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  • 1
    Publication Date: 2014-02-26
    Description: In this paper we consider the multiple knapsack problem which is defined as follows: given a set $N$ of items with weights $f_i$, $i \in N$, a set $M$ of knapsacks with capacities $F_k$, $k \in M$, and a profit function $c_{ik}, i \in N, k \in M$; find an assignment of a subset of the set of items to the set of knapsacks that yields maximum profit (or minimum cost). With every instance of this problem we associate a polyhedron whose vertices are in one to one correspondence to the feasible solutions of the instance. This polytope is the subject of our investigations. In particular, we present several new classes of inequalities and work out necessary and sufficient conditions under which the corresponding inequality defines a facet. Some of these conditions involve only properties of certain knapsack constraints, and hence, apply to the generalized assignment polytope as well. The results presented here serve as the theoretical basis for solving practical problems. The algorithmic side of our study, i.e., separation algorithms, implementation details and computational experience with a branch and cut algorithm are discussed in the companion paper SC 93-07.
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  • 2
    Publication Date: 2014-02-26
    Description: The Lanczos iteration for symmetric indefinite linear systems seems to be well--known for quite a while. However, in order to modify it with the aim of improved performance, the present paper studies certain aspects in terms of an adjoint scalar three--term recurrence. Thus, at least a different view is opened. Moreover, an alternative $3n$--implementation in terms of the Euclidean orthogonal basis has been found that easily permits generalizations. The study is understood as a start--off for further numerical investigations and experiments.
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  • 3
    Publication Date: 2020-10-02
    Description: We consider the discretization of obstacle problems for second order elliptic differential operators in three space dimensions by piecewise linear finite elements. Linearizing the discrete problems by suitable active set strategies, the resulting linear sub--problems are solved iteratively by preconditioned cg--iterations. We propose a variant of the BPX preconditioner and prove an $O(j)$ estimate for the resulting condition number. To allow for local mesh refinement we derive semi--local and local a posteriori error estimates. The theoretical results are illustrated by numerical computations.
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  • 4
    Publication Date: 2014-02-26
    Description: \def\KPA{\hbox{\rm KPA}}\def\A{{\rm A}}\def\KPW{\hbox{\rm KPW}}\def\W{{\rm W}}\def\B{{\rm B}} \def\D{{\rm D}} Recently M.~M.~Kapranov [Kap] defined a poset $\KPA_{n-1}$, called the {\it permuto-associahedron}, which is a hybrid between the face poset of the permutahedron and the associahedron. Its faces correspond to the partially parenthesized, ordered, partitions of the set $\{1,2,\ldots,n\}$, with a natural partial order. Kapranov showed that $\KPA_{n-1}$ is the face poset of a CW-ball, and explored its connection with a category-theoretic result of MacLane, Drinfeld's work on the Knizhnik-Zamolodchikov equations, and a certain moduli space of curves. He also asked the question of whether this CW-ball can be realized as a convex polytope. We show that this permuto-associahedron corresponds to the type $\A_{n-1}$ in a family of convex polytopes $\KPW$ associated to each of the classical Coxeter groups, $\W = \A_{n-1}, \B_n, \D_n$. The embedding of these polytopes relies on the secondary polytope construction of the associahedron due to Gel'fand, Kapranov, and Zelevinsky. Our proofs yield integral coordinates, with all vertices on a sphere, and include a complete description of the facet-defining inequalities. Also we show that for each $\W$, the dual polytope $\KPW^*$ is a refinement (as a CW-complex) of the Coxeter complex associated to $\W$, and a coarsening of the barycentric subdivision of the Coxeter complex. In the case $\W=\A_{n-1}$, this gives an elementary proof of Kapranov's original sphericity result.
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  • 5
    Publication Date: 2020-11-13
    Description: In this paper we describe and discuss a problem that arises in the (global) design of a main frame computer. The task is to assign certain functional units to a given number of so called multi chip modules or printed circuit boards taking into account many technical constraints and minimizing a complex objective function. We describe the real world problem. A thorough mathematical modelling of all aspects of this problem results in a rather complicated integer program that seems to be hopelessly difficult -- at least for the present state of integer programming technology. We introduce several relaxations of the general model, which are also $NP$-hard, but seem to be more easily accessible. The mathematical relations between the relaxations and the exact formulation of the problem are discussed as well.
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  • 6
    Publication Date: 2014-02-26
    Description: Cascadic conjugate gradient methods for the numerical solution of elliptic partial differential equations consists of Galerkin finite element methods as outer iteration and (possibly preconditioned) conjugate gradient methods as inner iteration. Both iterations are known to minimize the energy norm of the arising iterations errors. A simple but efficient strategy to control the discretization errors versus the PCG iteration errors in terms of energy error norms is derived and worked out in algorithmic detail. In a unified setting, the relative merits of different preconditioners versus the case of no preconditioning is compared. Surprisingly, it appears that the cascadic conjugate gradient method without any preconditioning is not only simplest but also fastest. The numerical results seem to indicate that the cascade principle in itself already realizes some kind of preconditioning. A theoretical explanation of these observations will be given in Part II of this paper.
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  • 7
    Publication Date: 2014-02-26
    Description: This paper throws light on the connection between the optimal condition number estimate for the BPX method and constructive approximation theory. We provide a machinery, which allows to understand the optimality as a consequence of an approximation property and an inverse inequality in $H^{1+\epsilon}$, $\epsilon 〉 0$. This machinery constructs so-called {\em approximation spaces}, which characterize a certain rate of approximation by finite elements and relates them with interpolation spaces, which characterize a certain smoothness.
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  • 8
    Publication Date: 2020-08-05
    Description: "`Telebus"' ist der soziale Behindertenfahrdienst im Land Berlin. Das Telebus-Forschungsprojekt des Konrad-Zuse-Zentrums für Informationstechnik (ZIB) hat das Ziel, den Fahrdienst (insbesondere die Disposition der Telebusse) zu verbessern, d.h. kundenfreundlicher zu gestalten und gleichzeitig billiger zu machen. In diesem Bericht werden die bisherigen Ergebnisse dargestellt und weitere Möglichkeiten zur Verbesserung des Service und zur Reduzierung der Kosten skizziert. \originalTeX
    Keywords: ddc:000
    Language: German
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  • 9
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    Publication Date: 2014-02-26
    Description: These lecture notes have several aims: \begin{itemize} \item to give an introduction to some basic facts about convex polytopes, with an emphasis on the basic methods that yield them (Fourier-Motzkin elimination, Schlegel diagrams, shellability, Gale transforms and oriented matroids), \item to discuss some important examples and elegant constructions (cyclic and neighborly polytopes, zonotopes, Minkowski sums, permutahedra and associahedra, fiber polytopes, the Lawrence construction) \item and to illustrate why polytope theory is exciting, with highlights like Kalai's new diameter bounds, the construction of non-rational polytopes, the Bohne-Dress tiling theorem, shellability and the upper bound theorem, .... \end{itemize} For several of these topics the decisive break-through is very recent, which suggests that there is much more discovered.
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  • 10
    Publication Date: 2020-03-11
    Description: GRAZIL ist ein interaktives Programmpaket zur grafischen Darstellung von zwei-dimensionalen Kurvenverläufen. Dem Benutzer stehen zahlreiche Kommandos und ein grafisches User-Interface zum Gestalten des Layouts der Zeichnung zur Verfügung. Die Eingabedaten müssen dem GRAZIL-Eingabe-Format genügen. Somit wird eine hohe Flexibilität und eine gro\"se Bandbreite der Einsatzmöglichkeiten erreicht. GRAZIL wurde mit der grafischen Grundsoftware GKS entwickelt. Dadurch kann ein breites Rechner- und Ausgabegerätespektrum genutzt werden.
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    Language: German
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  • 11
    Publication Date: 2019-05-10
    Description: The KASKADE toolbox defines an interface to a set of C subroutines which can be used to implement adaptive multilevel Finite Element Methods solving systems of elliptic equations in two and three space dimensions. The manual contains the description of the data structures and subroutines. The main modules of the toolbox are a runtime environment, triangulation and node handling, assembling, direct and iterative solvers for the linear systems, error estimators, refinement strategies, and graphic utilities. Additionally, we included appendices on the basic command language interface, on file formats, and on the definition of the partial differential equations which can be solved. The software is available on the ZIB ftp--server {\tt elib} in the directory {\tt pub/kaskade}. TR 93--5 supersedes TR 89--4 and TR 89--05.
