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  • 2005-2009
  • 1990-1994  (359)
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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
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    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.
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    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.
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    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
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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
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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
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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
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  • 36
    facet.materialart.
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    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
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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
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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
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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
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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
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  • 43
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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
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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
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  • 47
    ISSN: 1432-0533
    Keywords: Canine galactosialidosis ; Morphology ; Biochemistry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary An adult-onset lysosomal storage disorder was diagnosed in a 5-year-old Schipperke dog with progressive cerebellar and central vestibular signs. It was characterized by cerebellar atrophy with extensive loss of Purkinje and granular cells, and hydrocephalus. Enlarged and vacuolated neurons were observed in spinal cord and brain; pancreatic centrolobular and islet cells were also vacuolated. Ultrastructurally, enlarged secondary lysosomes laden with lamellated membrane structures were present in neurons and empty enlarged vacuoles were found in pancreatic centroacinar, ductal, and islet cells. On frozen sections neurons stained with Ricinus communis agglutinin-I and wheat germ agglutinin. On paraffin sections neurons stained with luxol fast blue, periodic acid-Schiff, Concanavalia ensiformis agglutinin, and were autofluorescent. These findings indicate an accumulation of glycolipids containing terminal β-galactosyl and α-sialyl residues, and N-linked oligosaccharides. Tissue activity of lysosomal β-galactosidase was 50% of normal and the activity of β-hexosaminidase was elevated. Brain lipid-bound sialic acid was twice normal, with a small increase of GM1-ganglioside, but there was a significant elevation of GM2 (GD2) and GM3 (GD3). In addition, significant elevations of sialylated and non-sialylated oligosaccharides were noted. These clinical, biochemical and pathological findings are similar to those observed in human patients with adult-onset galactosialidosis.
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  • 48
    ISSN: 1432-0878
    Keywords: Gap junction ; Cell junction ; Immunocytochemistry ; Biochemistry ; Heliothis virescens (Insecta)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Abstract Subcellular fractions enriched in gap junctions with an ultrastructure similar to those in intact insect tissue have been obtained by extracting crude membranes from the tobacco budworm Heliothis virescens (Lepidoptera: Noctuidae) with 2.5 mM NaOH. n-Octyl-β-d-glucopyranoside (OG) was used to further purify integral membrane proteins in the NaOH-extracted fractions. A polyclonal antibody (R16) is described that specifically labels nonextracted and NaOH-extracted gap junctions in cell fractions by electron microscope immunocytochemistry. R16 immunostaining of sectioned Heliothis testis at the light-microscope level yields a pattern of immunoreactivity consistent with the distribution of gap junctions in the tissue. R16 identifies a 40-kDa protein as a candidate gap junction protein on immunoblots of crude membrane, NaOH-extracted and NaOH/OG-extracted fractions.
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  • 49
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 24-25 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Measurements of surface tension of flame-, plasma- and UV-treated PP-EPDM samples show that all three methods of pretreatment significantly increase the surface tension. The flame or plasma pretreatment increases especially the polar element of surface tension while the UV-treatment enhances the disperse element. The measurements were carried out with a new fully automatic unit for determining contact angles (AURAM).
    Additional Material: 3 Ill.
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  • 50
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 35-39 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Experimental data are reported for ion exchange equilibria of binary systems on Amberlite IR-120 resin, at different temperatures and total ionic concentrations in aqueous solutions. These systems exhibit non-ideal behaviour in both phases, and the equilibrium characterization has been based on the law of mass action, using Wilson and Meisssner, and Kusik equations to correlate the activity coefficients in the resin and aqueous solutions, respectively. Equilibrium constants, standard thermodynamic properties (Gibbs free enthalpy changes, enthalpy and entropy) and Wilson binary parameters were obtained as functions of temperature.
    Additional Material: 4 Ill.
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  • 51
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993) 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 52
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 62-67 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The kinetics of methane oxidative coupling (OCM) was studied using 1 g of Na-Mn2O3 catalyst at 1073 to 1123 K, in an integral flow reactor (I.d. = 10 mm), at atmospheric pressure with methane and oxygen partial pressures of 0.27 and 0.13 bar, respectively, so that the ratio of CH4 to O2 was 2. The flow rate range was 50 to 200 ml/min. the kinetic data were analyzed by the Rideal-redox type of rate equation assuming the methyl radical and active surface oxygen to be the steady-state intermediates. Oxidation and reduction rate constants (Kox, Kred) for methane consumption were calculated from experimental catalysis results by computer simulation using the multiple least squares method. The activation energies at rate constants Kox and Kred for this type of catalyst were reported as 43.26 and 62.2 kcal/mol, respectively.
