Deterministic Chaos

Deterministic Chaos
Author: Heinz Georg Schuster
Publisher: John Wiley & Sons
Total Pages: 312
Release: 2006-03-06
Genre: Science
ISBN: 3527606416

A new edition of this well-established monograph, this volume provides a comprehensive overview over the still fascinating field of chaos research. The authors include recent developments such as systems with restricted degrees of freedom but put also a strong emphasis on the mathematical foundations. Partly illustrated in color, this fourth edition features new sections from applied nonlinear science, like control of chaos, synchronisation of nonlinear systems, and turbulence, as well as recent theoretical concepts like strange nonchaotic attractors, on-off intermittency and spatio-temporal chaotic motion.

Deterministic Chaos in General Relativity

Deterministic Chaos in General Relativity
Author: David Hobill
Publisher: Springer Science & Business Media
Total Pages: 472
Release: 2013-06-29
Genre: Science
ISBN: 1475799934

Nonlinear dynamical systems play an important role in a number of disciplines. The physical, biological, economic and even sociological worlds are comprised of com plex nonlinear systems that cannot be broken down into the behavior of their con stituents and then reassembled to form the whole. The lack of a superposition principle in such systems has challenged researchers to use a variety of analytic and numerical methods in attempts to understand the interesting nonlinear interactions that occur in the World around us. General relativity is a nonlinear dynamical theory par excellence. Only recently has the nonlinear evolution of the gravitational field described by the theory been tackled through the use of methods used in other disciplines to study the importance of time dependent nonlinearities. The complexity of the equations of general relativity has been (and still remains) a major hurdle in the formulation of concrete mathematical concepts. In the past the imposition of a high degree of symmetry has allowed the construction of exact solutions to the Einstein equations. However, most of those solutions are nonphysical and of those that do have a physical significance, many are often highly idealized or time independent.

Physics and Theoretical Computer Science

Physics and Theoretical Computer Science
Author: Jean-Pierre Gazeau
Publisher: IOS Press
Total Pages: 349
Release: 2007
Genre: Science
ISBN: 1586037064

Aims to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. This book assembles theoretical physicists and specialists of theoretical informatics and discrete mathematics in order to learn about developments in cryptography, algorithmics, and more.

Decision Theory and Choices: a Complexity Approach

Decision Theory and Choices: a Complexity Approach
Author: Marisa Faggini
Publisher: Springer Science & Business Media
Total Pages: 252
Release: 2010-12-28
Genre: Mathematics
ISBN: 8847017785

In economics agents are assumed to choose on the basis of rational calculations aimed at the maximization of their pleasure or profit. Formally, agents are said to manifest transitive and consistent preferences in attempting to maximize their utility in the presence of several constraints. They operate according to the choice imperative: given a set of alternatives, choose the best. This imperative works well in a static and simplistic framework, but it may fail or vary when 'the best' is changing continuously. This approach has been questioned by a descriptive approach that springing from the complexity theory tries to give a scientific basis to the way in which individuals really choose, showing that those models of human nature is routinely falsified by experiments since people are neither selfish nor rational. Thus inductive rules of thumb are usually implemented in order to make decisions in the presence of incomplete and heterogeneous information sets.

Overland Flow

Overland Flow
Author: Anthony J Parsons
Publisher: CRC Press
Total Pages: 437
Release: 1992-11-26
Genre: Science
ISBN: 0203498666

Encompassing geomorphology, hydrology and agricultural engineering, this provides an interdisciplinary review of a topic important in both Scientific And Practical Terms - With The Specific Aim Of Promoting interaction between modellers, field workers and laboratory experimentalists.

Processes of Emergence of Systems and Systemic Properties

Processes of Emergence of Systems and Systemic Properties
Author: Gianfranco Minati
Publisher: World Scientific
Total Pages: 839
Release: 2009
Genre: Mathematics
ISBN: 981279347X

This book contains the Proceedings of the 2007 Conference of the Italian Systems Society. Papers deal with the interdisciplinary study of processes of emergence, considering theoretical aspects and applications from physics, cognitive science, biology, artificial intelligence, economics, architecture, philosophy, music and social systems. Such an interdisciplinary study implies the need to model and distinguish, in different disciplinary contexts, the establishment of structures, systems and systemic properties. Systems, as modeled by the observer, not only possess properties, but are also able to make emergent new properties. While current disciplinary models of emergence are based on theories of phase transitions, bifurcations, dissipative structures, multiple systems and organization, the present volume focuses on both generalizing those disciplinary models and identifying correspondences and new more general approaches. The general conceptual framework of the book relates to the attempt to build a general theory of emergence as a general theory of change, corresponding to Von Bertalanffy''s project for a general system theory.

Randomness & Undecidability in Physics

Randomness & Undecidability in Physics
Author: Karl Svozil
Publisher: World Scientific
Total Pages: 314
Release: 1993
Genre: Science
ISBN: 9789810208097

Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an ?inner description?, a ?virtual physics? of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as ?randomness? in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the ?distant future?. In other words: no ?speedup? or ?computational shortcut? is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.

Integral Biomathics

Integral Biomathics
Author: Plamen L. Simeonov
Publisher: Springer Science & Business Media
Total Pages: 424
Release: 2012-07-13
Genre: Technology & Engineering
ISBN: 3642281117

Perhaps the most distinct question in science throughout the ages has been the one of perceivable reality, treated both in physics and philosophy. Reality is acting upon us, and we, and life in general, are acting upon reality. Potentiality, found both in quantum reality and in the activity of life, plays a key role. In quantum reality observation turns potentiality into reality. Again, life computes possibilities in various ways based on past actions, and acts on the basis of these computations. This book is about a new approach to biology (and physics, of course!). Its subtitle suggests a perpetual movement and interplay between two elusive aspects of modern science — reality/matter and potentiality/mind, between physics and biology — both captured and triggered by mathematics — to understand and explain emergence, development and life all the way up to consciousness. But what is the real/potential difference between living and non-living matter? How does time in potentiality differ from time in reality? What we need to understand these differences is an integrative approach. This book contemplates how to encircle life to obtain a formal system, equivalent to the ones in physics. Integral Biomathics attempts to explore the interplay between reality and potentiality.

Environmental Modelling and Prediction

Environmental Modelling and Prediction
Author: Gongbing Peng
Publisher: Springer Science & Business Media
Total Pages: 500
Release: 2001-11-06
Genre: Science
ISBN: 9783540674221

In this book the authors consider the natural environment as an integrated system. The physical, chemical and biological processes that govern the behaviour of the environmental system can thus be understood through mathematical modelling, and their evolution can be studied by means of numerical simulation. The book contains a summary of various efficient approaches in atmospheric prediction, such as numerical weather prediction and statistical forecast of climate change, as well as other successful methods in land surface modelling. The authors explore new theories and methods in environment prediction such as systems analysis and information theory. Attention is given to new achievements in remote sensing tele-metering and geographic information systems.