Shijun Liao's Books

Clean Numerical Simulation

By: Shijun Liao

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This book describes the basic principles of Clean Numerical Simulation (CNS) proposed by the author in 2009, as well as several of its applications. Unlike conventional algorithms, CNS gives in a sufficiently long interval of time a convergent chaotic trajectory whose numerical noise is much lower than the true physical solution, so that one can gain accurately. Thus, CNS provides for the first time an ability to check statistics stability of chaos, leading to a completely new concept of "ultra-chaos," which has both trajectory instability and statistics instability, and thus is of a higher disorder. Notably, it is impossible to repeat experimental results of ultra-chaos even in the statistical sense. However, the reproducibility of physical experiments forms a cornerstone for modern science. Thus, ultra-chaos reveals an incompleteness of the modern science paradigm. In addition, it also reveals statistics stability as a precondition for use of conventional algorithms, including direct numerical simulation (DNS). In Clean Numerical Simulation, several conjectures and open problems are proposed, including a modified fourth Clay millennium problem. Indeed, CNS opens the door for us to enter the "clean" numerical world of chaos and turbulence.

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Page Count

270

Publisher

CRC Press

Published Date

ISBN 10

1000963594

ISBN 13

9781000963595

Beyond Perturbation

Introduction to the Homotopy Analysis Method

By: Shijun Liao

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Beyond Perturbation

Introduction to the Homotopy Analysis Method

By: Shijun Liao

Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.

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Page Count

335

Publisher

CRC Press

Published Date

ISBN 10

1135438293

ISBN 13

9781135438296

Homotopy Analysis Method in Nonlinear Differential Equations

By: Shijun Liao

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Homotopy Analysis Method in Nonlinear Differential Equations

By: Shijun Liao

Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.

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566

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642251323

ISBN 13

9783642251320

Clean Numerical Simulation

By: Shijun Liao

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Clean Numerical Simulation

By: Shijun Liao

The author has been named among the top 2% of all scientists throughout the world in 2020. This book offers an entirely new approach to chaos and nonlinear dynamics. The book ties into the author's widely published and cited research.

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Page Count

161

Publisher

CRC Press

Published Date

ISBN 10

100096356X

ISBN 13

9781000963564

Tokamak Engineering Mechanics

By: Yuntao Song,Weiyue Wu,Shijun Du

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Tokamak Engineering Mechanics

By: Yuntao Song,Weiyue Wu,Shijun Du

Tokamak Engineering Mechanics offers concise and thorough coverage of engineering mechanics theory and application for tokamaks, and the material is reinforced by numerous examples. Chapter topics include general principles, static mechanics, dynamic mechanics, thermal fluid mechanics and multiphysics structural mechanics of tokamak structure analysis. The theoretical principle of the design and the methods of the analysis for various components and load conditions are presented, while the latest engineering technologies are also introduced. The book will provide readers involved in the study of mechanical/fusion engineering with a general understanding of tokamak engineering mechanics. Yuntao Song is Head of the Tokamak Design Division at the Institute of Plasma Physics, Chinese Academic of Science (ASIPP), China.

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Page Count

249

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642395759

ISBN 13

9783642395758

Homotopy Analysis Method in Nonlinear Differential Equations

By: Shijun Liao

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Homotopy Analysis Method in Nonlinear Differential Equations

By: Shijun Liao

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Page Count

566

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642251323

ISBN 13

9783642251320

Beyond Perturbation

Introduction to the Homotopy Analysis Method

By: Shijun Liao

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Beyond Perturbation

Introduction to the Homotopy Analysis Method

By: Shijun Liao

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Solve jigsaw puzzle

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Page Count

335

Publisher

CRC Press

Published Date

ISBN 10

1135438293

ISBN 13

9781135438296

Book's by Shijun Liao

Clean Numerical Simulation

Clean Numerical Simulation

Beyond Perturbation

Beyond Perturbation

Homotopy Analysis Method in Nonlinear Differential Equations

Homotopy Analysis Method in Nonlinear Differential Equations

Clean Numerical Simulation

Clean Numerical Simulation

Tokamak Engineering Mechanics

Tokamak Engineering Mechanics

Homotopy Analysis Method in Nonlinear Differential Equations

Homotopy Analysis Method in Nonlinear Differential Equations

Beyond Perturbation

Beyond Perturbation

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