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  • 12
    Publication Date: 2020-10-02
    Description: In this paper various algorithms for rendering gaseous phenomena are reviewed. In computer graphics such algorithms are used to model natural scenes containing clouds, fog, flames and so on. On the other hand it has become an important technique in scientific visualization to display three dimensional scalar datasets as cloudy objects. Our emphasis is on this latter subject of so-called {\em direct volume rendering}. All algorithms will be discussed within the framework of linear transport theory. The equation of transfer is derived. This equation is suitable to describe the radiation field in a participating medium where absorption, emission, and scattering of light can occur. Almost all volume rendering algorithms can be shown to solve special cases of the equation of transfer. Related problems like the mapping from data values to model parameters or possible parallelization strategies will be discussed as well.
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  • 13
    Publication Date: 2014-02-26
    Description: This report describes the new object oriented implementation of extrapolation codes {\sc Eulex, Eulsim, Difex} for ordinary differential equations. The resulting C++ class library provides a simple and flexible interface to these methods and incorporates advanced features like continuous output and order-stepsize freezing. The interface of the ODE classes allows in particular a user-defined solver for the linear systems occuring in the linearly implicit discretization scheme. The library also provides some classes for numerical objects such as vectors and (full) matrices. Due to the underlying data-view concept it is possible to access substructures without copying. In addition, we included several utility classes such as a timer and a minimal command language that may be useful in other contexts, too.
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  • 14
    Publication Date: 2014-02-26
    Description: Aus dem Inhalt: Vorwort; Leonhard Euler - aus der Zeit seines Wirkens in Berlin; Introductory Remarks.
    Keywords: ddc:000
    Language: German
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  • 15
    Publication Date: 2014-02-26
    Description: The problem of nonlocal correlation and symmetry in space is of great importance in physical phenomena like the \underline{Einstein-Poloski-Rosen-Paradox} and others. It is shown that in Cellular Automata (Rechnender Raum) the structure of the space offers solutions for such problems.
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  • 16
    Publication Date: 2014-02-26
    Description: A software package for the adaptive solution of time--dependent reaction--diffusion systems and linear elliptic systems in one space dimension is presented. The used algorithm is based on fundamental arguments in J.~Lang, A.~Walter: {\it A Finite Element Method Adaptive in Space and Time for Nonlinear Reaction--Diffusion Systems.} IMPACT of Computing in Science and Engineering, 4, p.~269--314 (1992). Here, only brief outlines of the algorithm are given. This software package is based on the KASKADE toolbox B.~Erdmann, J.~Lang, R.~Roitzsch: {\it KASKADE -- Manual.} To appear as Technical Report TR 93--5, Konrad--Zuse--Zentrum (ZIB) (1993).
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  • 17
    Publication Date: 2014-02-27
    Description: A new approach to inexact Gauss Newton methods for the solution of underdetermined nonlinear problems is presented. It is based on a convergence theorem being invariant under affine transformations of the domain and results in an easily implementable accuracy matching strategy for the arising linear subproblems which guarantees the quadratic convergence. Thanks to the weak assumptions on the given nonlinear problem, the results provide a general framework for multilevel Newton and continuation methods. As an example, a new multilevel Newton h-p collocation method for boundary value problems of ordinary differential equations is developed. It combines the inexact Newton method with a linear collocation solver using adaptive refinement and variable orders. The performance of the resulting C++ class library {\sc Cocon} is demonstrated by some numerical examples including singular perturbed problems. In addition, the new method is applied to a realistic railway bogie model in which a branch of periodic solutions emanates from a branch of fixed points at a Hopf bifurcation.
    Keywords: ddc:000
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 18
    Publication Date: 2014-02-27
    Description: A new method for the numerical solution of highly nonlinear, coupled systems of parabolic differential equations in one space dimension is presented. The approach is based on a classical method of lines treatment. Time discretization is done by means of the semi--implicit Euler discretization. Space discretization is done with finite differences on non--uniform grids. Both basic discretizations are coupled with extrapolation techniques. With respect to time the extrapolation is of variable order whereas just one extrapolation step is done in space. Based on local error estimates for both, the time and the space discretization error, the accuracy of the numerical approximation is controlled and the discretization stepsizes are adapted automatically and simultaneously. Besides the local adaptation of the space grids after each integration step (static regridding), the grid may even move within each integration step (dynamic regridding). Thus, the whole algorithm has a high degree of adaptivity. Due to this fact, challenging problems from applications can be solved in an efficient and robust way.
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    Type: doctoralthesis , doc-type:doctoralThesis
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  • 19
    Publication Date: 2014-02-26
    Description: We present an algorithm that is able to confirm projective incidence statements by carrying out calculations in the ring of all formal determinants (brackets) of a configuration. We will describe an implementation of this power and present a series of examples treated by the prover, including {\it Pappos' and Desargues' Theorems,} the {\it Sixteen Point Theorem, Saam's Theorem, }the {\it Bundle Condition,} the uniqueness of a harmonic Point and {\it Pascal's Theorem.}
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  • 20
    Publication Date: 2020-12-14
    Description: We consider the important practical and theoretical problem of designing a low-cost communications network which can survive failures of certain network components. Our initial interest in this area was motivated by the need to design certain ``two-connected" survivable topologies for fiber optic communication networks of interest to the regional telephone companies. In this paper, we describe some polyhedral results for network design problems with higher connectivity requirements. We also report on some preliminary computational results for a cutting plane algorithm for various real-world and random problems with high connectivity requirements which shows promise for providing good solutions to these difficult problems. \def\NP{$\cal NP$}
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  • 21
    Publication Date: 2014-02-26
    Description: The subject of this study is a multilevel Finite Element Method based on an error estimator and step by step grid refinement as an universal tool for solving time--independent Schrödinger--eigenvalue problems. Numerical results for standard problems appearing in vibrational motion and molecular electronic structure calculations are given and discussed.
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  • 22
    Publication Date: 2014-02-26
    Description: In two-parameter systems with symmetry two steady state bifurcation points of different symmetry types coalesce generically within one point. Under certain group theoretic conditions involving the action of the symmetry group on the kernels, we show that secondary Hopf bifurcation is borne by the mode interaction. We explain this phenomenon by using linear representation theory. For motivation an example with $D_3$-symmetry is investigated where the main properties causing the Hopf bifurcation are summarized.
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  • 23
    Publication Date: 2021-03-19
    Description: Adaptive numerical methods using the $h$-$p$-version of finite elements require special kinds of shape functions. Desirable properties of them are symmetry, hierarchy and simple coupling. In a first step it is demonstrated that for standard polynomial vector spaces not all of these features can be obtained simultaneously. However, this is possible if these spaces are extended. Thus a new class of polynomial shape functions is derived, which is well-suited for the $p$- and $h$-$p$-version of finite elements on unstructured simplices. The construction is completed by minimizing the condition numbers of the arising finite element matrices. The new shape functions are compared with standard functions widely used in the literature.
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  • 24
    Publication Date: 2019-05-10
    Description: {\def\enorm {\mathop{\mbox{\boldmath{$|\!|$}}}\nolimits} Let $u \in H$ be the exact solution of a given self--adjoint elliptic boundary value problem, which is approximated by some $\tilde{u} \in {\cal S}$, $\cal S$ being a suitable finite element space. Efficient and reliable a posteriori estimates of the error $\enorm u - \tilde{u}\enorm $, measuring the (local) quality of $\tilde{u}$, play a crucial role in termination criteria and in the adaptive refinement of the underlying mesh. A well--known class of error estimates can be derived systematically by localizing the discretized defect problem using domain decomposition techniques. In the present paper, we provide a guideline for the theoretical analysis of such error estimates. We further clarify the relation to other concepts. Our analysis leads to new error estimates, which are specially suited to three space dimensions. The theoretical results are illustrated by numerical computations.}
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  • 25
    Publication Date: 2014-02-26
    Description: The strategy for solving nonlinear equation systems automatically in the computer algebra system REDUCE is described. Kernel of the solver is a factoring Buchberger algorithm. Pre -- and postprocessors enable the use of the Gröbner techniques in a black box manner. In addition to polynomials equations with surds, trigonometric functions and separable transcendental functions are covered.