    Additional Material: 9 Ill.
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  • 53
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 130-146 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new set of rate equations for gas desorption has been derived from the laws of thermodynamics and motion and the kinetic theory of gases. The equations assume that gas desorption or absorption originally represents an isothermal change at the interface, similarly to condensation or vaporization. The mass transfer in gas desorption or absorption is initially caused by external work being done on the system and takes place as work done by the system which instantly develops a concentration gradient, increases in internal energy and temperature, and a deviation from the ideal gas behaviour inside MTZ in the process of mass transfer. After cessation of external work, these conditions disappear following the transfer of a small residual mass at a constant velocity and a decrease in internal energy inside the MTZ.
    Additional Material: 10 Ill.
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  • 54
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Theoretical and experimental investigations were performed with cold water models of bottom-blown metallurgical ladles in order to develop a mathematical description of the mixing processes in such reactors. This analytical model is based on the subdivision of the reactor into interacting subspaces, whereby each subspace is regarded as an ideal mixer. The convective mass transfer between the subspaces is represented by constant coupling coefficients, and the mass balance for the material to be mixed in provides a homogeneous system of differential equations to determine the time dependence of concentration in the individual subspaces. Different combinations of interacting subspaces are represented. The flow field and the distribution of turbulence intensity measured by LDA in water models and the concentration profiles in mercury models measured by EMF cells show that a subdivision into five subspaces is adequate. Size, position and interaction coefficients are also determined by experiments. The calculated mixing times agree well with those measured.
    Additional Material: 28 Ill.
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  • 55
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 200-205 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Henry's law is often used to correlate the solubility of a gas in water. Such an approach is frequently employed to calculate the solubility of hydrogen sulphide in water. However, Wright and Maass [1] clearly demonstrated that the strict Henry's law did not apply to the solubility of hydrogen sulphide in water. That is, the solubility of hydrogen sulphide is not directly proportional to its partial pressure, even at seemingly low pressures. By accounting for the non-idealities in the vapour phase, Carroll and Mather [2] showed how a simple modification of Henry's law could be used for moderate pressures (up to 1 MPa). In this paper, a further extension of Henry's law is used to model the vapour-liquid equilibrium at higher pressures and temperatures. It is also applied to liquid-liquid and vapour-liquid-liquid equilibria, areas where Henry's law is rarely used.
    Additional Material: 11 Ill.
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  • 56
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 213-217 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Treatment of a given multicomponent cationic mixture was studied applying the emulsion liquid membrane (ELM) separation technique for Zn recovery. Experimental apparatus and conditions are described. Comparative studies using two zinc-selective ion exchangers (thio-DEHPA and dithio-DEHPA) were carried out whereby the composition of the liquid membrane and the operating conditions were investigated for both extractants. A useful method of representing the concentrations of the feed and the receiving aqueous phase is proposed, which allows the occurrence of break-up and/or osmosis to be easily detected.
    Additional Material: 4 Ill.
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  • 57
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 238-242 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This contribution presents a method of evaluating electrical conductivities of pure organic liquids. Emphasis is placed on the methodology of selection, correlation and analysis of experimental data. The proposed method brings order out of conflicting, confusing and chaotic experimental observations. It is also shown that the consistent and evaluated data are generated at a fraction of the cost and time required for producing the original raw experimental data.
    Additional Material: 4 Ill.
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  • 58
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993) 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and 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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  • 59
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Based on the dispersion model rather than on the conventional pluf-flow model, a method of predicting the transient behaviour of parallel and counterflow heat exchangers is developed, whereby the effects of shell-side flow maldistribution and the finite heat capacities of both fluids, tube bundle and shell are considered. The final solution has been obtained by numerical inversion of the Laplace transform, to determine the transient responses to arbitrary inlet temperature variations. The experiment was carried out in a one pass tube heat exchanger. The comparison between therotical and experimental results is presented and the feasibility of this method is discussed.
    Additional Material: 6 Ill.
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  • 60
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 413-421 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This contribution reviews the models for equilibrium and kinetics of the system Zn/D2EHPA/n-dodecane (and other diluents), published during the past decade, as well as values of the appropriate model parameters, i.e. of equilibrium and reaction rate constants. The reviewed kinetic models comprise those for kinetic, diffusional and mixed mass transfer regimes. It is shown that, under certain conditions, the rate equation within the kinetic regime has the same mathematical structure as the equations for the overall mass transfer rate within the diffusional and mixed mass transfer regimes. This means that the same equation interprets experimental data from each of the three regimes. Thus, a fit of experimental data to a model is not sufficient for discriminating between the mass transfer regimes. Results of kinetic experiments, using a stirred mass transfer cell with constant interfacial area, are presented.
