Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis

Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Their Numerical Simulations

Author: Changpin Li,Yujiang Wu,Ruisong Ye

Publisher: World Scientific

ISBN: 981443647X

Category: Mathematics

Page: 416

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Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation. Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed. In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc. In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications. Contents:Gronwall Inequalities (Fanhai Zeng, Jianxiong Cao and Changpin Li)Existence and Uniqueness of the Solutions to the Fractional Differential Equations (Yutian Ma, Fengrong Zhang and Changpin Li)Finite Element Methods for Fractional Differential Equations (Changpin Li and Fanhai Zeng)Fractional Step Method for the Nonlinear Conservation Laws with Fractional Dissipation (Can Li and Weihua Deng)Error Analysis of Spectral Method for the Space and Time Fractional Fokker–Planck Equation (Tinggang Zhao and Haiyan Xuan)A Discontinuous Finite Element Method for a Type of Fractional Cauchy Problem (Yunying Zheng)Asymptotic Analysis of a Singularly Perturbed Parabolic Problem in a General Smooth Domain (Yu-Jiang Wu, Na Zhang and Lun-Ji Song)Incremental Unknowns Methods for the ADI and ADSI Schemes (Ai-Li Yang, Yu-Jiang Wu and Zhong-Hua Yang)Stability of a Collocated FV Scheme for the 3D Navier–Stokes Equations (Xu Li and Shu-qin Wang)Computing the Multiple Positive Solutions to p–Henon Equation on the Unit Square (Zhaoxiang Li and Zhonghua Yang)Multilevel WBIUs Methods for Reaction–Diffusion Equations (Yang Wang, Yu-Jiang Wu and Ai-Li Yang)Models and Dynamics of Deterministically Growing Networks (Weigang Sun, Jingyuan Zhang and Guanrong Chen)On Different Approaches to Synchronization of Spatiotemporal Chaos in Complex Networks (Yuan Chai and Li-Qun Chen)Chaotic Dynamical Systems on Fractals and Their Applications to Image Encryption (Ruisong Ye, Yuru Zou and Jian Lu)Planar Crystallographic Symmetric Tiling Patterns Generated From Invariant Maps (Ruisong Ye, Haiying Zhao and Yuanlin Ma)Complex Dynamics in a Simple Two-Dimensional Discrete System (Huiqing Huang and Ruisong Ye)Approximate Periodic Solutions of Damped Harmonic Oscillators with Delayed Feedback (Qian Guo)The Numerical Methods in Option Pricing Problem (Xiong Bo)Synchronization and Its Control Between Two Coupled Networks (Yongqing Wu and Minghai Lü) Readership: Senior undergraduates, postgraduates and experts in nonlinear dynamics with numerical analysis. Keywords:Fractional Dynamics;Infinite Dimensional Dynamics;Network Dynamics;Fractal DynamicsKey Features:The topics in this edited book are very hot and highly impressiveIssues and methods of such topics in this edited book have not been made available yetThe present edited book is suitable for various levels of researchers, such as senior undergraduates, postgraduates, and experts

Kernel-based Approximation Methods using MATLAB

Author: Gregory Fasshauer,Michael McCourt

Publisher: World Scientific Publishing Company

ISBN: 9814630152

Category: Mathematics

Page: 536

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In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Numerical Methods

Author: George Em Karniadakis

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110571064

Category: Mathematics

Page: 360

View: 8046

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This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This third volume collects authoritative chapters covering several numerical aspects of fractional calculus, including time and space fractional derivatives, finite differences and finite elements, and spectral, meshless, and particle methods.