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  • 26
    Publication Date: 2014-02-26
    Description: In diesem Aufsatz geben wir einen Bericht über den Stand der elektronischen Fachinformation in der Mathematik in Deutschland. Wir sehen diesen Bereich nicht als ein organisatorisch isoliertes Unterfangen, sondern eingebettet in weltweite Bestrebungen und Entwicklungen in der Informationstechnik, im wissenschaftlichen Publikationswesen und natürlich auch in der Mathematik selber. Unser Artikel endet mit einigen weitreichenden (und einigen Lesern möglicherweise spektakulär erscheinenden) Vorschlägen, die sowohl die Informationsanbieter (wie die Fachinformationszentren und Verlage), die öffentlichen Geldgeber als auch die mathematischen Organisationen (wie z.~B.~ die DMV und die mathematischen Fachbereiche) betreffen. Um den gegenwärtigen Zustand der elektronischen Fachinformation und unsere Gedanken zu diesem Thema adäquat beschreiben zu können, präsentieren wir eine breit angelegte Situationsanalyse. Wir stellen den gegenwärtigen Stand der technologischen Entwicklung im elektronischen Publizieren dar und skizzieren seine Auswirkungen. Wir beschreiben das Feld der Interessen und Kräfte im Bereich des mathematischen Publizierens. Wir geben einen kurzen historischen Abriss der Geschichte der Klassifikation und des Referatewesens und zeigen, wie dieses in die elektronische Fachinformation auf dem Gebiet der Mathematik mündete und dann zum DMV-Projekt Fachinformation führte, das der Anlass zur Abfassung dieses Artikels war. Wir skizzieren die gegenwärtige Rezeption elektronischer Fachinformation in der Mathematik in Deutschland. Ausgehend von einer Darstellung und Bewertung verschiedener Modelle des Referatewesens zeigen wir unter Einbeziehung der vorhandenen technischen Gegebenheiten (elektronische Netze etc.) verschiedene Möglichkeiten zur Liberalisierung und Rationalisierung des weltweiten mathematischen Informationswesens auf. Wir sehen den Austausch von Information in engem Zusammenhang mit dem Austausch von Software im Wissenschaftsbereich und regen auch in diesem Bereich an, internationale Kooperation und Offenheit anzustreben. \originalTeX
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    Language: German
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  • 27
    Publication Date: 2014-02-26
    Description: In this paper we describe a cutting plane based algorithm for the multiple knapsack problem. We use our algorithm to solve some practical problem instances arising in the layout of electronic circuits and in the design of main frame computers, and we report on our computational experience. This includes a discussion and evaluation of separation algorithms, an LP-based primal heuristic and some implementation details. The paper is based on the polyhedral theory for the multiple knapsack polytope developed in our companion paper SC 93-04 and meant to turn this theory into an algorithmic tool for the solution of practical problems.
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  • 28
    Publication Date: 2020-12-14
    Keywords: ddc:000
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  • 29
    Publication Date: 2014-02-26
    Description: One key problem in modern chemistry is the simulation of the dynamical reaction of a molecule subjected to external radiation. This is described by the Schrödinger equation, which, after eigenfunction expansion, can be written in form of a system of ordinary differential equations, whose solutions show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. This idea leads to the construction of a quasiresonant smoothing algorithm (QRS). In QRS, a natural and computationally available splitting parameter $\delta$ controls the smoothing properties. The performance of QRS is demonstrated in two applications treating the selective excitation of vibrational states by picosecond laser pulses. In comparison with standard methods a speedup factor of 60--100 is observed. A closer look to purely physically motivated quasiresonant approximations such as WFQRA shows some additional advantages of the above smoothing idea. Among these the possibility of an adaptive formulation of QRS via the parameter $\delta$ is of particular importance.
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  • 30
    Publication Date: 2020-11-16
    Description: This paper will appear as Chapter 28 of the forthcoming "Handbook on Combinatorics" (editors: R. Graham, M. Grötschel, L. Lovasz) to be published in 1994, by North-Holland.
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  • 31
    Publication Date: 2014-02-26
    Description: An analysis of relaxation oscillations in local Er-doped optically pumped lasers is reported. It is based on a time dependent rate equation model for a quasi-two-level-system with wavelength dependent emission- and absorption cross-sections. For the first time a numerically reliable simulation of the characteristic laser behaviour was possible: the onset and decay of the oscillations, the time-dependent repetition period and the steady state signal output power. The characteristic waveguide parameters, as the erbium-concentration profile, the polarization dependent pump- and signal mode intensity profiles, the scattering losses, the cavity length and the front and rear reflectivities were all taken into account. The basic formulas are general and can also be used for Er-doped fiber lasers. Mathematically the problem can be characterized as a large boundary value problem, which can approximately be replaced by a stiff initial value problem of ordinary differential equations. The used algorithmic replacement procedure is motivated and discussed in detail. Here, pump- and signal evolution versus time are presented for an planar Er-diffused $\rm Ti$:$\rm LiNbO_{3}$ waveguide laser. The numerically obtained results show a nearly quantitative agreement with experimental investigations. Simultanously they supply knowledge about non-measureable (space-dependent population dynamic of the Er-atoms) and till today not measured data (dynamical response of the laser by a sharp peak in the external pump).
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  • 32
    Publication Date: 2014-02-26
    Description: We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 33
    Publication Date: 2014-02-26
    Description: Extending well--known linear concepts of successive subspace correction, we arrive at extended relaxation methods for elliptic variational inequalities. Extended underrelaxations are called monotone multigrid methods, if they are quasioptimal in a certain sense. By construction, all monotone multigrid methods are globally convergent. We take a closer look at two natural variants, which are called symmetric and unsymmetric multigrid methods, respectively. While the asymptotic convergence rates of the symmetric method suffer from insufficient coarse--grid transport, it turns out in our numerical experiments that reasonable application of the unsymmetric multigrid method may lead to the same efficiency as in the linear, unconstrained case.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 34
    Publication Date: 2014-02-26
    Description: Elliptic boundary value problems are frequently posed on complicated domains which cannot be covered by a simple coarse initial grid as it is needed for multigrid like iterative methods. In the present article, this problem is resolved for selfadjoint second order problems and Dirichlet boundary conditions. The idea is to construct appropriate subspace decompositions of the corresponding finite element spaces by way of an embedding of the domain under consideration into a simpler domain like a square or a cube. Then the general theory of subspace correction methods can be applied.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 35
    Publication Date: 2014-02-26
    Description: We prove a natural bijection between the polytopal tilings of a zonotope $Z$ by zonotopes, and the one-element-liftings of the oriented matroid ${\cal M}(Z)$ associated with $Z$. This yields a simple proof and a strengthening of the Bohne-Dress Theorem on zonotopal tilings.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 36
    facet.materialart.
