Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.
Author: Herbert berall,Ardshir Guran,D. J. Inman
Publisher: World Scientific
This book is a collection of papers on the subject of applied system dynamics and control written by experts in this field. It offers the reader a sampling of exciting research areas in three fast-growing branches: (i) Wave Motion (ii) Intelligent Structures (iii) Nonlinear Mechanics. The topics covered include flow instability, nonlinear mode localization autoparametric systems with pendula, and geometric stiffening in multibody dynamics. Mathematical methods include perturbation methods, modern control theory, nonlinear neural nets, and resonance scattering theory of berall-Ripoche-Maze. Applications include sound-induced structural vibrations, fiber acoustic waveguides, vibration suppression of structures, linear control of gyroscopic systems, and nonlinear control of distributed systems.This book shows how applied system dynamics and control is currently being utilized and investigated. It will be of interest to engineers, applied mathematicians and physicists.
This undergraduate textbook on the physics of wave motion in optics and acoustics avoids presenting the topic abstractly in order to emphasize real-world examples. While providing the needed scientific context, Dr. Espinoza also relies on students' own experience to guide their learning. The book's exercises and labs strongly emphasize this inquiry-based approach. A strength of inquiry-based courses is that the students maintain a higher level of engagement when they are studying a topic that they have an internal motivation to know, rather than solely following the directives of a professor. "Wave Motion" takes those threads of engagement and interest and weaves them into a coherent picture of wave phenomena. It demystifies key components of life around us--in music, in technology, and indeed in everything we perceive--even for those without a strong math background, who might otherwise have trouble approaching the subject matter.
Book 3 is written for the compulsory part "Wave Motion". It is a useful supplement to textbook. The questions appear in the order of the syllabus for easy reference. All questions are carefully selected to cover various question types requiring different levels of skills. Solutions to calculations and explanations of different options in most multiple choice questions and full marking schemes for conventional questions are provided to help students consolidate their concepts and master their skills in answering examination type questions.
This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.
Waves have been a significant part of the development of telecommunications on Earth. Wave motion is a propagation of disturbances, which deviates from a state of rest or equilibrium, from place to place in a consistent and arranged way. The most common or familiar are surface waves on water, but sound and light both travel as wavelike disturbances, and the movement of all subatomic particles that displays wavelike characteristics. The study of waves adheres various forms that the topic of central importance in all physical sciences and engineering. Modern applications such as telephone, mobile phone, telecommunications and wireless technologies arise through the effort of studies confined to wave motion and applied science.The unifying theme of this book is wave motion; its many forms and the changes it undergoes. This book discusses the significance of wave''s motion and the applications it brought to the society. The content is divided into the following chapters:Chapter 1, Wave Motion, discusses the different forms of waves and their propagation. The units and measurement to be applied in the calculations of different kinds of waves, it may either be one dimensional waves or two dimensional waves. In this chapter, most theoretical concepts about waves are presented.Chapter 2, Light Wave, starts with the definition and properties of light, which is from the big family of Electromagnetic waves. Human eyes are very sensitive to this form of electromagnetic waves. This is the only EM which is visible to the naked eyes. Everyday occurrences are utilized to advantage to describe the properties of light. The discussion shows the benefits derivable form from light waves.Chapter 3, Electromagnetic waves, Wider Scope, focuses on the fundamentals of electromagnetic waves. Each form is being discussed broadly for better reference. The advantages that these forms can be used to enhance life, especially, in the field of medicine and engineering.Chapter 4, Radiation and the Earth, gave importance to the transformation of other forms of energy to other forms of energy. Electromagnetic forces and electromagnetic induction are also tackled in this chapter. The discussion also shows the beneficial effects that can be derived from and the environmental hazards and perils that nuclear energy brings.Chapter 5, Electrical waveforms and Signals, focuses on the use of electrical energy in the household. Concepts are tackled with the transformation of electrical energy to other forms, electrical energy consumption. The beneficial concepts that can be derived from electrical energy and the hazards that it may bring to every household that are consuming electrical energy.Chapter 6, Earthquake Waves, centers on the discussion about earthquake. It gives information about the nature of earthquake waves. People must be aware of the intensities brought by earthquake to give awareness and warn the people about the destructions it may cause to both life and properties.Chapter 7, Sound Waves, starts with the nature of sound and the energy it carries that brought different applications that may aid in the progress of the human life when it comes to technology.Chapter 8, Applied Science, denotes the nature of applied science and be aware of the branches that Applied Science has. The benefits and hazards of technology are also discussed in this chapter as well as an understanding of technology invading the society. Technology and courses are also provided for the students to infer and may help in deciding what course they have to take.Chapter 9, Energy Waves and Communication Technologies, tackles how communication evolved via sound waves. In this chapter, the history of the creation of telephone was discussed and how the telephone was considered as a major breakthrough in the field of science and technology. Concurrently to the creation of the telephone is the launching of electronic transport network. The telephone system or how the telephone transmits information from wire to wire.Chapter 10, Wireless Communication Technology, discusses the launching of wireless communication through radio transport network. Wireless technological advances are also presented to keep the society abreast with advances in science and technology. How communication keeps the people in touch who are separated by geographical distances. A historical concept of every topic in every chapter was given emphasis to provide the development of physical theories and technological advances is included to highpoint the humanistic aspect of Science.The author hopes that this book will be an instrument for every student to become more conscious of the significance and relevance of science, specifically physics and technology in their everyday life.
Nikolaos A. Kampanis,Vassilios Dougalis,John A. Ekaterinaris
Author: Nikolaos A. Kampanis,Vassilios Dougalis,John A. Ekaterinaris
Publisher: CRC Press
Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent years. Exploring the latest developments in the field, Effective Computational Methods for Wave Propagation presents several modern, valuable computational methods used to describe wave propagation phenomena in selected areas of physics and technology. Featuring contributions from internationally known experts, the book is divided into four parts. It begins with the simulation of nonlinear dispersive waves from nonlinear optics and the theory and numerical analysis of Boussinesq systems. The next section focuses on computational approaches, including a finite element method and parabolic equation techniques, for mathematical models of underwater sound propagation and scattering. The book then offers a comprehensive introduction to modern numerical methods for time-dependent elastic wave propagation. The final part supplies an overview of high-order, low diffusion numerical methods for complex, compressible flows of aerodynamics. Concentrating on physics and technology, this volume provides the necessary computational methods to effectively tackle the sources of problems that involve some type of wave motion.