Atlantis Studies in Mathematics for Engineering and Science

MEAN FIELD THEORIES AND DUAL VARIATION

A Mathematical Profile Emerged in the Nonlinear Hierarchy

Authors: Suzuki, Takashi

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-94-91216-22-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
About this book

A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.

Table of contents (2 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-94-91216-22-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
MEAN FIELD THEORIES AND DUAL VARIATION
Book Subtitle
A Mathematical Profile Emerged in the Nonlinear Hierarchy
Authors
Series Title
Atlantis Studies in Mathematics for Engineering and Science
Series Volume
2
Copyright
2009
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the authors
eBook ISBN
978-94-91216-22-0
DOI
10.2991/978-94-91216-22-0
Series ISSN
1875-7642
Edition Number
1
Number of Pages
X, 288
Topics