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  • 1
    Electronic Resource
    Electronic Resource
    Future Trends in Synergetics (2004)
    s.l. ; Stafa-Zurich, Switzerland
    Solid state phenomena Vol. 97-98 (Apr. 2004), p. 3-10 
    Details
    ISSN: 1662-9779
    Source: Scientific.Net: Materials Science & Technology / Trans Tech Publications Archiv 1984-2008
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://www.tib-hannover.de/fulltexts/2011/0528/02/26/transtech_doi~10.4028%252Fwww.scientific.net%252FSSP.97-98.3.pdf
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  • 2
    Electronic Resource
    Electronic Resource
    Synchronized oscillations in the visual cortex — a synergetic model (1996)
    Springer
    Biological cybernetics 74 (1996), S. 31-39 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model's behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00199135
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  • 3
    Electronic Resource
    Electronic Resource
    Synchronized oscillations in the visual cortex – a synergetic model (1995)
    Springer
    Biological cybernetics 74 (1995), S. 31-39 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract.  We present an oscillator network model for the synchronization of oscillatory neuronal activity underlying visual processing. The single neuron is modeled by means of a limit cycle oscillator with an eigenfrequency corresponding to visual stimulation. The eigenfrequency may be time dependent. The mutual coupling strengths are unsymmetrical and activity dependent, and they scatter within the network. Synchronized clusters (groups) of neurons emerge in the network due to the visual stimulation. The different clusters correspond to different visual stimuli. There is no limitation of the number of stimuli. Distinct clusters do not perturb each other, although the coupling strength between all model neurons is of the same order of magnitude. Our analysis is not restricted to weak coupling strength. The scatter of the couplings causes shifts of the cluster frequencies. The model’s behavior is compared with the experimental findings. The coupling mechanism is extended in order to model the influence of bicucullin upon the neural network. We additionally investigate repulsive couplings, which lead to constant phase differences between clusters of the same frequency. Finally, we consider the problem of selective attention from the viewpoint of our model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220050216
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  • 4
    Electronic Resource
    Electronic Resource
    Misinformation (1993)
    [s.l.] : Nature Publishing Group
    Nature 362 (1993), S. 509-509 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] INFORMATION theory and molecular biology are both large and important fields. In this book, H. P. Yockey tries to link the two. Quite often the word 'information' is used with different meanings, but from the very beginning he sticks to a single interpretation — Shannon information. This ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/362509a0
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  • 5
    Electronic Resource
    Electronic Resource
    An explicit construction of a class of suspensions and autonomous differential equations for diffeomorphisms in the plane (1987)
    Springer
    Communications in mathematical physics 111 (1987), S. 63-74 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract From a large class of diffeomorphisms in the plane, which are known to produce chaotic dynamics, we explicitly construct their continuous suspension on a three dimensional cylinder. This suspension is smooth (C 1) and can be characterized by the choice of two smooth functions on the unit interval, which have to fulfill certain boundary conditions. For the case of entire Cremona transformations, we are able to construct the corresponding autonomous differential equations of the flow explicitly. Thus it is possible to relate properties of discrete maps to those of ordinary differential equations in a quantitative manner. Furthermore, our construction makes it possible to study the exact solutions of chaotic differential-equations directly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01239015
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  • 6
    Electronic Resource
    Electronic Resource
    Zum Identitätsproblem bei Gruppen (1952)
    Springer
    Mathematische Zeitschrift 56 (1952), S. 335-362 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01686754
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  • 7
    Electronic Resource
    Electronic Resource
    Synergetik: Nichtgleichgewichte, Phasenübergänge und Selbstorganisation (1981)
    Springer
    Naturwissenschaften 68 (1981), S. 293-299 
    Details
