Download or read book Asymptotic Methods in Nonlinear Wave Phenomena written by Tommaso Ruggeri and published by World Scientific. This book was released on 2007 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together several contributions from leading experts in the field of nonlinear wave propagation. This field, which during the last three decades has seen important breakthroughs from the theoretical point of view, has recently acquired increased relevance due to advances in the technology of fluids e.g. at microscale or nanoscale and the recognition of crucial applications to the understanding of biological phenomena.Nonlinear wave theory requires the use of disparate approaches, including formal and rigorous asymptotic methods, Lie group theory, energy methods, numerical analysis, and bifurcation theory. This book presents a unique blend in which different aspects of the theory are enlightened and several real-life applications are investigated. The book will be a valuable resource for applied scientists interested in some of the most recent advances in the theory and in the applications of wave propagation, shock formation, nonequilibrium thermodynamics and energy methods.
Download or read book Linear and Nonlinear Waves in Microstructured Solids written by Igor V. Andrianov and published by CRC Press. This book was released on 2021-04-22 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.
Download or read book Asymptotic Methods in Nonlinear Wave Phenomena written by Tommaso Ruggeri and published by World Scientific. This book was released on 2007 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together several contributions from leading experts in the field of nonlinear wave propagation. This field, which during the last three decades has seen important breakthroughs from the theoretical point of view, has recently acquired increased relevance due to advances in the technology of fluids e.g. at microscale or nanoscale and the recognition of crucial applications to the understanding of biological phenomena. Nonlinear wave theory requires the use of disparate approaches, including formal and rigorous asymptotic methods, Lie group theory, energy methods, numerical analysis, and bifurcation theory. This book presents a unique blend in which different aspects of the theory are enlightened and several real-life applications are investigated. The book will be a valuable resource for applied scientists interested in some of the most recent advances in the theory and in the applications of wave propagation, shock formation, nonequilibrium thermodynamics and energy methods.
Download or read book Nonlinear Dispersive Waves written by Mark J. Ablowitz and published by Cambridge University Press. This book was released on 2011-09-08 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.
Download or read book A Nonlinear Progress to Modern Soliton Theory written by Colin Rogers and published by Cambridge Scholars Publishing. This book was released on 2022-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.
Download or read book 3D Modeling of Nonlinear Wave Phenomena on Shallow Water Surfaces written by Iftikhar B. Abbasov and published by John Wiley & Sons. This book was released on 2018-01-31 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: With climate change, erosion, and human encroachment on coastal environments growing all over the world, it is increasingly important to protect populations and environments close to the sea from storms, tsunamis, and other events that can be not just costly to property but deadly. This book is one step in bringing the science of protection from these events forward, the most in-depth study of its kind ever published. The analytic and numerical modeling problems of nonlinear wave activities in shallow water are analyzed in this work. Using the author's unique method described herein, the equations of shallow water are solved, and asymmetries that cannot be described by the Stokes theory are solved. Based on analytical expressions, the impacts of dispersion effects to wave profiles transformation are taken into account. The 3D models of the distribution and refraction of nonlinear surface gravity wave at the various coast formations are introduced, as well. The work covers the problems of numerical simulation of the run-up of nonlinear surface gravity waves in shallow water, transformation of the surface waves for the 1D case, and models for the refraction of numerical modeling of the run-up of nonlinear surface gravity waves at beach approach of various slopes. 2D and 3D modeling of nonlinear surface gravity waves are based on Navier-Stokes equations. In 2D modeling the influence of the bottom of the coastal zone on flooding of the coastal zone during storm surges was investigated. Various stages of the run-up of nonlinear surface gravity waves are introduced and analyzed. The 3D modeling process of the run-up is tested for the coast protection work of the slope type construction. Useful for students and veteran engineers and scientists alike, this is the only book covering these important issues facing anyone working with coastal models and ocean, coastal, and civil engineering in this area.
Download or read book Nonlinear Waves in Integrable and Non integrable Systems written by Jianke Yang and published by SIAM. This book was released on 2010-12-02 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).