    Additional Material: 5 Ill.
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  • 61
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The present work investigates the energy consumption of a solids production process. Such a process consists of three different operation units: crystallization/precipitation, solid-liquid separation by centrifuges or filters and drying of wet crystals. Each unit is analyzed with the objective of minimizing the energy consumption. Operating conditions, process design and other characteristic parameters (crystal size, porosity and physical proporties) are discussed with the aim to evaluate their influence on the process.
    Additional Material: 11 Ill.
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  • 62
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 102-108 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Power consumption under non-aerated and aerated conditions was measured in a 0.45 m diameter tank containing a range of xanthan gum solutions, using the Scaba 6SRGT impeller. Well-mixed caverns were measured in a transparent Carbopol solution. The data are compared with previous results obtained with a Rushton turbine in the range of Reynolds numbers, Re, between 1 and 2000. In each case, the non-aerated power numbers were similarly related to Re except that the Po values of the Scaba 6SRGT were 3 to 4 times smaller. Under aerated conditions, the aeration rate does not affect the power number, Pog, with the actual value falling as a result of increasing xanthan concentration. The Pog/Po vs Re curve passes through a minimum which is lower at higher xanthan concentrations. At the same Reynolds number, the decline in power consumption of the Scaba agitator due to aeration is 20 to 50% smaller than that observed with a Rushton turbine. Well-mixed cavern shapes and sizes are also very similar to those observed with Rushton turbines and can be predicted from equations available in literature. However, instabilities in torque could present a problem in broths containing xanthan in concentrations above 35 kg m-3. Nevertheless, the Scaba agitator offers an interesting retrofitting possibility for xanthan fermentation, which could lead to improved performance.
    Additional Material: 13 Ill.
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  • 63
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993) 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
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  • 64
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 153-160 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Large recirculation cyclones with high concentrations of particulate solids have gained considerable importance in the field of circulating fluidized bed technology. To calculate a combustion process, the influence of the cyclone on the circulating quantity of solids and their grain size distribution must be known. Measurements in a 105-MW-plant in 1989 showed that the existing cyclone theory was not sufficient for this purpose. In a laboratory cyclone (900 mm in diameter), the separation and classification of solids in a gas flow was investigated. The cyclone was fed from a fluidized bed and operated with cold air and quartz of various grain size distributions. Based on this experimental device and the theory of momentum transfer between solids and gas flow, a new, more accurate method of calculating the separation efficiency was developed.
    Additional Material: 15 Ill.
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  • 65
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    Chemical Engineering & Technology - CET 16 (1993), S. 186-190 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A kinetic model for the oxidation of phenol in high-pressure water has been developed and compared with experimental data taken from literature. The model assumes a chain reaction propagated by O⋅ and OH⋅. Production of the hydroxyl radical by the reaction of atomic oxygen and water induces a chain-branching effect, which is particularly effective at low temperatures and high pressures. The proposed model gives a fair correlation of the experimental data in the whole examined temperature and pressure range and appears significantly better than a simpler, power-law kinetic model. The relibility of the model is strengthened by the consideration of values obtained for the kinetic parameters (in particular for the activation energies) which compare well with the literature.
    Additional Material: 4 Tab.
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  • 66
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    Chemical Engineering & Technology - CET 16 (1993), S. 206-212 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Interfacial tension of the binary systems pelargonic acid/ethane, pelargonic acid/carbon dioxide, linoleic acid/ethane, and linoleic acid/carbon dioxide was measured at 313, 333, and 353 K and pressures ranging up to 250 bar, using the capillary rise and Du Nouy ring methods. Both these methods yield similar values. The surface excess of supercritical components is deduced from the measurement results with the aid of Gibbs adsorption equation. The surface excess concentration increases with increasing gas activity, runs through a pronounced maximum, later decreasing rapidly to very small values. Near the surface excess maximum, a falling film of fatty acids disintegrates into a mist of tiny droplets.
    Additional Material: 14 Ill.
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  • 67
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    Chemical Engineering & Technology - CET 16 (1993), S. 234-237 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A comparison is made between two different methods using laser induced fluorescence spectroscopy for measuring local concentration fluctuations in the same stirred tank. The first method using a single inert fluorescent tracer yields a segregation index quite different from that determined by the second method, which requires two inert tracers, a fluorescent one and a fluorescence quencher. By recalling the theoretical background, it is demonstrated that the characteristic segregation indices should be equal for the experiments under consideration. According to the discussion, it is likely that the double tracer method gives more reliable results.
