© 2006

Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

  • Alexander N. Gorban
  • Ioannis G. Kevrekidis
  • Constantinos Theodoropoulos
  • Nikolaos K. Kazantzis
  • Hans Christian Öttinger


  • Dealing with systems with many degrees of freedom and how they can be mathematically described in a way to manage the variety, this book explains how macroscopic properties arise from microscopic and nano-properties.


Table of contents

  1. Front Matter
    Pages I-XI
  2. Computation of Invariant Manifolds

    1. Front Matter
      Pages 1-1
    2. H. W. Broer, A. Hagen, G. Vegter
      Pages 17-37
    3. S. Borok, I. Goldfarb, V. Gol’dshtein, U. Maas
      Pages 55-79
    4. V. Bykov, I. Goldfarb, V. Gol’dshtein, S. Sazhin, E. Sazhina
      Pages 81-97
    5. N. P. Vora, M. -N. Contou-Carrere, P. Daoutidis
      Pages 99-113
  3. Coarse-Graining and Ideas of Statistical Physics

  4. Kinetics and Model Reduction

    1. Front Matter
      Pages 293-293
    2. M. R. Roussel, R. Zhu
      Pages 295-315
    3. H. Struchtrup
      Pages 317-341
    4. M. Slemrod
      Pages 365-371

About this book


Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering.


algorithm complexity dynamical systems dynamics dynamische Systeme evolution information theory mechanics model modeling optimization partial differential equation physics science simulation

Editors and affiliations

  • Alexander N. Gorban
    • 1
    • 2
  • Ioannis G. Kevrekidis
    • 3
  • Constantinos Theodoropoulos
    • 4
  • Nikolaos K. Kazantzis
    • 5
  • Hans Christian Öttinger
    • 6
  1. 1.Department of MathematicsUniversity of LeicesterLeicesterUK
  2. 2.Institute of Computational ModelingRussian Academy of SciencesRussia
  3. 3.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA
  4. 4.School of Chemical Engineering and Analytical ScienceUniversity of ManchesterManchesterUK
  5. 5.Department of Chemical EngineeringWorcester Polytechnic InstituteWorcesterUSA
  6. 6.Institut für PolymereETH ZürichZürichSwitzerland

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