Topics In the Theory of Random Noise


Book Description

In two main sections, this volume covers peaks of random functions and the effects of noise on relays and nonlinear self-excited oscillations in the presence of noise. Includes bibliographic references and index.







Transforming Noise


Book Description

Today, the concept of noise is employed to characterize random fluctuations in general. Before the twentieth century, however, noise only meant disturbing sounds. In the 1900s-50s, noise underwent a conceptual transformation from unwanted sounds that needed to be domesticated into a synonym for errors and deviations to be now used as all kinds of signals and information. Transforming Noise examines the historical origin of modern attempts to understand, control, and use noise. Its history sheds light on the interactions between physics, mathematics, mechanical technology, electrical engineering, and information and data sciences in the twentieth century. This book explores the process of engineers and physicists turning noise into an informational concept, starting from the rise of sound reproduction technologies such as the phonograph, telephone, and radio in the 1900s-20s until the theory of Brownian motions for random fluctuations and its application in thermionic tubes of telecommunication systems. These processes produced different theoretical treatments of noise in the 1920s-30s, such as statistical physicists' studies of Brownian fluctuations' temporal evolution, radio engineers' spectral analysis of atmospheric disturbances, and mathematicians' measure-theoretic formulation. Finally, it discusses the period during and after World War II and how researchers have worked on military projects of radar, gunfire control, and secret communications and converted the interwar theoretical studies of noise into tools for statistical detection, estimation, prediction, and information transmission. To physicists, mathematicians, electrical engineers, and computer scientists, this book offers a historical perspective on themes highly relevant in today's science and technology, ranging from Wi-Fi and big data to quantum information and self-organization. This book also appeals to environmental and art historians to modern music scholars as the history of noise constitutes a unique angle to study sound and society. Finally, to researchers in media studies and digital cultures, Transforming Noise demonstrates the deep technoscientific historicity of certain notions - information, channel, noise, equivocation - they have invoked to understand modern media and communication.




IUTAM Symposium on Nonlinear Stochastic Dynamics


Book Description

Non-linear stochastic systems are at the center of many engineering disciplines and progress in theoretical research had led to a better understanding of non-linear phenomena. This book provides information on new fundamental results and their applications which are beginning to appear across the entire spectrum of mechanics. The outstanding points of these proceedings are Coherent compendium of the current state of modelling and analysis of non-linear stochastic systems from engineering, applied mathematics and physics point of view. Subject areas include: Multiscale phenomena, stability and bifurcations, control and estimation, computational methods and modelling. For the Engineering and Physics communities, this book will provide first-hand information on recent mathematical developments. The applied mathematics community will benefit from the modelling and information on various possible applications.







Random Perturbation Methods with Applications in Science and Engineering


Book Description

This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.




Numerical Solution of Stochastic Differential Equations


Book Description

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP




Stochastic Dynamics of Power Systems


Book Description

This book discusses stochastic dynamics of power systems and the related analytical methodology. It summarizes and categorizes the stochastic elements of power systems and develops a framework for research on stochastic dynamics of power systems. It also establishes a research model for stochastic dynamics of power systems and theoretically proves stochastic stability in power systems. Further, in addition to demonstrating the stochastic oscillation mechanism in power systems, it also proposes methods for quantitative analysis and stochastic optimum control in the field of stochastic dynamic security in power systems. This book is a valuable resource for researchers, scholars and engineers in the field of electrics.




Geometry and Invariance in Stochastic Dynamics


Book Description

This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie’s Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.