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  • AMS(MOS) 65L05, 58F08, 58F22  (1)
  • Homoclinic orbits  (1)
  • Lagrange's equations of motion  (1)
  • Polymer and Materials Science  (1)
  • 1
    Electronic Resource
    Electronic Resource
    A Direct Approach to Homoclinic Orbits in the Fast Dynamics of Singularly Perturbed Systems (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 671-709 
    Details
    ISSN: 1572-9222
    Keywords: Homoclinic orbits ; singular perturbations ; bifurcation ; FitzHugh–Nagumo system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Homoclinic orbits in the fast dynamics of singular perturbation problems are usually analyzed by a combination of Fenichel's invariant manifold theory with general transversality arguments (see Ref. 29 and the Exchange Lemma in Ref. 16). In this paper an alternative direct approach is developed which uses a two-time scaling and a contraction argument in exponentially weighted spaces. Homoclinic orbits with one last transition are treated and it is shown how ε-expansions can be extracted rigorously from this approach. The result is applied to a singularity perturbed Bogdanov point in the FitzHugh–Nagumo system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022663512855
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On invariant closed curves for one-step methods (1987)
    Springer
    Numerische Mathematik 51 (1987), S. 103-122 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65L05, 58F08, 58F22 ; CR: G1.7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We show that a one-step method as applied to a dynamical system with a hyperbolic periodic orbit, exhibits an invariant closed curve for sufficiently small step size. This invariant curve converges to the periodic orbit with the order of the method and it inherits the stability of the periodic orbit. The dynamics of the one-step method on the invariant curve can be described by the rotation number for which we derive an asymptotic expression. Our results complement those of [2, 3] where one-step methods were shown to create invariant curves if the dynamical system has a periodic orbit which is stable in either time direction or if the system undergoes a Hopf bifurcation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399697
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Simulating the motion of the leech: A biomechanical application of DAEs (1998)
    Springer
    Numerical algorithms 19 (1998), S. 1-12 
    Details
    ISSN: 1572-9265
    Keywords: Lagrange's equations of motion ; viscoelasticity ; semi-explicit methods ; 92C10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper a mathematical model is developed for the dynamical behaviour of a hydrostatic skeleton. The basic configuration is taken from the worm-like shape of the medicinal leech. It consists of a sequence of hexahedra with damped elastic springs as edges to model the various parts of the musculature. The system is stabilized by the constraint of constant volume either in the whole body or in prescribed compartments. We set up Lagrange's equations of motion with the Lagrange multipliers being the pressure values in the compartments. The equations of motion lead to a large differential-algebraic system which is solved by an application of semi-explicit numerical methods. Though the model has not yet been adapted to experimental data, first simulations with a simplified set of parameters show that it is capable of generating basic movements of the leech such as crawling and swimming.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019146221279
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Ellipsometric investigation of single crystalline Cz—Si subjected to hydrostatic pressure (1994)
    Chichester [u.a.] : Wiley-Blackwell
    Surface and Interface Analysis 22 (1994), S. 346-349 
    Details
    ISSN: 0142-2421
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Physics
    Notes: The application of ellipsometry to study the SiOx/Si system subjected to hydrostatic pressures up to 1.8 GPa at temperatures up to 1280 °C is described. The theoretical model of defects as the spherical disturbances of material has been assumed. The ellipsometric parameters have been analysed as a function of defects size and density and compared with data obtained by etching and x-ray methods. The applicability of ellipsometry for near-surface defect structure analysis has been discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/sia.740220175
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    Paper (German National Licenses)
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