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    Keywords: Chemistry ; Chemical Engineering
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    AIChE Journal 7 (1961), S. 10-12 
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    Keywords: Chemistry ; Chemical Engineering
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    Notes: Rates of diffusion of helium, nitrogen, and carbon dioxide through alumina pellets were measured at atmospheric pressure and room temperature. The cylindrical pellets, ¾ in. diameter and ⅜ in. in length, were prepared from α-alumina particles with a mean pore radius of 65 Å. Surface area and pore volume data indicated that the corresponding mean pore radius of the micro and macropores in the whole pellet was 96 Å.The results showed that Knudsen type of diffusion was the controlling transport process despite the large fraction of void volume in the macropores. Carbon dioxide diffused more rapidly than expected, suggesting the possibility of migration of physically adsorbed molecules along the pore walls.The diffusion rates were about 16% higher than predicted, with a mean pore radius (Wheeler model) based upon the void volume of both micro and macropores used. However there is no logical basis for using this mean pore radius for a pellet having widely separated, micro and macropore size distributions.
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 7 (1961), S. 17-19 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The problem of defining an average diffusion coefficient of a gas arises in the application of the film resistance model for mass transfer to systems involving multicomponent mixtures of simultaneously diffusing gases and in the application of mass, momentum, and heat transfer analogies in such systems. It is shown that, in some cases, integration of the diffusion equation with an average value of the diffusion coefficient will not be valid. An approximate solution of the diffusion equation is obtained with the concentration dependence of the diffusion coefficient taken into account. Some numerical examples are constructed for comparison of this method and several methods for defining an average diffusion coefficient with an exact solution of the Stefan-Maxwell relations.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 7 (1961), S. 29-34 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Experimental heat transfer studies were carried out in beds of unconsolidated glass beads and sand through which fluids were flowing. The scope of the measurements included four fluids, helium, air, carbon dioxide, and water liquid at atmospheric pressure in beds packed with four sizes of glass beads, 110, 370, 570, and 1,020 μ and with two sizes of sand, 110 and 240 μ. Flow rates ranged form 1 to 26 lb./(hr. sq.ft.) in a direction parallel and countercurrent to energy flow.The data were interpreted in terms of apparent, effective thermal conductivities of the bed. The values of ke increase significantly with mass velocity of fluid.By considering the mechanism of heat transfer in porous media a relationship was developed between ke and the heat transfer coefficient between fluid and particle. Treatment of the experimental data in this fashion, combined with available information for larger particles, results in a correlation of Nusselt and Reynolds numbers for air that covers the range NRem = 10-1 to 104.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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