    Unknown
    Publication Date: 2015-06-01
    Description: Formal Laurent-Puiseux series of the form \[ f(x)=\sum \limits_{k=k_0}^{\infty}a_{k}x^{k/n} \] are important in many branches of mathematics. Whereas {\sc Mathematica} supports the calculation of truncated series with its {\tt Series} command, and the {\sc Mathematica} package {\tt SymbolicSum} that is shipped with {\sc Mathematica} version 2 is able to convert formal series of the type mentioned above in some instances to their corresponding generating functions, in six publications of the author we developed an algorithmic procedure to do these conversions that is implemented by the author, A.\ Rennoch and G.\ Stölting in the {\sc Mathematica} package {\tt PowerSeries}. The implementation enables the user to reproduce most of the results of the extensive bibliography on series of Hansen, E.\ R.: A table of series and products. Prentice-Hall, 1975. Moreover a subalgorithm of its own significance generates differential equations satisfied by the input function.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 37
    Publication Date: 2015-06-01
    Description: {\newcommand{\C}{{\rm {\mbox{C{\llap{{\vrule height1.52ex}\kern.4em}}}}}} \newcommand{\Z} {{\rm {\mbox{\protect\makebox[.2em][l]{\sf Z}\sf Z}}}} \newcommand{\Maple}{{\sc Maple}} Formal Laurent-Puiseux series of the form \[ f(x)=\sum\limits_{k=k_0}^{\infty}a_{k}x^{k/n} \label{eq:formalLPS} \] with coefficients $a_{k}\in\C\;(k\in\Z)$ are important in many branches of mathematics. \Maple\ supports the computation of {\em truncated\/} series with its {\tt series} command, and through the {\tt powerseries} package infinite series are available. In the latter case, the series is represented as a table of coefficients that have already been determined together with a function for computing additional coefficients. This is known as {\em lazy evaluation\/}. But these tools fail, if one is interested in an explicit formula for the coefficients $a_k$. In this article we will describe the \Maple\ implementation of an algorithm presented in several papers of the second author which computes an {\em exact\/} formal power series of a given function. This procedure will enable the user to reproduce most of the results of the extensive bibliography on series. We will give an overview of the algorithm and then present some parts of it in more detail. This package is available through the \Maple-share library with the name {\tt FPS}. We flavor this procedure with the following example. %\begin{maple} \begin{verbatim}〉 FormalPowerSeries(sin(x), x=0);\end{verbatim} \begin{samepage} \begin{verbatim} infinity ----- k (2 k + 1) \ (-1) x ) ---------------- / (2 k + 1)! ----- k = 0 \end{verbatim} \end{samepage} }
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 38
    Publication Date: 2014-02-26
    Description: One of the challenging problems in the design of electronic circuits is the so-called routing problem. Roughly speaking, the task is to connect so-called terminal sets via wires on a predefined area. In addition, certain design rules are to be taken into account and an objective function such as the wiring length must be minimized. The routing problem in general is too complex to be solved in one step. Depending on the user's choice of decomposing the chip design problem into a hierarchy of stages, on the underlying technology, and on the given design rules, various subproblems arise. We discuss several variants of practically relevant routing problems and give a short overview on the underlying technologies and design rules. Many of the routing problems that come up this way can be formulated as the problem of packing so-called Steiner trees in certain graphs. We consider the Steiner tree packing problem from a polyhedral point of view and present three possibilities to define an appropriate polyhedron. Weighing their pros and cons we decide for one of these polytopes and sketch some of our investigations.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 39
    Publication Date: 2014-02-26
    Description: We derive fast solvers for discrete elliptic variational inequalities of the second kind as resulting from the approximation by piecewise linear finite elements. Following the first part of this paper, monotone multigrid methods are considered as extended underrelaxations. Again, the coarse grid corrections are localized by suitable constraints, which in this case are fixed by fine grid smoothing. We consider the standard monotone multigrid method induced by the multilevel nodal basis and a truncated version. Global convergence results and asymptotic estimates for the convergence rates are given. The numerical results indicate a significant improvement in efficiency compared with previous multigrid approaches.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 40
    Publication Date: 2014-02-26
    Description: The design of cost-efficient networks satisfying certain survivability constraints is of major concern to the telecommunications industry. In this paper we study a problem of extending the capacity of a network by discrete steps as cheaply as possible, such that the given traffic demand can be accommodated even when a single edge or node in the network fails. We derive valid and non-redundant inequalities for the polyhedron of capacity design variables, by exploiting its relationship to connectivity network design and knapsack-like subproblems. Computational work using this model and the additional inequalities is in progress.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 41
    Publication Date: 2014-02-26
    Description: In this paper, a rather recent algorithmic approac to the numerical simulation of macromolecula processes is surveyed. It avoids the numerical stiff integration o thousands up to millions of ODE's by constructing a scale of discret Hilbert spaces, especially weighted sequence spaces, and establishing corresponding Galerkin method. Examples including polyreactions o industrial relevance and ecological waste management by biochemica recycling illustrate the importance and efficiency of the algorithm.
    Keywords: ddc:000
    Language: English
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  • 42
    Publication Date: 2014-02-26
    Description: We show that, given a wheel with nonnegative edge lengths and pairs of terminals located on the wheel's outer cycle such that no two terminal pairs cross, then a path packing, i.~e.,a collection of edge disjoint paths connecting the given terminal pairs, of minimum length can be found in strongly polynomial time. Moreover, we exhibit for this case a system of linear inequalities that provides a complete and nonredundant description of the path packing polytope, which is the convex hull of all incidence vectors of path packings and their supersets.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 43
    facet.materialart.
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    Publication Date: 2019-10-24
    Keywords: ddc:000
    Language: German
    Type: annualzib , doc-type:report
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  • 44
    facet.materialart.
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    Publication Date: 2019-10-24
    Keywords: ddc:000
    Language: German
    Type: annualzib , doc-type:report
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  • 45
    Publication Date: 2022-07-07
    Description: The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schrödinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 46
    Publication Date: 2022-07-19
    Description: Sparse LU factorization offers some potential for parallelism, but at a level of very fine granularity. However, most current distributed memory MIMD architectures have too high communication latencies for exploiting all parallelism available. To cope with this, latencies must be avoided by coarsening the granularity and by message fusion. However, both techniques limit the concurrency, thereby reducing the scalability. In this paper, an implementation of a parallel LU decomposition algorithm for linear programming bases is presented for distributed memory parallel computers with noticable communication latencies. Several design decisions due to latencies, including data distribution and load balancing techniques, are discussed. An approximate performance model is set up for the algorithm, which allows to quantify the impact of latencies on its performance. Finally, experimental results for an Intel iPSC/860 parallel computer are reported and discussed.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 47
    Electronic Resource
    Electronic Resource
    Springer
    Journal of science education and technology 2 (1993), S. 397-406 
    ISSN: 1573-1839
    Keywords: Engineering ; technological literacy ; hands-on experiments ; active learning ; content instruction ; videotaping
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General , Technology
    Notes: Abstract Media reports indicate the decline of the technological literacy of American youth, especially that students in other countries are better prepared in science and mathematics. Our active-learning program, which consists of numerous hands-on experiments, introduces engineering applications into science and math programs, that will demonstrate to students the usefulness of the theory that they currently do not see as useful. The program, when fully developed, will make optimum use of technology, especially computers and videotapes. The hands-on experiments allow students to discover fundamental principles through data analysis and then use the principles to synthesize a solution to a technological problem. This discovery-based education will help school systems better meet performance standards such as those in the Maryland School Performance Plan. The experimental approach to science education is especially important in a technology-oriented economy where children use the new technologies without understanding the principles on which they are based.
    Type of Medium: Electronic Resource
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  • 48
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 393-399 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The univariant element, Q1 P0, and the multivariant elements, Q1+P0 and R2+ P0, are compared for the numerical simulation of the flow in extrusion dies. The pressure distribution obtained by using the Q1 P0 element was found to be afflicted with the checkerboard pressure mode. On the other hand, the multivariant elements, Q1+ P0 and R2+ P0, gave accurate and physically reasonable velocity and pressure distributions. The computed values of the pressure drop across extrusion dies matched well with the pressure drop determined experimentally.
    Additional Material: 12 Ill.
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  • 49
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 377-382 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The viscoelastic responses of some molten polymers, and particularly of low density polyethylene (LDPE), are known to vary with processing history. Reasons for the variations include the effects of shear history on morphological states of the polymer, or on its molecular weight parameters. A typical low density polyethylene has been used to test the shear-history dependence concept following a variety of processing steps. The polymer was sheared in single-screw and twin-screw extruders, and in a high speed melter / mixer (Gelimat). Samples also were precipitated from very dilute solutions in trichlorobenzene and in p-xylene. GPC analyses showed that, in general, these procedures did not affect the various moments of molecular weight. An exception was the Gelimat-mixed sample, for which mild reductions in Mn and Mw were noted. In contrast, melt viscosity and elasticity readings, the former from low shear evaluations and the latter from extrudate swelling, were affected by the various procedures. A drop in melt viscosity and in elasticity was observed, being most pronounced for precipitated and twin-screw extruded versions of the LDPE. Reductions also were observed in the specimen sheared in the Gelimat instrument. Following conditioning at the test extrusion temperature (170°C), viscous and elastic responses tended to revert to those of the unsheared control sample, the exception again being the sample sheared in the Gelimat melter / mixer. Of the various mechanisms proposed in the literature to account for transient property changes such as those reported, temporary changes in the degree of chain entanglement appear the most satisfactory explanation. Irreversible alterations in viscoelastic properties may be associated with changes in molecular weights due to processing at high shear.
    Additional Material: 2 Ill.
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  • 50
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 400-409 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A model for the filling stage of injection molding of viscoelastic thermoplastics in cavities of complex shape is presented. The model considers two-dimensional melt flow, with converging and diverging flow patterns induced by complex boundary shape and by the presence of an obstacle. The model is non-isothermal (with the melt loosing heat to the mold walls as it travels into the cavity) and handles a viscoelastic (following the White-Metzner model) material with properties that vary with temperature, shear rate, and pressure. The numerical method is based on finite differences, with boundary fitted curvilinear coordinates used in the mapping of the flow field (which has an arbitrary shape that evolves with time) into a time invariant rectangle. The numerical results reveal geometry-induced asymmetries in the flow and thermal fields as well as the effect of various process parameters on the pressure and temperature profiles in the cavity. The model admits variable cavity thickness, thus allowing for a treatment of the cavity thickness as a process parameter in the simulations.
    Additional Material: 10 Ill.
