Nichtlineare Phänomene und Selbstorganisation
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Nichtlineare Phänomene und Selbstorganisation

Nichtlineare Phänomene und Selbstorganisation

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About the Book

Table of Contents:
1 Einleitung.- 1.1 Einführung.- 1.2 Unsere Welt ist nichtlinear.- 1.3 Chaos und Ordnung.- 1.4 Chaotisches Verhalten.- 1.5 Fraktale.- 1.6 Fraktale Muster in der Natur.- 2 Methoden der Analyse nichtlinearer Phänomene.- 2.1 Problemstellung.- 2.2 Qualitative Theorie von Differentialgleichungen.- 2.3 Schlußfolgerungen und Ergänzungen.- 2.4 Ljapunovexponenten.- 3 Diskrete dynamische Systeme.- 3.1 Diskrete Abbildungen.- 3.2 Die logistische Abbildung.- 3.3 Das Feigenbaum-Diagramm.- 3.4 Schlußfolgerungen aus der logistischen Gleichung.- 3.5 Stabilitätsanalyse für die logistische Abbildung.- 3.6 Voll entwickeltes Chaos.- 4 Klassische mechanische Systeme.- 4.1 Nichtlineare mechanische Beispiele.- 4.2 Allgemeine Eigenschaften einfacher Systeme.- 4.3 Resultate für höherdimensionale Systeme.- 4.4 Die Schlögl-Reaktion.- 4.5 Das Kettenkarussell.- 5 Grundideen der Synergetik.- 5.1 Thermodynamik und Chaos.- 5.2 Dämonen als Gegenspieler zum Chaos.- 5.3 Nichtgleichgewichtssysteme und Ordnung.- 5.4 Synergetische Konzepte.- 6 Das Kolmogorov-Arnold-Moser-Theorem (KAM-Theorem) und einige Konsequenzen.- 6.1 Einleitung.- 6.2 Zwei- und Mehrkörperprobleme.- 6.3 Das Kolmogorov — Arnold — Moser- Theorem.- 6.4 Chaos, KAM-Theorem und das Sonnensystem.- 7 Thermodynamik, Bilanzgleichungen und Evolutionskriterien.- 7.1 Evolution in Physik und Biologie.- 7.2 Grundideen der klassischen Thermodynamik.- 7.3 Beispiele und Konsequenzen.- 7.4 Thermodynamische Evolutionskriterien.- 8 Stochastische Prozesse und Strukturbildung.- 8.1 Gesetzmäßigkeit und Zufall.- 8.2 Beispiele für Zufallsprozesse.- 8.3 Beschreibung zufälliger Prozesse.- 8.4 Brownsche Bewegung.- 9 Stochastische Prozesse und Irreversibilität.- 9.1 Zeit als physikalische Größe.- 9.2 Irreversibilität bei stochastischenGleichungen.- 10 Evolution des Kosmos.- 10.1 Zur Geschichte der Evolution.- 10.2 Physikalische Beschaffenheit der Planeten.- 10.3 Evolution des Universums.- 11 Entstehung der Elemente oder Moderne Alchemie.- 11.1 Kräfte und Bausteine der Natur.- 11.2 Charakterisierung der Elemente.- 11.3 Element—Synthese.- 11.4 Expansion des Universums.- 11.5 Elementsynthese im Urknall.- 11.6 Elementsynthese in Sternen.- 11.7 Endphasen der Sternenentwicklung.- 12 Verteilung und Häufigkeit chemischer Elemente.- 12.1 Problemstellung.- 12.2 Erklärungsversuche.- 12.3 Weiterführende Fragen.- 13 Evolutionsprozesse in chemischen und biologischen Systemen.- 13.1 Einleitung.- 13.2 Mathematische Modelle.- 13.3 Strukturbildungsprozesse in chemischen Systemen.- 13.4 Selektion und Evolutionsprozesse.- 13.5 Interpretation: Extremalprinzipien.- 13.6 Anwendung physikalischer Methoden in der Modellierung.- 14 Selbstreproduktion, Clusterbildung und Konkurrenz in übersättigten Systemen.- 14.1 Die Hauptsätze der Thermodynamik.- 14.2 Konkurrenz und Selektion im Eigen-Modell.- 14.3 Konkurrenz zwischen Clustern.- 14.4 Molekulardynamik zur Clusterbildung.- 15 Zelluläre Automaten.- 15.1 Einleitung.- 15.2 Deterministische eindimensionale binäre CA.- 15.3 Zweidimensionale zelluläre Automaten.- 15.4 Stochastische zweidimensionale zelluläre Automaten.- 15.5 Universalitätsklassen eindimensionaler CA.- 16 Spingläser und neuronale Netzwerke.- 16.1 Spinsysteme.- 16.2 Neuronale Netze.


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Product Details
  • ISBN-13: 9783519030898
  • Publisher: Springer Fachmedien Wiesbaden
  • Binding: Paperback
  • No of Pages: 222
  • Returnable: Y
  • ISBN-10: 3519030896
  • Publisher Date: 01 Jan 1992
  • Language: gerger
  • Returnable: Y


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