    Additional Material: 4 Ill.
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  • 68
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    Chemical Engineering & Technology - CET 16 (1993), S. 243-251 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Using the micromixing concepts of Danckwerts and Zwietering, the Peclet number Pe has been correlated mathematically to the degree of segregation J for the axial dispersion model. The results were applied to compare the micromixing effects on a model, mixed-order parallel reaction system in continuous flow reactors. Axial dispersion model, and Ng and Rippin's two-environment model were used to find the micromixing effects in tubular and stirred tank reactors, respectively. The performance of these reactors, with varying geometries, has been evaluated in terms of overall conversion, selectivity, and yield under identical operating and reaction conditions. The overall conversion increases in a tubular reactor with the increase in J, irrespective of the kinetic orders. However, in a stirred tank reactor, the conversion is found to be micromixing-sensitive, depending on the order of reaction. For m = 1 and n = 2 (case 1), the conversion is fairly insensitive to micromixing effects while it decreases for m = 0.5 and n = 1 (case 2) with increasing J. For the same extent of micromixing, a tubular reactor gives, in both cases, a higher conversion than a stirred tank reactor. The selectivity, in either case, decreases in both reactors with increasing segregation effects. However, in each case, the selectivity of a tubular reactor was fairly close to that of a stirred tank reactor at the same value of J. As far as the yield is concerned, both reactors achieve nearly the same value, without significant micromixing effects.
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  • 69
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    Particle and Particle Systems Characterization 10 (1993), S. 7-10 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An image analysis system for extracting on-line quantitative geometric and densitometric information from images of ore samples is described. The apparatus employs a pulsed semiconductor laser as the light source for illuminating of a flowing stream of particles and a non-interlaced solid-state TV camera as size measurement device in a shadowgraph imaging system. The problem of the sampling volume is discussed and several size distributions of solid particulates are presented. The particle size measurement range is 2-400 μm.
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  • 70
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    Particle and Particle Systems Characterization 10 (1993), S. 11-18 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Accurate information on the size distribution of fly ash is needed to determine its role in the radiation transfer process in pulverized coal combustors. The Coulter Multisizer was used to determine the size distribution in the particle diameter range 1-200 μm. To size over such large diameter ranges, data must be obtained using several orifices, and then combined. In order to use the smaller orifices, the larger particles have to be removed from the sample. A wet-sieving apparatus, designed for accurate separation of the particles by size, is described. A scheme for combining data obtained using orifices of different diameters is presented. It appears from this study that the lower limit of size measurement using an orifice is set by sensitivity, rather than by signal/noise. A lognormal distribution function, truncated outside the measurement limits, fits the size distribution data well. This function allows detailed size information to be stored compactly using four parameters. Size parameters for six fly ashes representative of U. S. coals are presented.
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  • 71
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    Particle and Particle Systems Characterization 10 (1993), S. 38-38 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
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  • 72
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    Particle and Particle Systems Characterization 10 (1993), S. 26-32 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It is often necessary to estimate the properties of particle size distributions from limited samples taken from large populations. When the distributions are broad, and higher order moments required, as in the case of volume based particle size distributions, the inferred parameters d3,50 (volume median diameter) and GSD (geometric standard deviation) can have high intrinsic errors not immediately obvious to the measuring scientist. We show that there is a critical number of particles, Ncrit, which must be counted or else the error may blow up catastrophically. Ncrit is very sensitive to the width of the distribution, and is approximately proportional to GSD11 We develop formulae to estimate the random sampling error inherent in measured values of the d3,50 and GSD for the log-normal distribution; compare the predictions to a typical experimental particle size measurement; and then generalize to the median of any arbitrary moment, dr, 50.