    ISSN: 1432-1904
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Natural Sciences in General
    Notes: Abstract The formation of ordered structures seems to contradict fundamental principles of physics according to which disorder should ever increase. Synergetics deals with the question how in spite of these laws structures can arise. We shall give a number of explicit examples. Large classes of ordered states in open systems are determined by a new principle based on the growth rates of collective configurations. In contrast, concepts such as entropy or entropy production are inadequate to treat such phenomena.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01047471
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  • 8
    Electronic Resource
    Electronic Resource
    Zur Quantentheorie des Mehrelektronensystems im schwingenden Gitter. I (1956)
    Springer
    The European physical journal 146 (1956), S. 527-554 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Zusammenfassung Dem ersten Abschnitt wird eineSchödinger-Gleichung zugrunde gelegt, die beliebige abstands-, geschwindigkeits- und spinabhängige Wechselwirkungen zwischen den Elektronen umfaßt. Die Elektronen können sich außerdem in einem störstellenfreien Translationsgitter bewegen, das noch harmonische Gitterschwingungen ausführen darf. Auf Grund der Translationsinvarianz des Problems wird neben der schon in einer früheren Arbeit hergeleiteten Lösungsforme iAℜ U, bei derU noch eine bestimmte Struktur besitzt, noch eine zweite Lösungsform durch Entwicklung nach lokalisierten Elektronenfunktionen gewonnen. Diese Lösungsform besagt unter anderem, daß die kollektive Bewegung der Elektronen im Gitter von einer der Form nach völlig unveränderten Gitterdeformation begleitet wird. Das so gewonnene Aufbaugesetz wird im zweiten Abschnitt auf Probleme der Halbleiterelektronik polarer Medien angewendet. Einmal bietet es einen sehr anschaulichen Zugang zu einer Reihe bekannter Lösungsansätze aus der Polaronentheorie. Zum anderen ergibt sich eine Klasse von Lösungsansätzen für das Exziton (Elektron-Defektelektronenpaar) im schwingenden, polaren Kristall. Mit Hilfe der Methode der scheinbaren Masse und unter der Voraussetzung einer mittelstarken Kopplung zwischen dem Exziton und den Gitterschwingungen wird der Grundzustand nach einem Variationsverfahren bestimmt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01333179
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  • 9
    Electronic Resource
    Electronic Resource
    Berechnung der Energie des Exzitonen-Grundzustandes im polaren Kristall nach einem neuen Variationsverfahren von Feynman. I (1957)
    Springer
    The European physical journal 147 (1957), S. 323-349 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Zusammenfassung Mit der wohl einfachsten „Probe-Schrödinger-Gleichung“, die sich im Rahmen desFeynmanschen Variationsverfahrens bietet, wird die Energie des Exzitonen-Grundzustandes im polaren, schwingungsfähigen Kristall berechnet. Dabei ergeben sich als Spezialfälle die Ergebnisse der gewöhnlichen Störungsrechnung und eines Verfahrens von H. J.G.Meyer sowie bei kleinen Radien eine Verbesserung früherer Resultate des Verfassers und, zumindest teilweise, auch der vonDykman undPekar. Für die Rechnung erweist es sich als bequem, dasFeynmansche Variationsprinzip nicht in der ursprünglichen Formulierung mit Hilfe vonFeynmans Wegintegralen zu benutzen, sondern eine Übersetzung in die geläufige Ausdrucksweise der Quantentheorie zu verwenden. Die bereits vonFeynman aufgeworfene Frage, wie diese Übersetzung zu erfolgen hat, wird im Anhang behandelt. Hier wird auch eine Erweiterung des Verfahrens auf TemperaturenT〉0° K angegeben.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01333103
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  • 10
    Electronic Resource
    Electronic Resource
    Über den Einfluß von Gitterschwingungen auf Energie und Lebensdauer des Exzitons (1959)
    Springer
    The European physical journal 155 (1959), S. 223-246 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The exciton is treated as a system of two particles which interact via Coulomb potential −e 2/ɛ ∞ γ and are coupled to the quantized field of lattice vibrations. The ground state energy of the total system is calculated by means of a field theoretical variational method ofFeynman. The results are better than all those hitherto published which are obtained mostly as special cases, except the exact asymptotic solution at large distances, derived previously. By means of an extension ofFeynman's method which, however, invaliditates in general the variational principle, energies and lifetimes of excited states at temperaturesT〉0° K are calculated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01337938
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