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Asymptotic Methods for Relaxation Oscillations and Applications
In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.
Galileo Unbound
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying...
Asymptotic Perturbation Methods
Asymptotic Perturbation Methods Cohesive overview of powerful mathematical methods to solve differential equations in physics Asymptotic Perturbation Methods for Nonlinear Differential Equations in Physics addresses nonlinearity in various fields of physics from the vantage point of its mathematical description in the form of nonlinear partial differential equations and presents a unified view on nonlinear systems in physics by providing a common framework to obtain approximate solutions to the respective nonlinear partial differential equations based on the asymptotic perturbation method. Aside from its complete coverage of a complicated topic, a noteworthy feature of the book is the emphas...
Introduction to Nonlinear Dynamics for Physicists
This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon.
Topics in LC Oscillators
This book introduces an intuitive, self-sustained oscillator model and applies it to describe some of the most critical performance metrics of LC oscillators, such as phase noise, entrainment, and pulling. It also covers the related topics of magnetic coupling and inductor design. The author emphasizes the basic principles and illuminates them with approximate calculations, adopting a design-oriented approach that imparts intuition and complements simulations. This book constitutes a novel and fresh perspective on the subject and can be helpful to electrical engineering students and practicing engineers. It also serves as a bridge between the mathematical treatises of the subject and the more practical circuit-oriented approaches.
Nonlinear Physics with Mathematica for Scientists and Engineers
Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.
Acoustics & Vibration of Mechanical Structures
The book covers a broad range of topics related to acoustics and vibration problems encountered in various fields of engineering. It presents some analytical, numerical and experimental techniques applicable to analyze linear and non-linear noise and vibration problems. Volume is indexed by Thomson Reuters CPCI-S (WoS). The 58 papers are grouped as follow: Chapter 1: Analytical Approaches to Nonlinear Vibrations; Chapter 2: Damage Assessment of Structures; Chapter 3: Modeling and Simulation Techniques with Applications; Chapter 4: Biomechanics; Chapter 5: Environmental and Occupational Noise and Vibrations; Chapter 6: Structural Vibration, Attenuators and Isolation.