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  • 73
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    Particle and Particle Systems Characterization 10 (1993) 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
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  • 74
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    Particle and Particle Systems Characterization 10 (1993), S. 48-55 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The working principle of the single-fibre reflection (SFR) probe is that light emitted by a laser diode is guided into the measuring volume by the same fibre which receives the proportion of light reflected by the particles in the vicinity of the probe tip and transmits it back to a photosensitive element. In contrast to other configurations of fibre optical probes, the SFR probe is characterized by an unambiguous calibration graph over the entire range of solid volume concentration values. SFR probes have been successfully applied to different kinds of multiphase flow systems, e.g. fluidized beds, pneumatic conveying lines, elutriators and thickeners.A particular question for the interpretation of measurements has always been the effective size of the measuring volume, which is mainly determined by the solid volume concentration. In this paper a simplified mathematical model of the signal generation by backscattering of the emitted light at the particle surfaces is given. The theory takes into account the average optical properties of the solids and their particle size distributions.The particle properties are determined on the basis of this model, which finally delivers the shape, size and depth of the effective measuring volume. For particle sizes between 30 and 120 μm the depth of the measuring volume of a 600-μm fibre probe is between 0.2 mm for solid concentrations near the fixed-bed state and approximately 4 mm for solid volume concentrations as low as 0.1 vol.-%.
    Additional Material: 11 Ill.
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  • 75
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    Particle and Particle Systems Characterization 10 (1993), S. 86-91 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: To produce disperse products, the characterization of the disperse state and a knowledge of the property function are essential. Property functions are applied not only to characterize the quality of an end product, but also to determine the influence of different processing steps on its state. Hence it is necessary to know the property and process functions for quality assurance of the products and for safety of the processes.Good laboratory particle measuring technologies are available for investigating property and process functions. On the basis of these functions, process control takes place. On-line or, better, in-line measuring techniques are necessary to enable the accompanying process information to be obtained.
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  • 76
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    Particle and Particle Systems Characterization 10 (1993), S. 79-85 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The paper discusses the interest in conventional triaxial tests widely used in soil mechanics for a better understanding of both the mechanical behaviour and flow characteristics of granular bulk materials. It proposes a rheological characterization of granular foodstuffs on diverse types of stress path using a conventional triaxial cell. The characteristic state concept, defining the disaggregation threshold of the granular structure, is found to be suitable and even indispensible for examining the mechanical behaviour and the flowability of stored bulk materials. The experimental results readily suggest, as an indicator of the arching effect, a rheological index that characterizes the particle interlocking breakdown and hence the flowability of the stored materials. In addition, this study offers a realistic physical meaning for parameters in use in constitutive models (yield conditions and flow rules) when describing granular flow in various hopper geometries. The case of silos equipped with vibrating hoppers necessitates additionally the study of the rheological behaviour of materials under cyclic and vibratory loadings in order to analyse the processes of densification or disaggregation conditioning the flowability of the stored materials during emptying operations.
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  • 77
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    Particle and Particle Systems Characterization 10 (1993), S. 111-117 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The Extended Boundary Condition Method (EBCM), also known as the T-matrix method, is used to compute exactly the scattered intensities from homogeneous isotropic circular cylinders characterized by relative refractive index N, diameter D and length L. The domain of convergence of the method regarding the parameters N, D, L is established. The effect of the geometry of the fiber ends on the scattered intensities is considered. The incident field is assumed to be a linearly polarized plane harmonic wave.
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  • 78
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    Particle and Particle Systems Characterization 10 (1993), S. 252-261 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A review of existing and developing process tomographic instrumentation suitable for characterising dry and wet particulate systems is presented. Factors governing the selection of sensing techniques appropriate for static and dynamic imaging of a wide range of single and multiphase particulate processes are discussed. The paper presents a systematic comparison of different image reconstruction methods. Examples of existing, developing and proven applications are cited. Future needs and ways in which these needs can be met are suggested, including the use of multi-modality methods in which different types of sensing methods are embodied in a single tomographic instrument.
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  • 79
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    Particle and Particle Systems Characterization 10 (1993), S. 266-270 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: On-line characterization of powder and droplets during gas atomization of molten metals and alloys offers extensive opportunities for real-time process monitoring and control. The capability to make on-line measurements can significantly reduce tedious and costly powder classification, which, currently, is always carried out subsequent to the atomization process. Two laser-based particle sizing instruments, the EPCS (ensemble instrument) and PCSV (single particle instrument), were used during gas atomization of zinc with a double Coanda nozzle configuration. The laser instruments were positioned in the duct leading from the bottom of the atomization tower to the powder collection cyclone. The effect of gas to metal ratio on particle size was studied by varying the atomization gas pressure from 0.69 MPa to 1.03 MPa. Air was used as the atomizing gas for some of the 0.69 MPa runs, while nitrogen was used for all of the higher-pressure runs. Experimental apparatus and procedures for atomization and on-line powder sizing with the EPCS and PCSV are described. EPCS and PCSV measurements, which were compared with standard sieve analyses, indicate that the ensemble instrument is a good candidate for on-line process monitoring and control.