Recent Advances in Nonlinear Dynamics and Synchronization

Theory and Applications

Author: Kyandoghere Kyamakya,Herwig Unger,Jean Chamberlain Chedjou,Nikolai F. Rulkov,Zhong Li

Publisher: Springer

ISBN: 3642042279

Category: Computers

Page: 399

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In essence, the dynamics of real world systems (i.e. engineered systems, natural systems, social systesms, etc.) is nonlinear. The analysis of this nonlinear character is generally performed through both observational and modeling processes aiming at deriving appropriate models (mathematical, logical, graphical, etc.) to simulate or mimic the spatiotemporal dynamics of the given systems. The complex intrinsic nature of these systems (i.e. nonlinearity and spatiotemporal dynamics) can lead to striking dynamical behaviors such as regular or irregular, stable or unstable, periodicity or multi-periodicity, torus or chaotic dynamics. The various potential applications of the knowledge about such dynamics in technical sciences (engineering) are being intensively demonstrated by diverse ongoing research activities worldwide. However, both the modeling and the control of the nonlinear dynamics in a range of systems is still not yet well-understood (e.g. system models with time varying coefficients, immune systems, swarm intelligent systems, chaotic and fractal systems, stochastic systems, self-organized systems, etc.). This is due amongst others to the challenging task of establishing a precise and systematic fundamental or theoretical framework (e.g. methods and tools) to analyze, understand, explain and predict the nonlinear dynamical behavior of these systems, in some cases even in real-time. The full insight in systems’ nonlinear dynamic behavior is generally achieved through approaches involving analytical, numerical and/or experimental methods.

Advances in Numerical Analysis: Nonlinear partial differential equations and dynamical systems

Author: William Allan Light,Science and Engineering Research Council (Great Britain)

Publisher: Oxford University Press, USA

ISBN: 9780198534389

Category: Mathematics

Page: 288

View: 7066

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The aim of this volume is to present research workers and graduate students in numerical analysis with a state-of-the-art survey of some of the most active areas of numerical analysis. This, and a companion volume, arise from a Summer School intended to cover recent trends in the subject. The chapters are written by the main lecturers at the School. Each is an internationally renowned expert in his respective field. This volume covers research in the numerical analysis of nonlinear phenomena: evolution equations, free boundary problems, spectral methods, and numerical methods for dynamical systems, nonlinear stability, and differential equations on manifolds.

Advances in Numerical Simulation of Nonlinear Water Waves

Author: Qingwei Ma

Publisher: World Scientific

ISBN: 9812836500

Category: Mathematics

Page: 700

View: 786

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Most of the Earth''s surface is covered by water. Our everyday lives and activities are affected by water waves in oceans, such as the tsunami that occurred in the Indian Ocean on 26 December 2004. This indicates how important it is for us to fully understand water waves, in particular the very large ones. One way to do so is to perform numerical simulation based on the nonlinear theory. Considerable research advances have been made in this area over the past decade by developing various numerical methods and applying them to emerging problems; however, until now there has been no comprehensive book to reflect these advances. This unique volume aims to bridge this gap. This book contains 18 self-contained chapters written by more than 50 authors from 12 different countries, many of whom are world-leading experts in the field. Each chapter is based mainly on the pioneering work of the authors and their research teams over the past decades.The chapters altogether deal with almost all numerical methods that have so far been employed to simulate nonlinear water waves and cover many important and very interesting applications, such as overturning waves, breaking waves, waves generated by landslides, freak waves, solitary waves, tsunamis, sloshing waves, interaction of extreme waves with beaches, interaction with fixed structures, and interaction with free-response floating structures. Therefore, this book provides a comprehensive overview of the state-of-the-art research and key achievements in numerical modeling of nonlinear water waves, and serves as a unique reference for postgraduates, researchers and senior engineers working in industry.

Recent Advances in Partial Differential Equations, Venice 1996

Proceedings of a Conference in Honor of the 70th Birthdays of Peter D. Lax and Louis Nirenberg : June 10-14, 1996, Venice, Italy

Author: Peter D. Lax,L. Nirenberg,Renato Spigler,Stephanos Venakides

Publisher: American Mathematical Soc.

ISBN: 9780821867594

Category: Mathematics

Page: 392

View: 3409

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Lax and Nirenberg are two of the most distinguished mathematicians of our times. Their work on partial differential equations (PDEs) over the last half-century has dramatically advanced the subject and has profoundly influenced the course of mathematics. A huge part of the development in PDEs during this period has either been through their work, motivated by it or achieved by their postdocs and students. A large number of mathematicians honored these two exceptional scientists in a week-long conference in Venice (June 1996) on the occasion of their 70th birthdays. This volume contains the proceedings of the conference, which focused on the modern theory of nonlinear PDEs and their applications. Among the topics treated are turbulence, kinetic models of a rarefied gas, vortex filaments, dispersive waves, singular limits and blow-up solutions, conservation laws, Hamiltonian systems and others. The conference served as a forum for the dissemination of new scientific ideas and discoveries and enhanced scientific communication by bringing together such a large number of scientists working in related fields. THe event allowed the international mathematics community to honor two of its outstanding members.

