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  • 1
    Book
    Book
    Turbulence, coherent structures, dynamical systems and symmetry / (1998)
    Cambridge :Cambridge Univ. Press,
    Details
    Title: Turbulence, coherent structures, dynamical systems and symmetry /
    Author: Holmes, Philip
    Contributer: Lumley, John L. , Berkooz, Gal
    Edition: 1. paperback ed
    Publisher: Cambridge :Cambridge Univ. Press,
    Year of publication: 1998
    Pages: XVIII., 420 S. : , Ill ; , 23cm
    Series Statement: Cambridge monographs on mechanics
    ISBN: 0-521-63419-9 , 0-521-55142-0
    Type of Medium: Book
    Language: English
    URL: 01  (lizenzfrei)
    URL: 04
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  • 2
    Electronic Resource
    Electronic Resource
    Scale and space localization in the Kuramoto–Sivashinsky equation (1999)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 9 (1999), S. 452-465 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We describe a wavelet-based approach to the investigation of spatiotemporally complex dynamics, and show through extensive numerical studies that the dynamics of the Kuramoto–Sivashinsky equation in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wave number). A projection onto a spline wavelet basis enables good separation of scales, each with characteristic dynamics. At the large scales, one observes essentially slow Gaussian dynamics; at the active scales, structured "events" reminiscent of traveling waves and heteroclinic cycles appear to dominate; while the strongly damped small scales display intermittent behavior. The separation of scales and their dynamics is invariant as the length of the system increases, providing additional support for the extensivity of the spatiotemporally complex dynamics claimed in earlier works. We show also that the dynamics are spatially localized, discuss various correlation lengths, and demonstrate the existence of a characteristic interaction length for instantaneous influences. Our results motivate and advance the search for localized, low-dimensional models that capture the full behavior of spatially extended chaotic partial differential equations. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166419
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Pain responses, anxiety and aggression in mice deficient in pre-proenkephalin (1996)
    [s.l.] : Nature Publishing Group
    Nature 383 (1996), S. 535-538 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] The enkephalin gene was mutated to block enkephalin peptide production by replacing the 5' part of exon 3, which contains all enkephalin-coding sequences1, with PGK-neo (Fig. la). Chimae- ric mice were generated with two targeted embryonic stem (ES) cell lines, one of which transmitted the ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/383535a0
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Simple models for excitable and oscillatory neural networks (1998)
    Springer
    Journal of mathematical biology 37 (1998), S. 419-446 
    Details
    ISSN: 1432-1416
    Keywords: Key words: Bifurcation ; Coupling ; Oscillator ; Network
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators providing input to a kinematic musculature model of lamprey..
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850050136
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Erratum: The effect of modeled drag reduction on the Wall Region (1996)
    Springer
    Theoretical and computational fluid dynamics 8 (1996), S. 449-450 
    Details
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00455995
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  • 6
    Electronic Resource
    Electronic Resource
    Erratum: The Effect of Modeled Drag Reduction on the Wall Region1 (Theoret. Comput. Fluid Dynamics, 1:229—248, 1990) (1996)
    Springer
    Theoretical and computational fluid dynamics 8 (1996), S. 449-450 
    Details
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00455995
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Homoclinic Saddle‐Node Bifurcations and Subshifts in a Three‐Dimensional Flow (1998)
    Springer
    Archive for rational mechanics and analysis 145 (1998), S. 291-329 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract. We study a two‐parameter family of three‐dimensional vector fields that are small perturbations of an integrable system possessing a line Γ of degenerate saddle points connected by a manifold of homoclinic loops. Under perturbation, this manifold splits and undergoes a quadratic homoclinic tangency. Perturbation methods followed by geometrical analyses reveal the presence of countably‐infinite sets of homoclinic orbits to Γ and a non‐wandering set topologically conjugate to a shift on two symbols (a Smale horseshoe). We use the symbolic description to identify and partially order bifurcation sequences in which the homoclinic orbits appear, and we formally derive an explicit two‐dimensional Poincaré return map to further illustrate our results. The problem was motivated by the search for travelling ‘structures’ such as fronts and domain walls in partial differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002050050131
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Chaos in a mapping describing elastoplastic oscillations (1995)
    Springer
    Nonlinear dynamics 8 (1995), S. 111-139 
    Details
    ISSN: 1573-269X
    Keywords: Elastoplastic oscillator ; piecewise linear map ; chaos ; Smale horseshoe ; symbolic dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the local and global dynamical behavior of a two dimensional piecewise linear map which describes the asymptotic motions of a single degree of freedom, parametrically excited, elastoplastic oscillator after it has settled down to purely elastic oscillations. We give existence and stability conditions for periodic orbits and prove that chaos, in the form of a Smale horseshoe, exists at specific, but representative, parameter values. We interpret simulations of the elastoplastic oscillator itself in the light of these results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00045009
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    Paper (German National Licenses)
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