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  • 80
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    Particle and Particle Systems Characterization 10 (1993), S. 290-293 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
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  • 81
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    Particle and Particle Systems Characterization 10 (1993) 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
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  • 82
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    Particle and Particle Systems Characterization 10 (1993), S. 246-251 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A method for the rapid on-line determination of surface area and solids content in flowing concentrated slurries using low field NMR spin-lattice relaxation measurements has been developed and demonstrated. The relationship between flow and spin-lattice relaxation time (T1) of protons in water at 20 MHz was examined using aqueous copper sulfate solutions. The ability to measure surface area and solids concentration in both stagnant (stopped flow) and flowing systems via NMR was demonstrated using several different concentrated aqueous titania and glass slurries (20 to 80 weight percent) for which the dried powder surface area was previously determined via nitrogen adsorption/BET analysis and the solids content determined gravimetrically. Surface areas were also calculated from particle size analysis and found to vary by up to an order of magnitude from the adsorption and NMR results.
    Additional Material: 9 Ill.
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  • 83
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    Particle and Particle Systems Characterization 10 (1993), S. 239-245 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Aggregates formed from colloidal particles will vary in shape according to the aggregation regime prevalent. Compact structures are formed when the aggregation is slow, whilst loose tenuous structures are formed when rapid (or diffusion limited) aggregation prevails. These structures can be fractal in nature, that is, there is a relationship between porosity and the number of primary particles making up the aggregate, and is described by the fractal dimension, dF. Fractal dimensions of hematite aggregates have been measured experimentally using the static light scattering technique. Fractal dimensions varied with aggregation regimes; for the rapid aggregation regime, dF was found to be 2.8, whilst for conditions in which aggregation was slow (retardation forces prevail), dF's of 2.3 were measured. For conditions which lead to aggregation in which both diffusion and retardation forces play a part, structures with fractal dimensions such that 2.3 〈 dF 〈 2.8 were found.The effects of adsorbed fulvic acid, a naturally occuring organic acid, on the kinetics of hematite aggregation and on the resulting structure of hematite aggregates were also investigated. The study of aggregate structure shows that the fractal dimensions of hematite aggregates which are partially coated with fulvic acid molecules are higher than those obtained with no adsorbed fulvic acid. The scattering exponents obtained from static light scattering experiments of these aggregates range from 2.83 ± 0.08 to 3.42 ± 0.1. The scattering exponents of greater than 3 indicate that the scattering is the result of objects that contains pores which are bounded by surfaces with a fractal structure, and can be related only to surface fractal dimension. The high fractal dimensions are due to restructuring within the aggregates, which only occured at low coverage by the organic acid.
    Additional Material: 4 Ill.
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  • 84
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    Particle and Particle Systems Characterization 10 (1993), S. 234-238 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This work on imaging of particulate processes using electrical charge tomography uses two basic techniques: the multi-sensing of electrical charge in a cross-section of the flow pipe and a neural network based flow regime identification system to aid in the image reconstruction process.A measurement system, consisting of sixteen sensors, placed at equal distance from each other around the boundary of a circular 100 mm bore pipe, is used to determine the voltage profile of the flow for several artificially produced flow regimes: full, annular, core, half and stratified. A sand flow system is used to produce these different flow regimes, which are created artificially by using baffles of different shapes that obstruct the sand flow.The voltage profile from the sixteen sensors gives spatial information of the flow regime. These profiles are normalised and formed into patterns that are presented to a Kohonen neural network for classification. Two regime classification between clearly distinct regimes gives an accuracy of identification of 85%. Classification of closely similar patterns show much less accuracy of 30%.
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  • 85
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    Particle and Particle Systems Characterization 10 (1993), S. 262-265 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: In-process measurement of particle size and concentration distributions provides continuous analysis and quality control of a product stream. Elimination of sample handling and operator manipulation is now possible for most pneumatic flows using optical methods which are properly interfaced with the process stream.The EPCS (Ensemble Particle Concentration & Size) described in the following has been used to obtain detailed size distribution measurements in powder production facilities at two second intervals, and has been successfully used for automatic feedback control.
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  • 86
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    Particle and Particle Systems Characterization 10 (1993), S. 271-274 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The paper discusses the application of image analysis to multiphase mineral particles. The emphasis is on the development of automatic and routine methods which provide reliable data for the process engineer. Optical systems are discussed briefly, but electron beam instruments are shown to offer many advantages for the identification and discrimination of mineral species. Image capture and analysis procedures are described together with the application of the measured data to aid our understanding of the processing properties of particles of complex structure. Examples are given from studies of beach sands, silver minerals, flyashes, ore characterisation, flotation of base metals, grinding and liberation.