Advances in Dynamical Systems and Control

Author: Victor A. Sadovnichiy,Mikhail Z. Zgurovsky

Publisher: Springer

ISBN: 3319406736

Category: Technology & Engineering

Page: 471

View: 8812

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Focused on recent advances, this book covers theoretical foundations as well as various applications. It presents modern mathematical modeling approaches to the qualitative and numerical analysis of solutions for complex engineering problems in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions by an international team of respected authors bridge the gap between abstract mathematical approaches, such as applied methods of modern analysis, algebra, fundamental and computational mechanics, nonautonomous and stochastic dynamical systems on the one hand, and practical applications in nonlinear mechanics, optimization, decision making theory and control theory on the other. As such, the book will be of interest to mathematicians and engineers working at the interface of these fields.

Computational Methods in Nonlinear Structural and Solid Mechanics

Papers Presented at the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics

Author: Ahmed K. Noor,Harvey G. McComb

Publisher: Elsevier

ISBN: 1483145646

Category: Technology & Engineering

Page: 470

View: 6764

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Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.

Recent Advances in Multidisciplinary Applied Physics

Proceedings of the First International Meeting on Applied Physics (APHYS 2003) October 13-18th, 2003, Badajoz, Spain

Author: A. Méndez-Vilas

Publisher: Elsevier

ISBN: 9780080446486

Category: Science

Page: 973

View: 1907

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The 1st International Meeting on Applied Physics (APHYS-2003) succeeded in creating a new international forum for applied physics in Europe, with specific interest in the application of techniques, training, and culture of physics to research areas usually associated with other scientific and engineering disciplines. This book contains a selection of peer-reviewed papers presented at APHYS-2003, held in Badajoz (Spain), from 15th to 18th October 2003, which included the following Plenary Lectures: * Nanobiotechnology - Interactions of Cells with Nanofeatured Surfaces and with Nanoparticles * Radiation Protection of Nuclear Workers - Ethical Issues * Chaotic Data Encryption for Optical Communications

Applied Nonlinear Dynamics

Analytical, Computational, and Experimental Methods

Author: Ali H. Nayfeh,Balakumar Balachandran

Publisher: John Wiley & Sons

ISBN: 3527617558

Category: Science

Page: 700

View: 6476

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A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.

Recent Advances in Mathematical and Statistical Methods

IV AMMCS International Conference, Waterloo, Canada, August 20–25, 2017

Author: D. Marc Kilgour,Herb Kunze,Roman Makarov,Roderick Melnik,Xu Wang

Publisher: Springer

ISBN: 331999719X

Category: Computers

Page: 646

View: 9217

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This book focuses on the recent development of methodologies and computation methods in mathematical and statistical modelling, computational science and applied mathematics. It emphasizes the development of theories and applications, and promotes interdisciplinary endeavour among mathematicians, statisticians, scientists, engineers and researchers from other disciplines. The book provides ideas, methods and tools in mathematical and statistical modelling that have been developed for a wide range of research fields, including medical, health sciences, biology, environmental science, engineering, physics and chemistry, finance, economics and social sciences. It presents original results addressing real-world problems. The contributions are products of a highly successful meeting held in August 2017 on the main campus of Wilfrid Laurier University, in Waterloo, Canada, the International Conference on Applied Mathematics, Modeling and Computational Science (AMMCS-2017). They make this book a valuable resource for readers interested not only in a broader overview of the methods, ideas and tools in mathematical and statistical approaches, but also in how they can attain valuable insights into problems arising in other disciplines.