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  • 51
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 497-500 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The use of polymeric materials in building or construction applications is steadily increasing. Therefore, the potential for these materials to be exposed to fire is also increased. The understanding of the pyrolysis characteristics of these materials is thus a necessity. There are many standard tests used to evaluate materials. Unfortunately, the correlation between these tests and large scale fire is less than desirable. A new bench scale rate of heat release apparatus, the Cone Calorimeter, is now being used more frequently in pyrolysis testing of polymeric materials. This apparatus has been shown to correlate much better between room scale testing and large scale fire testing. The cone Calorimeter provides a pyrolysis profile of a material under ambient oxygen conditions. Characteristics such as ignition time, total heat release, maximum rate of heat release, mass loss during pyrolysis, CO2, CO, and smoke production are determined. In this work several almost neat polymers are examined and the general pyrolysis characteristics of these polymers are discussed. The objective of this work is to provide information of basic polymeric pyrolysis properties of these materials. Variations in the material, i.e., molecular weight, polydispersity, and residual catalysis, along with changes in testing procedures, can have dramatic effects on results. Obviously the addition of flame retardant and flame retardant packages to any of these materials will have dramatic effects on results.
    Additional Material: 4 Ill.
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  • 52
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993) 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 53
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 513-521 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The overall isothermal crystallization kinetics for nucleated and non-nucleated isotactic polypropylene (iPP)-dotriacontane systems was investigated. Adipic acid was used as the nucleating agent. Half-time was determined via differential scanning calorimetry as a function of the experimentally controlled variables dilution, crystallization temperature, and the addition of nucleating agent. The influence of these variables on crystallization mechanism and spherulitic structure, as implied by the Avrami analysis, was determined. The influence of these variables on fold surface energy was examined by the Lauritzen and Hoffman analysis.
    Additional Material: 6 Ill.
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  • 54
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The overall non-isothermal crystallization kinetics for nucleated and non-nucleated isotactic polypropylene (iPP) in dotriacontane systems was investigated. Adipic acid was used as the nucleating agent. Crystallization peak temperature was determined via differential scanning calorimetry as a function of the experimentally controlled variables iPP concentration, cooling rate, and nucleating agent concentration. The influence of these variables on crystallization mechanism and spherulitic structure as implied by the Ozawa and Ziabicki analyses was determined. The non-isothermal crystallization kinetics presented here are the first for iPP-diluent systems with and without nucleating agent.
    Additional Material: 8 Ill.
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  • 55
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 543-548 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The static shear strength and static friction of three thermoplastics have been investigated for the case of contact between a bulk plastic sample and a very smooth metallic plate. The minimum tangential force required to shear the interfacial adhesion bonds between the two surfaces was measured and defined as the adhesion component of friction Fa. Experimental results showed that Fa is large when the surface energy is high or the interfacial energy is small and that a correlation may exist between this force and the work of adhesion evaluated from Dupré equation. The real area of contact Ar was also measured using an optical device designed to handle samples and experimental conditions similar to the static friction tests. It was found that Ar is proportional to Pa0.9 where Pa is the apparent pressure of contact and an increase of Fa with Pr was observed. The static shear strength τ has been evaluated as the ratio Fa/Ar, and its relationships with the real contact pressure P approximated by linear functions. It was concluded that τ increases at high P, although it has not been verified for ultra-high-molecular-weight polyethylene. An attempt has been made to explain the observed break in the data. The results indicated that (τ/τb) = κ′(τa/Pa) where b refers to bulk, a to apparent values, and κ′ is a proportionality constant that depends on the plastic material.
    Additional Material: 10 Ill.
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  • 56
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 549-558 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A variety of different styrene monomers [styrene (S), p-fluorostyrene (p-FS), pentafluorostyrene (PFS), p-chlorostyrene (p-ClS), p-bromostyrene (p-BrS), p-methylstyrene (p-MS), p-tert-butylstyrene (p-tBS), p-methoxystyrene (p-MOS), p-ethoxystyrene (p-EOS), and p-propoxystyrene (p-POS)] have been polymerized by radical and cationic mechanisms. Copolymers of S/PFS, S/p-ClS, S/2-vinyl-naphthalene (2-VN), and S/p-phenylstyrene (p-PhS) were prepared by radical polymerization. All polymers were fully amorphous and transparent and exhibited only one glass transition temperature in the temperature range 77 to 141°C. Thin films of the polymers were subjected to external electrical partial discharges (PD). Typically, 20 PD experiments were conducted for each polymer and the data for the time to breakdown were adapted to the two-parameter Weibull distribution function. The resistance towards PD of the various polymers was found to depend strongly on the monomeric structure. Complementary PD experiments on a series of narrow molecular mass polystyrenes confirmed that the minor variation in molecular mass between the different styrene polymers is of no importance for the PD resistance. The PD resistance of the homopolymers decreased in the following order: PS ≍ P(p-MS) 〉 P(p-tBS) ≍ P(p-BrS) 〉 P(p-POS) 〉 P(p-ClS) ≍ P(p-MOS) 〉 P(p-EOS) ≍ P(p-FS) 〉 P(PFS). The time to breakdown for copolymers of S and PFS decreased monotonously with increasing PFS content. Styrene copolymers with low molar contents of 2- VN and p-PhS exhibited a higher resistance towards PD than PS. The results are discussed with reference to various properties of the studied polymers, such as segmental mobility, ionization potential, resonance stabilization, and reactivity of the radicals formed.
    Additional Material: 10 Ill.
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  • 57
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993) 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
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  • 58
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 614-621 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The glass transition temperatures in bismaleimide-based resins were investigated using different stoichiometric ratios of 1, 1′-(methylenedi-4, 1-phenylene)bismaleimide (BMI) and 4, 4′-methylenedianiline (MDA). The resin cure involves a low temperature primary amine addition to the maleimide double bonds and a high temperature homopolymerization of the maleimide double bonds. The network topology and the glass transition temperature changes with resin composition and curing conditions were determined using differential scanning calorimetry (DSC). An empirical model was used to relate the glass transition temperature to the extents of the amine addition and the homopolymerization reactions in 1:1 and 2:1 BMI:MDA resins. The changes in thermal properties with resin post-cure were also examined.
    Additional Material: 7 Ill.
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  • 59
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 640-644 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Dynamic mechanical properties, tensile properties, and scanning electron microscopy of blends of poly(methyl methacrylate) and polycarbonate were investigated after phase separation above their cloud point temperature by annealing in a hot press. The dynamic mechanical properties show that phase separation proceeds more distinctly for the blends annealed at higher temperature and for longer time. The scanning electron micrographs show that the morphology of phase separated blends varies with the conditions of heat treatment. The tensile properties of phase separated blends deteriorate on account of the coarsening of the brittle dispersed phase over the optimum size and the occurrence of voiding during the heat treatment.
    Additional Material: 6 Ill.
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  • 60
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993), S. 665-674 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The packing stage starts at the end of mold filling. During this stage, additional material is forced into the mold to compensate for the shrinkage during subse-quent cooling. Underpacking results in molded parts with dimensional variation. Overpacking causes flash at the parting lines, stick during ejection, and excess residual stresses resulting in warpage. The packing stage is thus extremely important in the determination of the final quality of the product. Despite its importance, analysis of the packing stage has been relatively ignored, particularly the viscoelastic effect. In this work, the analysis of the isothermal packing stage is presented for a Maxwell fluid. A set of governing equations is derived for a two-dimensional mold and solved using the Galerkin finite element method. In addition to the distribution of velocity and pressure, the model predicts the stresses in the planar direction, which could be used for subsequent calculation of the residual stresses.
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  • 61
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    Polymer Engineering and Science 33 (1993), S. 675-685 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The objective this work was to determine the effects of selected polyester catalysts on the reaction of a polyester with epoxy functional polymers. Polyesters containing various catalyst metals were melt blended with either an ethylene-co-glycidyl methacrylate or a styrene-co-glycidyl methacrylate copolymer. The viscosities of the blends were monitored as a function of mixing time using torque rheometry. In addition, the molecular weight distributions of selected samples were analyzed using gel permeation chromatography. Both the torque rheometry and the gel permeation chromatography results indicate that the polyester reacts with epoxy functional polymers. This reaction occurs under conditions and at processing times which are readily obtainable in conventional melt processing equipment. Furthermore, the reaction kinetics of polyesters with glycidyl methacrylate copolymers are dramatically affected by the nature of the catalyst system used to prepare the polyester. Under the conditions used, antimony catalysts are particularly effective at promoting the reaction between polyesters and the epoxy functionality and the activity of the catalysts studied appears to decrease in the following order: antimony 〉 gallium 〉 tin ≃ titanium 〉 germanium. Manipulation of the polyester catalyst system may offer a method to control the extent of reaction obtained in reactive processing of polyesters with epoxy functional compounds.
