Muutke küpsiste eelistusi

Model Emergent Dynamics in Complex Systems [Pehme köide]

  • Formaat: Paperback, 760 pages, kõrgus x laius x paksus: 229x152x32 mm, kaal: 1330 g, illustrations
  • Sari: Mathematical Modeling and Computation
  • Ilmumisaeg: 30-Dec-2014
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611973554
  • ISBN-13: 9781611973556
Teised raamatud teemal:
Model Emergent Dynamics in Complex SystemsSuurem pilt
  • Formaat: Paperback, 760 pages, kõrgus x laius x paksus: 229x152x32 mm, kaal: 1330 g, illustrations
  • Sari: Mathematical Modeling and Computation
  • Ilmumisaeg: 30-Dec-2014
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 1611973554
  • ISBN-13: 9781611973556
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781611973556.html
Märksõnad:
Contributing to the modern dynamical systems theory, Roberts explains how to derive relatively simple dynamical equations that model complex physical interactions. Because of his background, many of the example applications involve fluid flows and other continuum dynamics. He assumes common undergraduate linear algebra, calculus, and differential equations but not functional analysis, advanced differential geometry, or even complex analysis. His central theme is that coordinate transforms and center manifolds provide a powerfully enhanced and unified view of a swath of other methods for modeling complex systems, such as averaging, homogenizations, multiple scales, singular perturbations, two timing, and WKB theory. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)

A book that explores the derivation of multiscale models for dynamical systems, partnering algebra and geometry with a visual approach.
* Part I: Asymptotic methods solve algebraic and differential equations*
Chapter 1: perturbed algebraic equations solved iteratively*
Chapter 2: power series solve ordinary differential equations*
Chapter 3: A normal form of oscillations illuminate their character* Part I Summary* Part II: Center manifolds underpin accurate modeling*
Chapter 4: The center manifold emerges*
Chapter 5: Construct slow center manifolds iteratively* Part II Summary* Part III: Macroscale spatial variations emerge from microscale dynamics*
Chapter 6: Conservation underlies mathematical modeling of fluids*
Chapter 7: Cross-stream mixing causes longitudinal dispersion along pipes*
Chapter 8: Thin fluid films evolve slowly over space and time*
Chapter 9: Resolve inertia in thicker faster fluid films* Part III Summary* Part IV: Normal forms illuminate many modeling issues*
Chapter 10: Normal-form transformations simplify evolution*
Chapter 11: Separating fast and slow dynamics proves modeling*
Chapter 12: Appropriate initial conditions empower accurate forecasts*
Chapter 13: Subcenter slow manifolds are useful but do not emerge* Part IV Summary* Part V: High fidelity discrete models use slow manifolds*
Chapter 14: Introduce holistic discretization on just two elements*
Chapter 15: Holistic discretization in one space dimension* Part V Summary* Part VI: Hopf bifurcation: Oscillations within the center manifold*
Chapter 16: Directly model oscillations in Cartesian-like variables*
Chapter 17: Model the modulation of oscillations* Part VI Summary* Part VII: Avoid memory in modeling nonautonomous systems, including stochastic*
Chapter 18: Averaging is often a good first modeling approximation*
Chapter 19: Coordinate transforms separate slow from fast in nonautonomous dynamics*
Chapter 20: Introducing basic stochastic calculus*
Chapter 21: Strong and weak models of stochastic dynamics* Part VII Summary
A. J. Roberts is a Professor and Chair in the School of Mathematical Sciences at the University of Adelaide. He has lectured and conducted research at the University of New South Wales and the University of Southern Queensland and has published over 100 refereed international journal articles. As a leader in developing and applying a branch of modern dynamical systems theory, in conjunction with new computer algebra algorithms in scientific computing, Professor Roberts derives and interprets mathematical and computational models of complex multiscale systems, both deterministic and stochastic.