Singular Phenomena and Scaling in Mathematical Models

Singular Phenomena and Scaling in Mathematical Models
Author: Michael Griebel
Publisher: Springer Science & Business Media
Total Pages: 432
Release: 2013-11-18
Genre: Computers
ISBN: 3319007866

The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.

Mathematical Modelling of Waves in Multi-Scale Structured Media

Mathematical Modelling of Waves in Multi-Scale Structured Media
Author: Alexander B. Movchan
Publisher: CRC Press
Total Pages: 317
Release: 2017-11-09
Genre: Mathematics
ISBN: 1351651420

Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.

Singularities: Formation, Structure and Propagation

Singularities: Formation, Structure and Propagation
Author: J. Eggers
Publisher: Cambridge University Press
Total Pages: 471
Release: 2015-09-10
Genre: Mathematics
ISBN: 1107098416

This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.

Multiple Time Scale Dynamics

Multiple Time Scale Dynamics
Author: Christian Kuehn
Publisher: Springer
Total Pages: 816
Release: 2015-02-25
Genre: Mathematics
ISBN: 3319123165

This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.

Mathematics Applied to Deterministic Problems in the Natural Sciences

Mathematics Applied to Deterministic Problems in the Natural Sciences
Author: C. C. Lin
Publisher: SIAM
Total Pages: 646
Release: 1988-12-01
Genre: Mathematics
ISBN: 9780898712292

This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers.

Control and Dynamic Systems V38: Advances in Aeronautical Systems

Control and Dynamic Systems V38: Advances in Aeronautical Systems
Author: C.T. Leonides
Publisher: Academic Press
Total Pages: 420
Release: 2012-12-02
Genre: Transportation
ISBN: 032316286X

Advances in Aeronautical Systems shows that real-time simulation of aeronautical systems is fundamental in the analysis, design, and testing of today's increasingly complex aeronautical systems. Perhaps more important is the fact that simulation, including 3-D vision and motion simulation techniques, is an essential element in pilot training for both commercial and military aircraft. An essential characteristic of all modern aeronautical systems is their avionics system, which is composed of many elements, in particular sensor systems. This book comprises eight chapters, with the first focusing on aircraft automatic flight control system with model inversion. The following chapters then discuss information systems for supporting design of complex human-machine systems and formulation of a minimum variance deconvolution technique for compensation of pneumatic distortion in pressure-sensing devices. Other chapters cover synthesis and validation of feedback guidance laws for air-to-air interceptions; multistep matrix integrators for real-time simulation; the role of image interpretation in tracking and guidance; continuous time parameter estimation: analysis via a limiting ordinary differential equation; and in-flight alignment of inertial navigation systems. This book will be of interest to practitioners in the fields of engineering and aeronautics.

Nonlinear Time Scale Systems in Standard and Nonstandard Forms

Nonlinear Time Scale Systems in Standard and Nonstandard Forms
Author: Anshu Narang-Siddarth
Publisher: SIAM
Total Pages: 231
Release: 2014-01-01
Genre: Mathematics
ISBN: 1611973341

This book introduces key concepts for systematically controlling engineering systems that possess interacting phenomena occurring at widely different speeds. The aim is to present the reader with control techniques that extend the benefits of model reduction of singular perturbation theory to a larger class of nonlinear dynamical systems. New results and relevant background are presented through insightful examples that cover a wide range of applications from different branches of engineering. This book is unique because it: presents a new perspective on existing control methods and thus broadens their application to a larger class of nonlinear dynamical systems; discusses general rather than problem-specific developments to certain applications or disciplines in order to provide control engineers with useful analytical tools ; addresses new control problems using singular perturbation methods, including closed-form results for control of nonminimum phase systems.