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  • 1
    Digitale Medien
    Digitale Medien
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 5 (1996), S. 393-416 
    ISSN: 1022-1344
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: This article describes the development of a comprehensive solver for the differential equations arising from the modeling of molecular weight distributions in polyreactions. Based on a series of numerical developments, the software package PREDICI combines new directions in mathematics, chemical computing and implementation. The algorithm is based on a so-called discrete Galerkin h-p-method, which allows the efficient treatment of numerous polymerization reaction types. The abilities of the new concept are demonstrated on challenging examples.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Weinheim : Wiley-Blackwell
    Macromolecular Theory and Simulations 6 (1997), S. 393-426 
    ISSN: 1022-1344
    Schlagwort(e): Chemistry ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: The pulsed laser polymerization technique is now a well accepted method to determine propagation rate coefficients for radical polymerization from molar mass distributions resulting from intermittent initiation. A simplified apparatus for the periodic photoinitiation is used which is much less expensive than the laser equipment. The usefulness of the simplified equipment was proved by the determination of kp for styrene at technically relevant temperatures up to 130°C for the first time. Furthermore, careful inspection of the molar mass distribution (mmd) reveals that depending on the reaction conditions, inflection points (Li) can not only be found at integer multiples of kp • to • [M] but also at 0.5i • kp • to • [M], i = 1, 2, 3, … . A rule to find the inflection points leading to correct values for kp is proposed. It is shown that the shape of the mmd inter alia depends on the amount of primary radical termination compared to the termination reaction between growing chains. With dominant primary termination, the maxima of the distribution will give the correct kp, whereas in the absence of primary termination the inflection points should be used. Experimental conditions like initiator concentration, light intensity etc. may influence the position of the Li at least to some extent, and so may give a small but principal error or uncertainty in kp. A new mathematical method for the time-dependent simulation of the resulting mmd is presented which allows the calculations being performed on a PC within an acceptable time.
    Zusätzliches Material: 15 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 3
    Publikationsdatum: 2014-02-26
    Beschreibung: The description of chain length distributions in macromolecular reaction kinetics leads to so-called countable systems of differential equations. In particular, when the appearing reaction rate coefficients depend on the chain length of the reacting macromolecules itself, an efficient numerical treatment of these systems is very difficult. Then even the evaluation of the right-hand side of the system can become prohibitively expensive with respect to computing time. In this paper we show how the discrete Galerkin method can be applied to such problems. The existing algorithm CODEX is improved by use of a multiplicative error correction scheme for time discretization and a new type of numerical preprocessing by means of a Gauss summation. Both ideas are exemplary for a wide class of approximation types and are described very briefly here. The new numerical techniques are tested on an example from soot formation, where the coagulation of molecules is modeled in terms of reaction coefficients depending on the surface of the particles and their collision frequency.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 4
    Publikationsdatum: 2014-02-26
    Beschreibung: Models for occupation dynamics in discrete quantum systems lead to large or even infinite systems of ordinary differential equations. Some new mathematical techniques, developed for the simulation of chemical processes, make a numerical solution of countable systems of ordinary differential equations possible. Both, a basic physical concept for the construction of such systems and the structure of the numerical tools for solving them are presented. These conceptual aspects are illustrated by a simulation of an occupation process from spectroscopy. In this example the structures of rotation spectra observed in infrared spectroscopy are explained and some possibilities for an extension of the model are shown.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 5
    Publikationsdatum: 2014-02-26
    Beschreibung: Countable systems of ordinary differential equations appear frequently in chemistry, physics, biology and medicine. They can be considered as ordinary differential equations in sequence spaces. In this work, a full adaptive algorithm for the computational treatment of such systems is developed. The method combines time discretization with extrapolation in Hilbert spaces with a discrete Galerkin approach as discretization of the stationary subproblems. The Galerkin method is based on orthogonal functions of a discrete variable , which are generated by certain weight functions. A theory of countable systems in the associated weighted sequence spaces is developed as well as a theory of the Galerkin method. The Galerkin equations can be assembled either by use of analytical properties of the orthogonal functions or numerically by a multilevel summation algorithm. The resulting algorithm CODEX is applied to many examples of technological interest, in particular from polymer chemistry.
    Schlagwort(e): ddc:000
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 6
    Publikationsdatum: 2020-12-14
    Sprache: Englisch
    Materialart: article , doc-type:article
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 7
    Publikationsdatum: 2020-03-20
    Sprache: Englisch
    Materialart: bookpart , doc-type:bookPart
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 8
    Publikationsdatum: 2020-03-20
    Sprache: Englisch
    Materialart: article , doc-type:article
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 9
    Publikationsdatum: 2020-03-20
    Sprache: Englisch
    Materialart: bookpart , doc-type:bookPart
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 10
    Publikationsdatum: 2020-10-02
    Sprache: Englisch
    Materialart: article , doc-type:article
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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