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  • 62
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    Polymer Engineering and Science 33 (1993), S. 709-715 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The flow kinematics of power-law fluids in fishtail dies is studied. A general isothermal three-dimensional finite element code developed by the authors is used for the flow analysis purpose. The basic geometry of the fishtail die is defined by simple super-elliptical curves, which allows a smooth transition from a circle to a slit. The three-dimensional path line and the residence time distribution (RTD) are calculated from the velocity field obtained from the finite element solution of the conservation equations. The effects of the rheological properties and the die geometry on the path line pattern and the residence time distribution are investigated. The results indicate that as both the length of the transition zone and the fishtail angle increases, the residence time distribution becomes more uniform. However, the power-law index does not affect the residence time distribution significantly.
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  • 63
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    Polymer Engineering and Science 33 (1993), S. 736-741 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The polymers of the aromatic nitrogen compounds N-methyl-pyrrole (P-N-Me-PPY), carbazole (PCarb), and aniline (PANI) have been investigated with electro-optical and surface analytical methods. The in-situ reflection spectra indicate the formation of polarons or bipolarons during electrochemical oxidation, depending on polymer type. The absorption bands can be attributed to changes in the electronic structure with regard to the applied potential. Photocurrent spectra of P-N-Me-PPY and PCarb show a p-type semiconducting behaviour for the polymers in the reduced state. The transition to the oxidized state with quasi-metallic properties is indicated by a significant shift in the Fermi level energy and can be followed with XPS and UPS measurements.
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  • 64
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    Polymer Engineering and Science 33 (1993), S. 838-844 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Extruded films of liquid crystalline polymer (LCP)/fluoropolymer blends were melt drawn to develop uniaxial orientation of a microfibrillar dispersed LCP phase. The anisotropy of the films increased with increasing draw and LCP content in the blend. Laminated composite plates were prepared using the extruded sheets as prepreg. The mechanical properties and coefficient of thermal expansion (CTE) of the prepreg and laminates agreed well with predictions from composite lamination theories. The potential for replacing glass fiber reinforced fluoropolymers with LCP/fluoropolymer blends in applications such as microwave circuit boards is discussed.
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  • 65
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    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 33 (1993) 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 66
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    Polymer Engineering and Science 33 (1993), S. 865-876 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: This review presents a general picture of suspension, dispersion, and interfacial polycondensation processes employed for the preparation of beaded resins, dry powders, and high solid dispersions. The polymer systems covered include polyamides, polyesters, polycarbonates, polyurethanes, and phenol-formaldehyde and urea-formaldehyde resins. Basic features of heterogeneous polycondensation processes are outlined, and different mechanisms of particle formation in suspension, dispersion, and interfacial polycondensation are discussed. Effects of manufacturing parameters such as feed ratio, droplet/particle stabilizer, and stirrer speed on product characteristics are also briefly covered.
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  • 67
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    Polymer Engineering and Science 33 (1993), S. 781-788 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The extrudate swell and the dynamic rheological properties of poly(butylene terephthalate) (PBT) and polyamide 6 (PA6) binary blends were investigated at 240°C. The extrudate swell of the blend varies with the viscosity ratio and composition of constituents, and it is several times larger than that of homopolymers when the viscosity ratio of constituents is around unity. The dynamic oscillatory data could be interpreted by Oldroyd's emulsion model proposed by Graebling, et al. These results suggest that the extrudate swell is caused by the shape recovery of the dispersed particles. A semi-empirical method to estimate the terminal relaxation time with experimental data was introduced, and a clear correlation between the extrudate swell and the terminal relaxation time was obtained.
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  • 68
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    Polymer Engineering and Science 33 (1993), S. 819-826 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Much work in recent years had focused on the improvements of the impact properties of engineering thermoplastics by the addition of a low modulus modifier that contains polar moieties as a result of polymerization or that has been modified to contain polar moieties as a result of various grafting techniques. Styrenic block copolymers (styrene-ethylene/butylene-styrene) functionalized with maleic anhydride have proved useful as impact modifiers and compatibilizers in blends with engineering thermoplastics. This paper focuses on the use of these functionalized elastomers to modify nylon 6. In such compositions, a nylon material with unique mechanical performance may be achieved using the functionalized elastomer either alone or in combination with an unfunctionalized styrenic block copolymer. The optimization of performance in these rubber toughened polyamide blends using various types of styrenic block copolymers is discussed. The morphology as it pertains to performance is also reviewed. The information contained herein may prove useful in obtaining a better understanding of the mechanisms of compatibilization and modification of nylon 6 systems.
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  • 69
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    Polymer Engineering and Science 33 (1993), S. 827-837 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Oriented blends of poly(ethylene terephthalate) (PET) and high density polyethylene (HDPE) with and without compatibilizing agent have been studied with regard to orientation temperature, stretch rate, extension ratio, mode of orientation, and blend composition. These oriented blends have been characterized using infrared spectroscopy and differential scanning calorimetry. The tensile and tensile impact properties were also investigated. The results show that blends with compatibilizer show strain hardening upon orientation, whereas the blend without compatibilizer does not strain harden upon orientation. The blends with less PET content have been difficult to orient. The morphology of these blends show fibril structure, highly oriented in the direction of stretch. Infrared measurements show that PET within the blend has undergone strain induced crystallization upon orientation. It has also been observed that the mechanical properties, such as the modulus and ultimate stress, show improvement upon orientation. Simultaneously stretched blends show better physical properties than sequentially oriented blends.
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  • 70
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    Polymer Engineering and Science 33 (1993), S. 895-900 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: This paper illustrates the factors that control brittle failure under fatigue loading for test specimens cut from medium-density polyethylene pipes for gas distribution. A square bar specimen cut from a pipe with a notch was made and a fatigue test was conducted to cause a brittle failure. To obtain the correlation among stress range, frequency, temperature, and cycles to failure in this fatigue test, Coffin-Manson's frequency-modified fatigue life equation was adopted and the material constants were determined. By gradually lowering the frequency, the resistance to creep can be estimated because cycles to failure - indicating the fatigue damage - decreased, and the actual loading time - indicating the creep damage - increased.
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  • 71
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    Polymer Engineering and Science 33 (1993), S. 923-930 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The interfacial tension, phase morphology, and phase growth was determined for four polymer blend systems: polyethylene/polystyrene, polyethylene/polyamide-6, polystyrene/polyamide-6, and polystyrene/poly(ethylene terephthalate). Generally, high interfacial tension correlates with coarse phase morphology and rapid phase coalescence. The addition of various potential compatibilizing agents to these binary blend systems results in lowered interfacial tension, finer and stabilized phase morphologies. The characteristics of different compatibilizing agents were compared for several of the blend systems. We also look at the influences of compatibilizing agents on mechanical properties of the blend systems. Some compatibilizing agents are able to produce substantial improvements in ultimate properties.
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  • 72
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    Polymer Engineering and Science 33 (1993), S. 937-943 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Unidirectional sheets were extruded of an in-situ composite of thermotropic liquid crystalline Vectra B950 in a matrix of polyphenylene-ether and polystyrene. Three important processing parameters were systematically varied: draw-ratio, slit opening and extruder throughput. Morphology and mechanical properties of these films were determined, and qualitatively related to the processing conditions.
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  • 73
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    Polymer Engineering and Science 33 (1993), S. 959-970 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: It is of great importance to accurately measure or predict the Residence Time Distribution (RTD) in designing extruders and/or in setting up a proper operating condition, because chemical reactions depend significantly on the RTD and temperature when chemical reactions take place during the extrusion process. A previous method to predict the RTD can analytically determine RTD, Residence Time Distribution Function f(t) and Cumulative Residence Time Distribution Function F(t), based on a simplified two-dimensional velocity field in an extruder. However, this previous method cannot accurately take into account the three-dimensional circulatory flow inside the extruder. The present paper suggests a new method to accurately determine the RTD taking into account the three-dimensional circulatory flow and presents a new formula derived to calculate f(t). In order to demonstrate the applicability of the new method including the circulatory flow effect, RTD, f(t) and F(t) were calculated based on a three-dimensional velocity field obtained via a quasi-three-dimensional finite element analysis. It was found that the previous method has a tendency to underestimate the RTD, owing to the neglect of the three-dimensional circulatory flow in comparison with the new method.
