Tag: Nonlinear

Free Download Calculus of Variations and Nonlinear Partial Differential Equations: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 – July 2, 2005 by Luigi Ambrosio , Luis Caffarelli , Michael G. Crandall , Lawrence C. Evans , Nicola Fusco
English | PDF | 2008 | 213 Pages | ISBN : 3540759131 | 2.9 MB
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo.

Free Download A³N²M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models: Proceedings of the 50th John H. Barrett Memorial Lectures by Tadele Mengesha, Abner J. Salgado
English | PDF EPUB (True) | 2023 | 325 Pages | ISBN : 3031340884 | 48 MB
This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.

Free Download Advances in Computational Nonlinear Mechanics by I. St. Doltsinis
English | PDF | 1989 | 248 Pages | ISBN : 3211821139 | 17 MB
Advanced computational methods in nonlinear mechanics of solids and fluids are dealt with in this volume. Contributions consider large deformations of structures and solids, problems in nonlinear dynamics, aspects of earthquake analysis, coupled problems, convection-dominated phenomena, and compressible and incompressible viscous flows. Selected applications indicate the relevance of the analysis to the demands of industry and science. The contributors are from research institutions well-known for their work in this field.

Free Download Nonlinear Waves and Inverse Scattering Transform (197 Pages)
by Spencer Kuo
English | 2023 | ISBN: 1800614039 | 198 pages | True PDF | 7.91 MB
Nonlinear waves are essential phenomena in scientific and engineering disciplines. The features of nonlinear waves are usually described by solutions to nonlinear partial differential equations (NLPDEs). This book was prepared to familiarize students with nonlinear waves and methods of solving NLPDEs, which will enable them to expand their studies into related areas. The selection of topics and the focus given to each provide essential materials for a lecturer teaching a nonlinear wave course. Chapter 1 introduces "mode" types in nonlinear systems as well as Bäcklund transform, an indispensable technique to solve generic NLPDEs for stationary solutions. Chapters 2 and 3 are devoted to the derivation and solution characterization of three generic nonlinear equations: nonlinear Schrödinger equation, Korteweg-de Vries (KdV) equation, and Burgers equation. Chapter 4 is devoted to the inverse scattering transform (IST), addressing the initial value problems of a group of NLPDEs. In Chapter 5, derivations and proofs of the IST formulas are presented. Steps for applying IST to solve NLPDEs for solitary solutions are illustrated in Chapter 6.

Free Download Nonlinear Systems : Stability, Dynamics and Control (233 Pages)
by Guanrong Chen
English | 2023 | ISBN: 9811278989 | 234 pages | True PDF | 6.62 MB
The topic of nonlinear systems is fundamental to the study of systems engineering. So extensive investigations have been carried out by both the nonlinear control and nonlinear dynamics communities, but the focus can be different – on controllers design and dynamics analysis, respectively. The last two decades have witnessed the gradual merging of control theory and dynamics analysis, but not yet to the extent of controlling nonlinear dynamics such as bifurcations and chaos. This monograph is an attempt to fill that gap while presenting a rather comprehensive coverage of the fundamental nonlinear systems theory in a self-contained and approachable manner. This introductory treatise is written for self-study and, in particular, as an elementary textbook that can be taught in a one-semester course to advanced undergraduates or entrance level graduates with curricula focusing on nonlinear systems, both on control theory and dynamics analysis.

Free Download Nonlinear Field Theories and Unexplained Phenomena in Nature (321 pages)
by Alexander S Rabinowitch
English | 2023 | ISBN: 9811264112 | 322 pages | True PDF | 11.03 MB
The book is devoted to several topical questions in modern mathematical and theoretical physics, astrophysics, geophysics, and cosmology that remain unsolved within the framework of the standard approaches. To them, one can attribute unexplained properties of the magnetic fields of stars and planets, puzzles of the Earth’s atmosphere, the phenomenon of ball lightning, the problem of a qualitative description for nuclear forces and their well-known property of saturation, enigmatic properties of spiral galaxies, the problem of the cosmological singularity, mysteries of the dark matter and dark energy, amongst others. To find theoretical ways for understanding such phenomena, new nonlinear generalizations of the classical field theories and advanced methods to solve nonlinear equations arising in them are studied and presented in this book.

Free Download Nonlinear Dynamics
by Axelle Amon, Marc Lefranc
English | 2023 | ISBN: 3110677865 | 214 pages | True PDF EPUB | 80.98 MB
Many nonlinear systems around us can generate a very complex and counter-intuitive dynamics that contrasts with their simplicity, but their understanding requires concepts that are outside the basic training of most science students. This textbook, which is the fruit of graduate courses that the authors have taught at their respective universities, provides a richly illustrated introduction to nonlinear dynamical systems and chaos and a solid foundation for this fascinating subject. It will satisfy those who want discover this field, including at the undergraduate level, but also those who need a compact and consistent overview, gathering the concepts essential to nonlinear scientists.

Free Download Chromophores with Nonlinear Optical Properties and Their Applications
by Marinescu, Maria;
English | 2023 | ISBN: 979-8886975253 | 154 pages | True PDF | 22.64 MB
"This book is intended to be a useful tool for academia and researchers interested in the chemistry and applications of organic chromophores with nonlinear optical properties (NLO). This book aims to review the various types of organic chromophores reported in literature with NLO properties, such as alkynes, tetraenes, azo dyes, chalcones, heterocyclic compounds, fullerenes, perylenes, ferrocenes and polymers, their structural features, properties and their nonlinear optics. parameters. 380 chromophores with NLO properties are presented in this book. The various applications of organic NLO chromophores, in medicine as luminescent materials, molecular switches, laser technology, spectroscopic and electrochemical sensors, microfabrication and imaging, datastorage, optical signal modulation, telecommunications, make this field highly sought after and explored by researchers in the last decade"-

Free Download Chaos, Complexity, and Nonlinear Economic Theory (227 Pages)
by Wei-Bin Zhang
English | 2023 | ISBN: 9811267413 | 228 pages | True PDF | 37.08 MB
What do economic chaos and uncertainties mean in rational or irrational economic theories? How do simple deterministic interactions among a few variables lead to unpredictable complex phenomena? Why is complexity of economies causing so many conflicts and confusions worldwide? This book provides a comprehensive introduction to recent developments of complexity theory in economics. It presents different models based on well-accepted economic mechanisms such as the Solow model, Ramsey model, and Lucas model. It is focused on presenting complex behaviors, such as business cycles, aperiodic motion, bifurcations, catastrophes, chaos, and hidden attractors, in basic economic models with nonlinear behavior. It shows how complex nonlinear phenomena are identified from various economic mechanisms and theories. These models demonstrate that the traditional or dominant economic views on evolution of, for instance, capitalism market, free competition, or Keynesian economics, are not generally valid. Markets are unpredictable and nobody knows with certainty the consequences of policies or other external factors in economic systems with simple interactions.

Free Download Power Scaling of Enhancement Cavities for Nonlinear Optics by Ioachim Pupeza
English | PDF | 2012 | 106 Pages | ISBN : 1461440998 | 2.9 MB
Enhancement cavities are passive optical resonators in which continuous-wave laser radiation or pulses of a frequency comb are coherently overlapped, allowing for a power and intensity scaling of up to several orders of magnitude. A prominent application is the table-top generation of bright, laser-like radiation in spectral regions where direct laser action is inefficient or not available at all, via intracavity nonlinear optical processes. However, to exploit the full capacity of this technique further progress is needed.