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Phenomenology

—Renormalization and Asymptotic Analysis—
  • Yoshitsugu Oono
Chapter
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

Despite scale interference that characterizes our nonlinear world, this world does not look so lawless as chaos suggests. There are extensive effects of noises (interference with the unknowable scales) to the phenomena we experience on our scale. However, these effects show up rather systematically at restricted places. The phenomenological way to appreciate the world is to exploit this special feature of the world. The existence of mathematical structures we can phenomenologically recognize in the world is a prerequisite of the existence of intelligent beings. The chapter begins with characterization of phenomenology. The renormalization group approach is then introduced as a means to extract phenomenological descriptions of various phenomena. An elementary introduction to renormalization group theory is followed by its application to system reduction and singular perturbation with some technical details. Technical aspects of the renormalization group theory applied to critical phenomena and polymers may be found in the accompanying webpages to the book.

Keywords

Renormalization Group Singular Perturbation Invariant Manifold Renormalization Group Equation Renormalization Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 2013

Authors and Affiliations

  • Yoshitsugu Oono
    • 1
  1. 1.University of IllinoisUrbanaUSA

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