Download or read book Proceedings WASCOM 2007 written by Natale Manganaro and published by World Scientific. This book was released on 2008 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the fifth in a series of proceedings which started in 1999. The contributions include the latest results on the theory of wave propagation, extended thermodynamics, and the stability of the solutions to partial differential equations. Sample Chapter(s). Chapter 1: Reciprocal Transformations and Integrable Hamiltonian Hydrodynamic Type Systems (334 KB). Contents: Quantitative Estimates for the Large Time Behavior of a Reaction-Diffusion Equation with Rational Reaction Term (M Bisi et al.); Linearized Euler''s Variational Equations in Lagrangian Coordinates (G Boillat & Y J Peng); Restabilizing Forcing for a Diffusive Prey-Predator Model (B Buonomo & S Rionero); Fluid Dynamical Features of the Weak KAM Theory (F Cardin); Ricci Flow Deformation of Cosmological Initial Data Sets (M Carfora & T Buchert); Fuchsian Partial Differential Equations (Y Choquet-Bruhat); Analytic Structure of the Four-Wave Mixing Model in Photoreactive Material (R Conte & S Bugaychuk); A Note about Waves in Dissipative and Dispersive Solids (M Destrade & G Saccomandi); Exponential and Algebraic Relaxation in Kinetic Models for Wealth Distribution (B Dring et al.); Solitary Waves in Dispersive Materials (J Engelbrecht et al.); A GinzburgOCoLandau Model for the Ice-Water and Liquid-Vapor Phase Transitions (M Fabrizio); Stability Considerations for Reaction-Diffusion Systems (J N Flavin); A Mechanical Model for Liquid Nanolayers (H Gouin); A Particle Method for a Lotka-Volterra System with Nonlinear Cross and Self-Diffusion (M Groppi & M Sammartino); Transport Properties of Chemically Reacting Gas Mixtures (G M Kremer); Navier-Stokes in Aperture Domains: Existence with Bounded Flux and Qualitative Properties (P Maremonti); On Two-Pulse Interaction in a Class of Model Elastic Materials (A Mentrelli et al.); On a Particle-Size Segregation Equation (C Mineo & M Torrisi); Problems of Stability and Waves in Biological Systems (G Mulone); Multiple Cold and Hot Second Sound Shocks in HE II (A Muracchini & L Seccia); Differential Equations and Lie Symmetries (F Oliveri et al.); Bifurcation Analysis of Equilibria in Competitive Logistic Networks with Adaptation (A Raimondi & C Tebaldi); Poiseuille Flow of a Fluid Overlying a Porous Media (B Straughan); Analysis of Heat Conduction Phenomena in a One-Dimensional Hard-Point Gas by Extended Thermodynamics (S Tanigushi et al.); On Waves in Weakly Nonlinear Poroelastic Materials Modeling Impacts of Meteorites (K Wilmanski et al.); and other papers. Readership: Researchers in mathematics, physics, chemistry and engineering."
Download or read book WASCOM 2009 written by Antonio Maria Greco and published by World Scientific. This book was released on 2010 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains contributions in the field of waves propagation and stability in continuous media.
Download or read book Waves And Stability In Continuous Media Proceedings Of The 15th Conference On Wascom 2009 written by Antonio Maria Greco and published by World Scientific. This book was released on 2010-04-29 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains recent contributions in the field of waves propagation and stability in continuous media. The volume is the sixth in a series published by World Scientific since 1999.
Download or read book Classical and Relativistic Rational Extended Thermodynamics of Gases written by Tommaso Ruggeri and published by Springer Nature. This book was released on 2021-04-22 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rational extended thermodynamics (RET) is the theory that is applicable to nonequilibrium phenomena out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to present, in a systematic way, new results obtained by RET of gases in both classical and relativistic cases, and it is a natural continuation of the book "Rational Extended Thermodynamics beyond the Monatomic Gas" by the same authors published in 2015. However, this book addresses much wider topics than those of the previous book. Its contents are as follows: RET of rarefied monatomic gases and of polyatomic gases; a simplified RET theory with 6 fields being valid far from equilibrium; RET where both molecular rotational and vibrational modes exist; mixture of gases with multi-temperature. The theory is applied to several typical topics (sound waves, shock waves, etc.) and is compared with experimental data. From a mathematical point of view, RET can be regarded as a theory of hyperbolic symmetric systems, of which it is possible to conduct a qualitative analysis. The book represents a valuable resource for applied mathematicians, physicists, and engineers, offering powerful models for many potential applications such as reentering satellites into the atmosphere, semiconductors, and nanoscale phenomena.
Download or read book Nonlinear PDE s Dynamics and Continuum Physics written by J. L. Bona and published by American Mathematical Soc.. This book was released on 2000 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions. The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.
Download or read book Compendium on Gradient Materials written by Albrecht Bertram and published by Springer Nature. This book was released on 2022-05-28 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers frameworks for the material modeling of gradient materials both for finite and small deformations within elasticity, plasticity, viscosity, and thermomechanics. The first chapter focuses on balance laws and holds for all gradient materials. The next chapters are dedicated to the material modeling of second and third-order materials under finite deformations. Afterwards the scope is limited to the geometrically linear theory, i.e., to small deformations. The next chapter offers an extension of the concept of internal constraints to gradient materials. The final chapter is dedicated to incompressible viscous gradient fluids with the intention to describe, among other applications, turbulent flows, as already suggested by Saint-Venant in the middle of the 19th century.
Download or read book Nonlinear Waves Hamiltonian Systems written by Ricardo Carretero-González and published by Oxford University Press. This book was released on 2024-11-05 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear waves are of significant scientific interest across many diverse contexts, ranging from mathematics and physics to engineering, biosciences, chemistry, and finance. The study of nonlinear waves is relevant to Bose-Einstein condensates, the interaction of electromagnetic waves with matter, optical fibers and waveguides, acoustics, water waves, atmospheric and planetary scales, and even galaxy formation. The aim of this book is to provide a self-contained introduction to the continuously developing field of nonlinear waves, that offers the background, the basic ideas, and mathematical, as well as computational methods, while also presenting an overview of associated physical applications. Originated from the authors' own research activity in the field for almost three decades and shaped over many years of teaching on relevant courses, the primary purpose of this book is to serve as a textbook. However, the selection and exposition of the material will be useful to anyone who is curious to explore the fascinating world of nonlinear waves.
Download or read book Nonlinear Wave Dynamics written by J. Engelbrecht and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.
Download or read book Nonlinear Waves written by Lokenath Debnath and published by CUP Archive. This book was released on 1983-12-30 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Download or read book Recent Mathematical Methods in Nonlinear Wave Propagation written by Guy Boillat and published by Springer. This book was released on 2006-11-14 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.