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  • 74
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    Polymer Engineering and Science 33 (1993), S. 980-988 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Experimental data confirm the utility of the following simple equation in predicting the spin coating behavior of polyimide precursor solutions: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm h} = {\rm c\beta }_{\rm 0} {\rm k}^{{\rm \beta }_{\rm 1} } {\rm \omega }^{{\rm \beta }_{\rm 2} } {\rm t}^{{\rm \beta }_{\rm 3} } \quad\quad\quad\quad{\rm (1)} $$\end{document} in which \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {c = {\rm polymer\, solution\, solid\, weight\, fraction;}} \\ {\beta _i = {\rm fitted\, coefficient\, (Greek\, letter\, beta)};} \\ \quad{h = {\rm film\, thickness\, after\, cure\, or\, solvent\, removal};} \\ \quad{k = {\rm polymer\, solution\, kinematic\, viscosity, centistokes};} \\ {t = {\rm time},{\rm and;}} \\ \quad{\omega = {\rm wafer\, spin\, speed, rpm (Greek\, letter\, omega)}.} \\ \end{array} $$\end{document}.
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  • 75
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Ternary systems consisting of polypropylene (PP), ethylene-propylene-dieneterpolymer (EPDM) and different types of inorganic fillers (kaolin, BaSO4) have been investigated with respect to their mechanical behavior. On the basis of an Interphase model, it was possible using the modified van der Poel equation to describe the temperature dependence of the storage modulus G′(T) and the loss modulus G″(T). The interphase properties G′(T) and G″(T) could be calculated.
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  • 76
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    Polymer Engineering and Science 33 (1993), S. 1251-1260 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Signal deterioration of optical discs depends strongly on the substrate surface roughness. Characteristics of surface roughness of the molded substrate have been studied in order to clarify the transcription mechanism of smooth surfaces in injection molding of polycarbonate resin. When the melt temperature, mold temperature, and injecting rate are low, microscopic flow marks more than 5 nm deep are observed on the surface. These flow marks are formed when the melted resin near the mold wall is cooled to the no-flow temperature of resin before it comes into contact with the mold wall. Molding transcription improves by optimizing the molding conditions for preventing these flow marks. As a result, the surface roughness of the molded substrate obtained is 3.2 nm in maximum height Rmax, which is nearly equal to that of the mold stamper at 2.7 nm in Rmax.
    Additional Material: 17 Ill.
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  • 77
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    Polymer Engineering and Science 33 (1993), S. 1279-1287 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: A finite element numerical analysis of preform inflation associated with the injection blow molding process has been developed using a neo-Hookean constitutive model. The analysis is capable of predicting final wall thickness distributions for axisymmetric mold geometries. Experimental studies were conducted on a Uniloy injection blow molding machine (Model 189-3 and Model 122). A twelve ounce (355 mL) cylindrical bottle mold was instrumented with contact sensors, thermocouples, and pressure transducers. Visualization studies of the inflation process were performed using specialized tooling and high-speed video cameras. The experimental studies provide justification for analyzing the deformation by means of a static elastic approach. The predicted wall thickness distribution is in reasonable agreement with the experimental data. Nonuniformities in the temperature distribution in the preform were found to have the most significant impact on the inflation behavior and the resulting wall thickness.
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  • 78
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    Polymer Engineering and Science 33 (1993), S. 1301-1307 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Dielectric α-relaxation of a bisphenol-A type epoxide oligomer has been investigated in the vicinity of the glass transition temperature (Tg) by the direct current (DC) transient method. The logarithm of the DC transient current for the oligomer was well approximated by the third order function of the logarithm of time. The complex dielectric constant was calculated through the Fourier transformation of that approximation function according to Simpson's integration rule in a frequency range of 10-5 - 1 Hz. At the temperature around the Tg (45°C), the dielectric α-relaxation process of the oligomer was found to be governed by the Havriliak-Negami equation. The relationship between the DC conductivity (σ) and the dielectric relaxation time (τ), σ·τm = const, is valid near and above the Tg of the oligomer. The DC transient current method combined with the DC conduction and the dielectric bridge measurements is considered to be a practical tool for analyzing the dielectric α-relaxation process of the epoxide oligomer over a wide frequency and temperature range.
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  • 79
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    Polymer Engineering and Science 33 (1993), S. 1329-1335 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: In this study, styrene-(ethylene-co-butylene)-styrene (SEBS) triblock copolymer (Kraton G-1652) was modified with maleic anhydride (MA). The maleated SEBS was used as compatibilizer for the blends of Nylon 6 (PA6) and SEBS. The morphology and impact strength of the blends were measured as functions of concentration and MA graft ratio of maleated SEBS. The compatibility and fracture mechanism of the blends were evaluated from the SEM micrographs of the xylene-etched surfaces and of fractured surfaces. Some of the blends exhibited an impact strength up to about 30 fold greater than neat PA6. The fracture involved both both cavitation and shear yielding. The mechanism of compatibilization of maleated SEBS in the ternary components blends was proposed.
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  • 80
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    Polymer Engineering and Science 33 (1993), S. 1341-1351 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: This paper reports on the theoretical and experimental studies of structure formation and strengthening (stiffening) of flexible-chain polymers. Two techniques of strengthening relying on the melt extrusion, i.e., orientational crystallization (crystallization initiated by melt extension) and drawing (uniaxial stretching of a crystallized polymer) are analysed by theory. The experiments involved preparation and study of melt extruded films and film fibers of linear polyethylene formed by the two techniques mentioned above. The effect of the degree of orientation and other parameters of the formation processes on the mechanical characteristics and the factors limiting the ultimate values of these characteristics are discussed. It is shown that multistage drawing succeeds in achieving a higher tensile strength and elastic modulus (1.2 and 35 GPa, respectively) than the orientational crystallization, which gives 0.8 and 15 GPa. The strengthening by drawing is accompanied by microcrack formation. In contrast, no discontinuities are observed in orientationally crystallized samples up to their ultimate extension.
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  • 81
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    Polymer Engineering and Science 33 (1993), S. 1370-1371 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Additional Material: 1 Ill.
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  • 82
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    Polymer Engineering and Science 33 (1993), S. 1381-1389 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Because of the inability of existing automotive bumpers to absorb energy during impacts over the supports, energy absorbers have to be used to make bumpers effective in barrier impacts. A parametric analysis of a novel double-beam bumper concept has shown that its performance, in terms of energy absorption and impact forces, is insensitive to the location of the point of impact. Physical realizations of this concept, which may not require more material than existing designs, and which are particularly suited to thermoplastic materials, have been developed.
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  • 83
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    Polymer Engineering and Science 33 (1993), S. 1270-1278 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Flow in a three-dimensional channel with a sinusoidally-wavy, vertical wall is examined for the case of applied down- and cross-channel velocity components. An important parameter for the analysis of the nature of laminar mixing in the flow field occurs when the changes in the downstream direction can be decoupled from the changes in the cross-channel direction, thereby allowing for a two-dimensional solution of the system of equations. This paper shows the effect on the nature of laminar mixing when the decoupling of the momentum equations from a fully three-dimensional case to one where a two-dimensional solution can be performed. Experiments are performed on a channel with sinusoidally varying vertical walls that cover the range of decoupling criteria. Silicone pigmented either white or black was run in the apparatus, cured, and cross-sectioned. The cross sections embody a local, detailed history of the state of mixing as it proceeds down the mixer. The amount of mixing is presented as a function of position at each cross section for the different channel configurations. The nature of mixing changes from a linear growth rate in the amount of interfacial area to an exponential rate as the amplitude of the wave is increased. Results demonstrate the existence of chaos, islands, and the factors affecting the mixing behavior.
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  • 84
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    AIChE Journal 39 (1993), S. 422-433 
    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 memory integral based on convolution of the unit step response to loading a clean pellet with concentration history at the pellet surface is proposed for computations of mass transfer in adsorption process simulation. Although rate laws are widely used to describe diffusion and sorption in pellets for slow (Glueckauf, 1955) and moderate (Kim, 1989) rates of mass transfer, these models fail to describe mass transfer at short contact times because the concentration history experienced by the pellet is not accounted for. To facilitate memory integral computations, approximations to the unit step response to loading a clean pellet are derived based on a single moving finite element and by asymptotic matching in time. Numerical evaluation of the memory integral is demonstrated on simple cycles which show the merits of this approach.
