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1680 results in Nonlinear Science and Fluid Dynamics

Page 10 of 84

  • 1 - Analytical Methods

  • from Part One - Theory
  • Yuri A. Kuznetsov, Universiteit Utrecht, The Netherlands, Hil G. E. Meijer, University of Twente, Enschede, The Netherlands
  • Book:
    Numerical Bifurcation Analysis of Maps
    Published online:
    15 March 2019
    Print publication:
    28 March 2019, pp 3-29
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Numerical Bifurcation Analysis of Maps
  • From Theory to Software
  • Yuri A. Kuznetsov, Hil G. E. Meijer
  • Published online:
    15 March 2019
    Print publication:
    28 March 2019
  • This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze more complicated models from modern engineering, ecology, and economics.

Chaotic Dynamics
  • Fractals, Tilings, and Substitutions
  • Geoffrey R. Goodson
  • Published online:
    30 January 2019
    Print publication:
    28 December 2016
  • This undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete applications of real analysis and metric space theory to dynamical problems. Proofs are complete and carefully explained, and there is opportunity to practice manipulating algebraic expressions in an applied context of dynamical problems. After presenting a foundation in one-dimensional dynamical systems, the text introduces students to advanced subjects in the latter chapters, such as topological and symbolic dynamics. It includes two-dimensional dynamics, Sharkovsky's theorem, and the theory of substitutions, and takes special care in covering Newton's method. Mathematica code is available online, so that students can see implementation of many of the dynamical aspects of the text.

Turbulence and Random Processes in Fluid Mechanics
  • 2nd edition
  • M. T. Landahl, E. Mollo-Christensen
  • Published online:
    12 October 2018
    Print publication:
    25 September 1992
  • Fluid flow turbulence is a phenomenon of great importance in many fields of engineering and science. Turbulence and related areas have continued to be subjects of intensive research over the last century. In this second edition of their successful textbook Professors Landahl and Mollo-Christensen have taken the opportunity to include recent developments in the field of chaos and its applications to turbulent flow. This timely update continues the original theme of the book: presenting the fundamental concepts and basic methods of fluid flow turbulence which enable the reader to follow the literature and understand current research. The emphasis upon the dynamic processes that create and maintain turbulent flows gives this book an original approach. This book should be useful to graduate students and researchers in fluid dynamics and, in particular, turbulence and related fields.

Fluid Mechanics
  • 2nd edition
  • Gregory Falkovich
  • Published online:
    04 August 2018
    Print publication:
    12 April 2018
  • The multidisciplinary field of fluid mechanics is one of the most actively developing fields of physics, mathematics and engineering. This textbook, fully revised and enlarged for the second edition, presents the minimum of what every physicist, engineer and mathematician needs to know about hydrodynamics. It includes new illustrations throughout, using examples from everyday life, from hydraulic jumps in a kitchen sink to Kelvin–Helmholtz instabilities in clouds, and geophysical and astrophysical phenomena, providing readers with a better understanding of the world around them. Aimed at undergraduate and graduate students as well as researchers, the book assumes no prior knowledge of the subject and only a basic understanding of vector calculus and analysis. It contains forty-one original problems with very detailed solutions, progressing from dimensional estimates and intuitive arguments to detailed computations to help readers understand fluid mechanics.

Turbulence
  • The Legacy of A. N. Kolmogorov
  • Uriel Frisch
  • Published online:
    28 May 2018
    Print publication:
    30 November 1995
  • This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.

Page 10 of 84