Recent Advances in Robotics and Automation

Author: Gourab Sen Gupta,Donald Bailey,Serge Demidenko,Dale Carnegie

Publisher: Springer

ISBN: 3642373879

Category: Computers

Page: 344

View: 586

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There isn’t a facet of human life that has not been touched and influenced by robots and automation. What makes robots and machines versatile is their computational intelligence. While modern intelligent sensors and powerful hardware capabilities have given a huge fillip to the growth of intelligent machines, the progress in the development of algorithms for smart interaction, collaboration and pro-activeness will result in the next quantum jump. This book deals with the recent advancements in design methodologies, algorithms and implementation techniques to incorporate intelligence in robots and automation systems. Several articles deal with navigation, localization and mapping of mobile robots, a problem that engineers and researchers are grappling with all the time. Fuzzy logic, neural networks and neuro-fuzzy based techniques for real world applications have been detailed in a few articles. This edited volume is targeted to present the latest state-of-the-art computational intelligence techniques in Robotics and Automation. It is a compilation of the extended versions of the very best papers selected from the many that were presented at the 5th International Conference on Automation, Robotics and Applications (ICARA 2011) which was held in Wellington, New Zealand from 6-8 December, 2011. Scientists and engineers who work with robots and automation systems will find this book very useful and stimulating.

Instabilities, Chaos and Turbulence

An Introduction to Nonlinear Dynamics and Complex Systems

Author: Paul Manneville

Publisher: Imperial College Press

ISBN: 9781860944918

Category: Science

Page: 391

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This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and potentially to anyone who wants to learn about recent advances in the field of applied nonlinear dynamics. Technicalities are, however, not completely avoided. They are instead explained as simply as possible using heuristic arguments and specific worked examples.

Advances in Applied Mathematics and Global Optimization

In Honor of Gilbert Strang

Author: David Y. Gao,Hanif D. Sherali

Publisher: Springer Science & Business Media

ISBN: 0387757147

Category: Mathematics

Page: 520

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The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.

Topics in Experimental Dynamic Substructuring, Volume 2

Proceedings of the 31st IMAC, A Conference on Structural Dynamics, 2013

Author: Randy Mayes,Daniel Rixen,Matt Allen

Publisher: Springer Science & Business Media

ISBN: 1461465400

Category: Science

Page: 332

View: 8353

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Topics in Experimental Dynamics Substructuring, Volume 2: Proceedings of the 31st IMAC, A Conference and Exposition on Structural Dynamics, 2013, the second volume of seven from the Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Nonlinear Substructures SEM Substructures Wind Turbine Testbed – Blade Modeling & Correlation Substructure Methods SEM Substructures Wind Turbine Testbed Frequency Based Substructures Fixed Base Substructure Methods Substructure Methods SEM Substructures Wind Turbine Testbed Frequency Based Substructures Fixed Base Substructure Methods

Advances in Nonlinear Dynamics and Control: A Report from Russia

A Report from Russia

Author: A. B. Kurzhanskiĭ

Publisher: Springer Science & Business Media

ISBN: 9780817637361

Category: Science

Page: 276

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This work presents overviews of Soviet research on nonlinear dynamics, particularly as applied to uncertain systems in a deterministic setting. The book concentrates on the three main branches of uncertain dynamics: differential games; evolution, estimation and control; and robust stabilization.

Dynamics of Coupled Structures, Volume 1

Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014

Author: Matt Allen,Randy Mayes,Daniel Rixen

Publisher: Springer Science & Business

ISBN: 3319045016

Category: Technology & Engineering

Page: 472

View: 1209

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This first volume of eight from the IMAC-XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data

Recent Advances in Intelligent Control Systems

Author: Wen Yu

Publisher: Springer Science & Business Media

ISBN: 184882548X

Category: Technology & Engineering

Page: 376

View: 722

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"Recent Advances in Intelligent Control Systems" gathers contributions from workers around the world and presents them in four categories according to the style of control employed: fuzzy control; neural control; fuzzy neural control; and intelligent control. The contributions illustrate the interdisciplinary antecedents of intelligent control and contrast its results with those of more traditional control methods. A variety of design examples, drawn primarily from robotics and mechatronics but also representing process and production engineering, large civil structures, network flows, and others, provide instances of the application of computational intelligence for control. Presenting state-of-the-art research, this collection will be of benefit to researchers in automatic control, automation, computer science (especially artificial intelligence) and mechatronics while graduate students and practicing control engineers working with intelligent systems will find it a good source of study material.