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  • 1
    Electronic Resource
    Electronic Resource
    Numerical Taylor expansions of invariant manifolds in large dynamical systems (1998)
    Springer
    Numerische Mathematik 80 (1998), S. 1-38 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 34C35, 58F14, 65F50, 65H17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. In this paper we develop a numerical method for computing higher order local approximations of invariant manifolds, such as stable, unstable or center manifolds near steady states of a dynamical system. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear (black box) solver and a low dimensional invariant subspace is available, but for which methods like the QR–Algorithm are considered to be too expensive. Our method is based on an analysis of the multilinear Sylvester equations for the higher derivatives which can be solved under certain nonresonance conditions. These conditions are weaker than the standard gap conditions on the spectrum which guarantee the existence of the invariant manifold. The final algorithm requires the solution of several large linear systems with a bordered Jacobian. To these systems we apply a block elimination method recently developed by Govaerts and Pryce [12, 14].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050357
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  • 2
    Electronic Resource
    Electronic Resource
    The correction factors and their new curve for the measurement of sheet resistance of a square sample with a square four-point probe (1992)
    [S.l.] : American Institute of Physics (AIP)
    Review of Scientific Instruments 63 (1992), S. 3752-3756 
    Details
    ISSN: 1089-7623
    Source: AIP Digital Archive
    Topics: Physics , Electrical Engineering, Measurement and Control Technology
    Notes: In this article, a new curve of the correction factor for the measurement of sheet resistance of a square sample with a square four-point probe is presented by using the theory of conformal transformation. This curve is quite different from that obtained by using the theory of infinite dipoles. An experimental curve is recommended to use. The function of the conformal transformation used in this article is simple and can be easily used for solving the problem of boundary effect of current field. The theoretical curve is suitable to the boundary areas of wafers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1143608
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Determination of the areas of a square sample suitable to the resistance measurement by Van der Pauw's method (1992)
    [S.l.] : American Institute of Physics (AIP)
    Review of Scientific Instruments 63 (1992), S. 3757-3762 
    Details
    ISSN: 1089-7623
    Source: AIP Digital Archive
    Topics: Physics , Electrical Engineering, Measurement and Control Technology
    Notes: By using conformal transformation to take account of the boundary effect, it has been confirmed that there are some areas of a square sample near the corners besides the boundary suitable to the resistance measurement of Van der Pauw's method. The theoretical criterion of the suitability is whether Van der Pauw's formula for calculation of the sheet resistance is still valid provided the voltage values in the formula for two times the measurement are substituted with those obtained by using the theory of conformal transformation. The experimental criterion is whether the experimental values of sheet resistance for probes in some areas are equal to that for them at the boundary for the same sample. The experimentally confirmed areas are larger than what the theory predicts. Our repeated experiments show that the areas out of the circle tangent to the boundary are suitable to Van der Pauw's method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1143266
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  • 4
    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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  • 5
    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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  • 6
    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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