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  • 87
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    Particle and Particle Systems Characterization 10 (1993), S. 279-289 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The response of the Partec laser backscatter particle size analyzer has been tested under a variety of conditions. Various materials posessing different light scattering characteristics have been examined and the response of the Partec instrument has been evaluated. In particular the system response to transparent particle systems (e.g. oil in water emulsions) tas been studied. It has been found that the Partec laser backscatter instrument provides reasonably accurate and reproducible results when used to characterize opaque, highly reflective particles such as hydrated alumina, but suffers from a lack of sensitivity to fine transparent particles such as oil droplets. The instrument does, however, readily detect the presence of opaque particle contaminants in oil-water emulsions.
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  • 88
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    Particle and Particle Systems Characterization 10 (1993), S. 357-363 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Concrete quality is influenced to a high degree by the granulometry of the aggregates used. In the construction industry, the grain size coefficient of K-coefficient is used as a quantity for the characterization of granulometry. In practice, this quantity is determined experimentally, and it is therefore a random variable influenced by material heterogeneity and errors in sampling, sample preparation and size analysis. Depending on the final use, in concrete production often an aggregate is required, the grain size coefficient of which can be adjusted to a given value Krequ with a prescribed precision. For this reason, continuous supervision of the aggregate quality is necessary using, e. g., automatic sampling and opto-electronic measuring equipment. In order to determine the optimum conditions for the installation of such equipment, the variances of the possible errors must be established. Further, methods for their restriction are necessary. In this paper, investigations involving hand sampling and hand sieving and on the example of a reference gravel plant are reported. The investigations reveal that, for the materials involved, primary samples of at least 1600 g were necessary, which then could be reduced to 200 g by sample splitting, in order to obtain the accuracy desired.
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  • 89
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new experimental technique with periodic laser heating is described and applied to the measurement of local heat transfer coefficients at the inner surface of an agitated vessel. Only radiative surface temperature measurements on the outer wall of the vessel are necessary.
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  • 90
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    Chemical Engineering & Technology - CET 16 (1993), S. 114-118 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The bulk density of a catalyst bed in two-dimensional reactor model has been measured by a radiogauging method. Three ways of introducing the catalyst were used. Attention was paid to bulk density near the wall and the bottom of the model. A homogeneous distribution of the catalyst was obtained in the case of the “rainy” (uniform) filling method using a grid distributor.
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  • 91
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Biological processes are becoming increasingly popular in dealing with waste air problems. Compared to chemical and physical treatment methods, they offer several advantages, especially in handling of waste air contaminated with low concentrations of biodegradable organic and, occasionally, inorganic substances. Two types of commercial systems are currently in use: biofilters and bioscrubbers. The aim of our studies was to develop an innovative concept of reactor design and engineering called “biocatalyst” (Biokatalysator). Our biocatalytic three-phase system lies in between the conventional biofilter and bioscrubber, using biomass immobilized on macroporous, tubiform supports installed in parallel to the air flow. In laboratory-scale investigations, a bioreactor was continuously fed with solvent-laden air, which produced a more cost-effective mode of operation than the conventional bioscrubber systems.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 92
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 82-88 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Approximate as well as reasonably exact numerical solutions of the equation of conservation have previously predicted that sudden heating of a solid surface adjacent to a region of gas will generate a slightly supersonic wave with small positive amplitudes in pressure, temperature and density, and thereby a small mass velocity in the direction of wave propagation. If the gas is confined by a second parallel surface, the wave is predicted to be reflected repeatedly from both surfaces and to decay slowly due to viscous and thermal dispersion. This process, which has been termed thermoacoustic convection, is presumed to result in transient heating of the confined gas and heat transfer through it at rates greatly exceeding that of pure thermal conduction. The current work constitutes the first quantitative experimental confirmation of this behaviour. Numerical solutions obtained for support and guidance of the experimental work define for the first time the conditions required for the generation of a wave of significant strength.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 93
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemical Engineering & Technology - CET 16 (1993), S. 109-113 
    ISSN: 0930-7516
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Mixing of gas, solids and heat in a commercial FCC regenerator, 5.76 m in diameter, was investigated. This regenerator was operated at a high superficial gas velocity (〉1.2 m/s) and high temperature (650-710°C). It is classified as a highly efficient regenerator. The profiles of coke content in the catalyst, gas composition, temperature and pressure were obtained by sampling and instrumental measurement. It was confirmed that a proposed axial dispersion model could be used for a satisfactory prediction of these experimental profiles. The values of gas and solids dispersion coefficients are also presented.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 94
