State Space Consistency And Differentiability

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State Space Consistency And Differentiability

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Author : Demetrios Serakos
language : en
Publisher: Springer
Release Date : 2015-01-08

State Space Consistency And Differentiability written by Demetrios Serakos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-08 with Mathematics categories.

​By investigating the properties of the natural state, this book presents an analysis of input-output systems with regard to the mathematical concept of state. The state of a system condenses the effects of past inputs to the system in a useful manner. This monograph emphasizes two main properties of the natural state; the first has to do with the possibility of determining the input-output system from its natural state set and the second deals with differentiability properties involving the natural state inherited from the input-output system, including differentiability of the natural state and natural state trajectories. The results presented in this title aid in modeling physical systems since system identification from a state set holds in most models. Researchers and engineers working in electrical, aerospace, mechanical, and chemical fields along with applied mathematicians working in systems or differential equations will find this title useful due to its rigorous mathematics.​

Generalized Adjoint Systems

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Author : Demetrios Serakos
language : en
Publisher: Springer
Release Date : 2015-04-06

Generalized Adjoint Systems written by Demetrios Serakos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-06 with Mathematics categories.

This book defines and develops the generalized adjoint of an input-output system. It is the result of a theoretical development and examination of the generalized adjoint concept and the conditions under which systems analysis using adjoints is valid. Results developed in this book are useful aids for the analysis and modeling of physical systems, including the development of guidance and control algorithms and in developing simulations. The generalized adjoint system is defined and is patterned similarly to adjoints of bounded linear transformations. Next the elementary properties of the generalized adjoint system are derived. For a space of input-output systems, a generalized adjoint map from this space of systems to the space of generalized adjoints is defined. Then properties of the generalized adjoint map are derived. Afterward the author demonstrates that the inverse of an input-output system may be represented in terms of the generalized adjoint. The use of generalized adjoints to determine bounds for undesired inputs such as noise and disturbance to an input-output system is presented and methods which parallel adjoints in linear systems theory are utilized. Finally, an illustrative example is presented which utilizes an integral operator representation for the system mapping.

Causality Measurement Theory And The Differentiable Structure Of Space Time

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Author : R. N. Sen
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-11

Causality Measurement Theory And The Differentiable Structure Of Space Time written by R. N. Sen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-11 with Science categories.

Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.

Applied Differential Geometry A Modern Introduction

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Author : Vladimir G Ivancevic
language : en
Publisher: World Scientific
Release Date : 2007-05-21

Applied Differential Geometry A Modern Introduction written by Vladimir G Ivancevic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-21 with Mathematics categories.

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.

Advances In Applied Self Organizing Systems

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Author : Mikhail Prokopenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08

Advances In Applied Self Organizing Systems written by Mikhail Prokopenko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-08 with Computers categories.

How do we design a self-organizing system? Is it possible to validate and control non-deterministic dynamics? What is the right balance between the emergent patterns that bring robustness, adaptability and scalability, and the traditional need for verification and validation of the outcomes? The last several decades have seen much progress from original ideas of “emergent functionality” and “design for emergence”, to sophisticated mathematical formalisms of “guided self-organization”. And yet the main challenge remains, attracting the best scientific and engineering expertise to this elusive problem. This book presents state-of-the-practice of successfully engineered self-organizing systems, and examines ways to balance design and self-organization in the context of applications. As demonstrated in this second edition of Advances in Applied Self-Organizing Systems, finding this balance helps to deal with practical challenges as diverse as navigation of microscopic robots within blood vessels, self-monitoring aerospace vehicles, collective and modular robotics adapted for autonomous reconnaissance and surveillance, self-managing grids and multiprocessor scheduling, data visualization and self-modifying digital and analog circuitry, intrusion detection in computer networks, reconstruction of hydro-physical fields, traffic management, immunocomputing and nature-inspired computation. Many algorithms proposed and discussed in this volume are biologically inspired, and the reader will also gain an insight into cellular automata, genetic algorithms, artificial immune systems, snake-like locomotion, ant foraging, birds flocking, neuromorphic circuits, amongst others. Demonstrating the practical relevance and applicability of self-organization, Advances in Applied Self-Organizing Systems will be an invaluable tool for advanced students and researchers in a wide range of fields.

The History Of Theoretical Material And Computational Mechanics Mathematics Meets Mechanics And Engineering

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Author : Erwin Stein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-04

The History Of Theoretical Material And Computational Mechanics Mathematics Meets Mechanics And Engineering written by Erwin Stein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-04 with Science categories.

This collection of 23 articles is the output of lectures in special sessions on “The History of Theoretical, Material and Computational Mechanics” within the yearly conferences of the GAMM in the years 2010 in Karlsruhe, Germany, 2011 in Graz, Austria, and in 2012 in Darmstadt, Germany; GAMM is the “Association for Applied Mathematics and Mechanics”, founded in 1922 by Ludwig Prandtl and Richard von Mises. The contributions in this volume discuss different aspects of mechanics. They are related to solid and fluid mechanics in general and to specific problems in these areas including the development of numerical solution techniques. In the first part the origins and developments of conservation principles in mechanics and related variational methods are treated together with challenging applications from the 17th to the 20th century. Part II treats general and more specific aspects of material theories of deforming solid continua and porous soils. and Part III presents important theoretical and engineering developments in fluid mechanics, beginning with remarkable inventions in old Egypt, the still dominating role of the Navier-Stokes PDEs for fluid flows and their complex solutions for a wide field of parameters as well as the invention of pumps and turbines in the 19th and 20th century. The last part gives a survey on the development of direct variational methods – the Finite Element Method – in the 20th century with many extensions and generalizations.

Scientific Computing With Ordinary Differential Equations

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Author : Peter Deuflhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Scientific Computing With Ordinary Differential Equations written by Peter Deuflhard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

Differential Geometrical Methods In Mathematical Physics

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Author : P. L. Garcia
language : en
Publisher: Springer
Release Date : 2006-11-15

Differential Geometrical Methods In Mathematical Physics written by P. L. Garcia and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

From Micro To Macro Quantum Systems A Unified Formalism With Superselection Rules And Its Applications

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Author : K Kong Wan
language : en
Publisher: World Scientific
Release Date : 2006-03-03

From Micro To Macro Quantum Systems A Unified Formalism With Superselection Rules And Its Applications written by K Kong Wan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-03 with Science categories.

Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations.This book also discusses various topics of interest such as the asymptotic treatment of quantum state preparation and quantum measurement, local observables and local values, Schrödinger's cat states in superconducting systems, and a path space formulation of quantum mechanics.This self-contained book is complete with a review of relevant geometric and operator theories, for example, vector fields and operators, symmetric operators and their maximal symmetric extensions, direct integrals of Hilbert spaces and operators./a

Simulation And Control Of Chaotic Nonequilibrium Systems With A Foreword By Julien Clinton Sprott

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Author : William Graham Hoover
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-02-02

Simulation And Control Of Chaotic Nonequilibrium Systems With A Foreword By Julien Clinton Sprott written by William Graham Hoover and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-02 with Science categories.

This book aims to provide a lively working knowledge of the thermodynamic control of microscopic simulations, while summarizing the historical development of the subject, along with some personal reminiscences. Many computational examples are described so that they are well-suited to learning by doing. The contents enhance the current understanding of the reversibility paradox and are accessible to advanced undergraduates and researchers in physics, computation, and irreversible thermodynamics.