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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 53 (1992), S. 37-57 
    ISSN: 1572-9478
    Keywords: Two-fixed-centre problem ; restricted three-body problem ; binary stellar wind
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The envelope of iso-energetic trajectories in the (repulsive) two-fixed-centre problem is derived. Our analytical calculations finally lead to a transcendental equation, only containing elliptic integrals and the Weierstraßp function, from which the envelope is constructed. The results may serve as a simple model for the boundary layer between two colliding supersonic stellar wind flows in binary systems, in which at least one of the components has a strong radiation field. Beyond this, the effect of non-inertial forces (centrifugal and Coriolis force) due to the binary's orbital motion has been estimated by a numerical analysis within the scope of the (repulsive) restricted three-body problem. All calculations have been performed for a hot model (Wolf-Rayet/O-star) binary system with a set of parameters which might be appropriate for HD 152270. The envelope may be well approximated by a hyperboloid. The non-inertial forces slightly turn the envelope against the line connecting both stars.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 43 (1987), S. 185-191 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The best way to investigate the long-time behaviour of dynamical systems is to introduce an appropriate Poincaré mapping P and study its iterates. Two cases of physical interest arise: Conservative and dissipative systems. While the latter has been considered by a great many authors, much less is known for the first one (according to Liouville's theorem, here the mapping leaves a certain measure in phase space invariant). In this paper, we concentrate our attention on compact phase spaces (or, rather, surfaces of section). This assumption is mathematically useful and physically reasonable. We consider the simplest possible (2-dimensional) systems whehre the phase space is the compact unit disk D in ℝ2. A family of simple area-preserving mappings from D onto itselves will be given and discussed in detail. It is shown that general characteristics of the dynamics are quite similar to those of e.g. the Hénon-Heiles system, while other features, as the structure of invariant curves, are different.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 56 (1993), S. 353-371 
    ISSN: 1572-9478
    Keywords: least squares techniques ; numerical parameter estimation ; boundary value problem approach ; dynamical systems ; Hénon-Heiles system ; Lyapunov spectrum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A recent least squares algorithm, which is designed to adapt implicit models to given sets of data, especially models given by differential equations or dynamical systems, is reviewed and used to fit the Hénon-Heiles differential equations to chaotic data sets. This numerical approach for estimating parameters in differential equation models, called theboundary value problem approach, is based on discretizing the differential equations like a boundary value problem,e.g. by a multiple shooting or collocation method, and solving the resulting constrained least squares problem with a structure exploiting generalized Gauss-Newton-Method (Bock, 1981). Dynamical systems like the Hénon-Heiles system which can have initial values and parameters that lead to positive Lyapunov exponents or phase space filling Poincaré maps give rise to chaotic time series. Various scenarios representing ideal and noisy data generated from the Hénon-Heiles system in the chaotic region are analyzedw.r.t. initial conditions, parameters and Lyapunov exponents. The original initial conditions and parameters are recovered with a given accuracy. The Lyapunov spectrum is then computed directly from the identified differential equations and compared to the spectrum of the “true” dynamics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 43 (1987), S. 399-408 
    ISSN: 1572-9478
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Special solutions of the planar rectilinear elliptic restricted 3-body problem are investigated for the limiting case e=1. Numerical integration is performed for primaries of equal masses. Starting values which define circular orbit solutions lead to bounded solutions if the initial radius a0 is larger than 3.74 in units of the primaries' semimajor axis a. A comparison with the Eulerian two-fixedcentre problem is presented in order to understand qualitatively the characteristic features of bounded orbits and the transition to escape orbits.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Chemie Ingenieur Technik - CIT 66 (1994), S. 207-209 
    ISSN: 0009-286X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Title: Gemischt-ganzzahlige Optimierung : Modellierung in der Praxis ; mit Fallstudien aus Chemie, Energiewirtschaft, Metallgewerbe, Produktion und Logistik
    Author: Kallrath, Josef
    Edition: 1. Aufl.
    Publisher: Braunschweig ; Wiesbaden :Vieweg,
    Year of publication: 2002
    Pages: XVI, 291 S. : graph. Darst.
    Series Statement: Studium und Praxis
    ISBN: 3-528-03141-7
    Type of Medium: Book
    Language: German
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  • 7
    Title: Modeling languages in mathematical optimization /; 88
    Contributer: Kallrath, Josef
    Publisher: Boston [u.a.] :Kluwer,
    Year of publication: 2004
    Pages: XXX, 407 S.
    Series Statement: Applied optimization 88
    ISBN: 1-4020-7547-2
    Type of Medium: Book
    Language: English
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  • 8
    Book
    Book
    Heidelberg [u.a.] :Springer,
    Title: Algebraic modeling systems /; 104
    Contributer: Kallrath, Josef , Gesellschaft für Operations-Research
    Publisher: Heidelberg [u.a.] :Springer,
    Year of publication: 2012
    Pages: XXVI, 236 S. : , graph. Darst.
    Series Statement: Applied optimization 104
    ISBN: 978-3-642-23591-7 , 3-642-23591-3 , 978-3-642-23592-4
    Type of Medium: Book
    Language: English
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