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 39 (1993), S. 397-412 
    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 bulk, transition and Knudsen regime diffusion in structures of freely overlapping fibers of various orientation distributions was numerically investigated, and the interrelation of the resulting effective diffusivities was examined. Fibers were randomly positioned and oriented in d = 1, 2, or 3 directions. A Monte Carlo simulation scheme was employed to determine the effective diffusivities from the mean-square displacement of random walkers traveling in the interior of the porous structure. The effective diffusivity was found to depend strongly on the orientational distribution of the fibers, porosity of the fibrous structures, and Knudsen number. The tortuosity factor decreased in general with increasing porosity, approaching at the limit of dilute beds the lower bound derived for each direction of diffusion from variational principles. The simulation results agreed well with experimental values of the bulk tortuosity of fibrous beds from the literature. It was also found that the reciprocal additivity or harmonic average effective diffusivity expression (Bosanquet formula), commonly used to estimate transition regime diffusivities from the values at the ordinary and Knudsen diffusion limits, provides an excellent approximation for the effective diffusivity of fibrous beds, except for that parallel to the fibers of a unidirectional structure.
    Additional Material: 17 Ill.
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  • 86
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    AIChE Journal 39 (1993), S. 461-470 
    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 asymptotic behavior of fixed-point methods in the complex domain is studied. Both direct substitution and Newton's method exhibit stable periodic and aperiodic behavior from real- or complex-valued starting points. Moreover, multiple stable periodic orbits can exist for direct substitution. Traditional trust region (or dogleg) methods, on the other hand, often terminate at singular points, which correspond to nonzero-valued saddlepoints in the least-squares function that can be arbitrarily far from a solution. Furthermore, the basins of attraction of these singular points are usually dispersed throughout the basin boundaries in the complex domain, clearly illustrating that singular points (via the dogleg strategy) also attract either real- or complex-valued starting points.In light of this, an extension of the dogleg strategy to the complex domain, based on a simple norm-reducing, singular point perturbation, is proposed. This extended trust region method removes all forms of nonconvergent behavior and always terminates at a fixed point, even from critical point (worst-case) initial values. Many numerical results and geometric illustrations using chemical process simulation examples are presented.
    Additional Material: 9 Ill.
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  • 87
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    AIChE Journal 39 (1993), S. 446-460 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Most of the advanced nonlinear control algorithms require a model of the system to be controlled. Unfortunately, most of the processes in the chemical industry are nonlinear, and fundamental models describing them are lacking. Thus there is a need for the identification and control of nonlinear systems through available inputoutput data. In this article, we briefly introduce the input-output model used (polynomial ARMA models), and analyze its stability and invertibility. This paves the way to the development of a nonlinear-model-predictive controller. Implementation issues such as modeling of disturbance, state and parameter estimation are discussed. The theory presented is illustrated through examples.
    Additional Material: 6 Ill.
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  • 88
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    AIChE Journal 39 (1993), S. 471-492 
    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 separation of a binary mixture, using a third component having intermediate adsorptivity as desorbent, in a four section countercurrent adsorption separation unit is considered. A procedure for the optimal and robust design of the unit is developed in the frame of Equilibrium Theory, using a model where the adsorption equilibria are described through the constant selectivity stoichiometric model, while mass-transfer resistances and axial mixing are neglected.By requiring that the unit achieves complete separation, it is possible to identify a set of implicit constraints on the operating parameters, that is, the flow rate ratios in the four sections of the unit. From these constraints explicit bounds on the operating parameters are obtained, thus yielding a region in the operating parameters space, which can be drawn a priori in terms of the adsorption equilibrium constants and the feed composition.This result provides a very convenient tool to determine both optimal and robust operating conditions. The latter issue is addressed by first analyzing the various possible sources of disturbances, as well as their effect on the separation performance. Next, the criteria for the robust design of the unit are discussed. Finally, these theoretical findings are compared with a set of experimental results obtained in a six port simulated moving bed adsorption separation unit operated in the vapor phase.
    Additional Material: 18 Ill.
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  • 89
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 39 (1993), S. 505-509 
    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: 2 Ill.
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  • 90
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    AIChE Journal 39 (1993), S. 513-517 
    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: 6 Ill.
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  • 91
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    AIChE Journal 39 (1993), S. 518-520 
    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 Tab.
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  • 92
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    AIChE Journal 39 (1993), S. 510-512 
    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: 4 Ill.
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  • 93
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    AIChE Journal 39 (1993), S. 1716-1720 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Chabazite zeolites are used at Oak Ridge National Laboratory to decontaminate wastewaters containing 90Sr and 137Cs. Treatability studies show that chabazite can remove trace amounts of these nuclides from wastewaters containing much higher concentrations of calcium and magnesium. The design of ion-exchange columns for multicomponent systems requires a method for predicting multicomponent equilibria from binary, ternary and quaternary experiments, since the number of experiments required for an empirical equilibrium model is not generally feasible. Binary interaction parameters for the Wilson equation are used to predict solid-phase activity coefficients for the five-component system. The sum of squares of deviations between experimental and predicted solution concentrations for the data points available is calculated. The average deviation per data point for the five-component system is lower than for some of the ternary-and four-component data sets containing calcium or magnesium.
    Additional Material: 3 Ill.
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  • 94
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    AIChE Journal 39 (1993), S. 1708-1715 
    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 limiting current technique was used to measure area-averaged mass-transfer coefficients for surfaces containing many small reactive areas arranged in various patterns. Partially masked platinum electrodes were fabricated using photolithography, and mass-transfer measurements were performed with a rotating disk apparatus. The average mass-transfer coefficient was sensitive to the fraction of the electrode area exposed (ε), declining from values near that for a fully exposed surface for ε = 0.5 to less than 1% of the fully exposed value for ε = 0.001. For any given ε, the mass-transfer coefficient declined with increased spacing between reactive sites. The results were relatively insensitive to details of the site distribution, such as whether the sites were arranged in regular arrays (square or hexagonal lattices) or distributed randomly over the surface. For all conditions studied, the mass-transfer coefficient greatly exceeded that predicted by conventional models which apply the stagnant film approximation to the fluid surrounding a representative active site. This finding is qualitatively consistent with recent computational results, which suggest that convective transport enhances mass transfer at partially active surfaces to an extent not accounted for by adjustments in the effective film thickness.
    Additional Material: 6 Ill.
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  • 95
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    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 39 (1993), S. 1720-1720 
    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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  • 96
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    AIChE Journal 39 (1993), S. 1272-1280 
    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 instability analysis has been carried out to elucidate the unsteady flow conditions encountered in the typical circulating fluidized bed units in light of the conveyor-solids feeder interaction. The results successfully predict the critical velocity and the maximum solids circulation rates reported in the literature and explain the origin of such unstable conditions. Furthermore, the simulation, for the first time, reveals the importance of unit structure in improving the performance of circulating fluidized bed systems. Finally, the concept of a high-density circulating fluidized bed is proposed.
    Additional Material: 12 Ill.
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  • 97
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    AIChE Journal 39 (1993), S. 1303-1321 
    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 product compositions in single-feed distillation columns can be specified only in certain regions of the composition space, which depend only on the pressure, feed, and vapor-liquid equilibrium for the mixture. In nonideal mixtures, even without azeotropes, the regions may allow unusual product distributions. For example, the distillate in a “direct split” is composed primarily of the lightest component. Intuition and experience with relatively ideal mixtures suggest that the next most plentiful component is the intermediate boiler. In nonideal mixtures, however, with or without azeotropes, the next most plentiful component may be the highestboiling species with only trace amounts of the intermediate boiler. For azeotropic mixtures, distillation boundaries may give rise to additional restrictions on the product compositions. We describe how simple distillation boundaries deform into continuous distillation boundaries and, in a limited number of cases, how the simple distillation boundaries can be crossed in continuous columns for certain ranges of the design variables. Unfortunately, such designs may be quite sensitive to model uncertainties or to disturbances in the parameters.
    Additional Material: 24 Ill.
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  • 98
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    AIChE Journal 39 (1993), S. 1377-1388 
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Deposition of wax on the wall of oil pipelines is often regarded as a problem since the tube diameter is reduced. Consequently, more power is needed to force the same amount of oil through the system. A mathematical model for quantitative prediction of wax deposition for each hydrocarbon component has been developed. Each component is characterized by weight fraction, heat of fusion, and melting point temperature. A model explains how a phase transition in the flow from liquid oil to waxy crystals may create a local density gradient and mass flux, which depends on the local temperature gradient. The model predicts that wax deposition can be considerably reduced even when the wall temperature is below the wax appearance point, provided the liquid/solid phase transition, expressed by the change in moles of liquid with temperature, is small at the wall temperature. Deposition as function of time has been obtained as a solution of differential equations derived from the principles of mass and energy conservation and the laws of diffusion.
    Additional Material: 9 Ill.
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  • 99
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    AIChE Journal 39 (1993), S. 1411-1414 
    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: 7 Ill.
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  • 100
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    AIChE Journal 39 (1993), S. 1415-1419 
    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: 3 Ill.
    Type of Medium: Electronic Resource
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