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 10 (1993), S. 40-40 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 95
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 10 (1993), S. 1-6 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This paper describes preliminary work carried out on the applicability of fractal geometry in describing the products of comminution events.A nickel sulphide ore was subjected to two comminution events, impact shattering and ball milling. Fractal analysis was performed on samples of the resulting comminution products.Two differing fractal populations resulted, with the impact sample exhibiting particles having higher boundary fractal dimensions than the milled sample. The fractal dimension of the impact fragments increased with decreasing size, whereas the milled particles displayed a more complex distribution.The under-fractal distributions, of the two populations of fragments, generate straight lines when plotted on Gaussian probability paper. This leads to the possibility of being able to predict the distribution of fragments, in fractal terms, of a particular material when subjected to comminution.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 96
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 10 (1993), S. 19-25 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The angular patterns of the polarization ratio were calculated for droplets with diameters between 0.020 and 50 μm at 500 nm wavelength. It was observed that the patterns for droplets slightly smaller than 1 μm were dominated by a backward peak belonging to the glory. The peak was successfully used to characterize aerosols of light and heavy oils with a Junge-like size distribution. Experiments conducted with heavy oil sprays produced by air-assisted atomization presented the same feature. A quantitative comparison of the experimental results with the Lorenz-Mie theory showed that the size distribution of these sprays was bimodal.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 97
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 10 (1993) 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 10 (1993), S. 33-37 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A scattered light photometer which monitors the particle number concentration of aerosols is described. The photometer measures the scattered light from illuminated submicron particle clouds with known material properties at certain scattering angles. Intensity ratios in combination with the degree of polarization are used to determine the mean particle diameter and the geometric standard deviation of an assumed log-normal particle size distribution. The determination of the particle size distribution is based on an algorithm which compares the measured and calculated (Mie theory) relative intensity quantities described. Furthermore, the particle number concentration is monitored from a single absolute intensity measurement at one scattering angle. In order to obtain quantitative results a spherical particle shape is required.
    Additional Material: 8 Ill.
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  • 99
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 10 (1993), S. 41-47 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A laser-Doppler instrument has been used to measure the migration velocity of NaCl particles in an electrohydrodynamic flow field of an electrical precipitator. The measured average migration velocity of 1.40-μm particles (number distribution median with a geometric standard devitation of 1.46) is approximately five to six times higher than the calculated steady-state velocity for a 1.40-μm particle, provided there is a saturation charge of at least 90f%. Further, the particle velocities in the main flow direction are also influenced by the electrical operation conditions. Both observations demonstrate the important role of the state of the electrohydrodynamic flow field (superposition of moving gas ions and neutral gas molecules) on the particle transport, characterized by the dimensionless electrohydrodynamic number NEHD. A comparison between six different electrohydrodynamic states revealed that NEHD ≍ 1 is a critical value for the mutual interactions between the gas ions and the neutral gas phase. Whereas for NEHD values 〉 1 the stochastic particle motion is chiefly determined by the nonsteady-state character of the negative corona, for NEHD values 〈 1 the particle velocity fluctuations are governed by the turbulence level of the neutral fluid. These finding might be helpful in adjusting the operating conditions in electrical precipitators for and optimized particle separation.
    Additional Material: 8 Ill.
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  • 100
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 10 (1993), S. 62-69 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Two undesirable effects occur in particle sizing by dynamic light scattering; statistical noise, and distortion of correlation data. Statistical noise in the correlation data, caused by estimating the autocorrelation of scattered laser light by a time average, leads to non-physical artifacts in the resulting linewidth distribution. These may be removed by regularization, computer modeling, or other techniques. The regularized kernel function for inverting the Laplace transform is calculated, and used to illustrate the problem of noise. Correct choice of the regularization parameter gives the minimum overall error. It is found that excessive error occurs unless the linewidth distribution is modeled over a finite range. Analytical models for the linewidth with finite range, based on the beta distribution of probability theory, are given.Distortion of correlation data may occur in three ways, through a focused or otherwise nonuniform laser beam in the optical system, by insufficient bit resolution in the quantized detection of scattered laser light, or by calculating a first order field autocorrelation from a second order intensity autocorrelation. Unlike noise, distortion cannot be removed by any known methods, since the exact nature of the distortion is unknown. Several examples illustrate how distortion can lead to artifacts in the linewidth distribution which could easily be misinterpreted as segments of a size distribution, not present in the physical sample.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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