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Random Differential Equations in Scientific Computing

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ISBN: 9788376560267 Year: Pages: 650 DOI: 10.2478/9788376560267 Language: English
Publisher: De Gruyter
Subject: Mathematics
Added to DOAB on : 2014-03-05 13:15:31
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This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.

Dynamical Systems

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ISBN: 9783906980478 9783906980522 Year: Pages: 551 DOI: 10.3390/books978-3-906980-52-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Added to DOAB on : 2015-01-12 10:53:34
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Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...]

Dynamical Systems - Analytical and Computational Techniques

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ISBN: 9789535130154 9789535130161 Year: Pages: 274 DOI: 10.5772/63189 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:49

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There has been a considerable progress made during the recent past on mathematical techniques for studying dynamical systems that arise in science and engineering. This progress has been, to a large extent, due to our increasing ability to mathematically model physical processes and to analyze and solve them, both analytically and numerically. With its eleven chapters, this book brings together important contributions from renowned international researchers to provide an excellent survey of recent advances in dynamical systems theory and applications. The first section consists of seven chapters that focus on analytical techniques, while the next section is composed of four chapters that center on computational techniques.

Fractal Analysis - Applications in Physics, Engineering and Technology

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ISBN: 9789535131915 9789535131922 Year: Pages: 294 DOI: 10.5772/65531 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:50

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Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: ""Part I: Petroleum Industry and Numerical Analysis""; ""Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure""; and ""Part III: Scattering Theory, Porosity, and Turbulence."" It's impossible to picture today's research without fractal analysis.

Complexity in Biological and Physical Systems - Bifurcations, Solitons and Fractals

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ISBN: 9781789230505 9781789230512 Year: Pages: 202 DOI: 10.5772/intechopen.68687 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:51

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Modeling and simulating biological and physical systems are nowadays active branches of science. The diversity and complexity of behaviors and patterns present in the natural world have their reciprocity in life systems. Bifurcations, solitons and fractals are some of these ubiquitous structures that can be indistinctively identified in many models with the most diverse applications, from microtubules with an essential role in the maintenance and the shaping of cells, to the nano/microscale structure in disordered systems determined with small-angle scattering techniques. This book collects several works in this direction, giving an overview of some models and theories, which are useful for the study and analysis of complex biological and physical systems. It can provide a good guidance for physicists with interest in biology, applied research scientists and postgraduate students.

Nonlinear Systems - Modeling, Estimation, and Stability

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Book Series: Nonlinear Systems ISSN: 26315335 ISBN: 9781789234046 9781789234053 Year: Volume: 1 Pages: 262 DOI: 10.5772/intechopen.71815 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:51

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This book focuses on several key aspects of nonlinear systems including dynamic modeling, state estimation, and stability analysis. It is intended to provide a wide range of readers in applied mathematics and various engineering disciplines an excellent survey of recent studies of nonlinear systems. With its thirteen chapters, the book brings together important contributions from renowned international researchers to provide an excellent survey of recent studies of nonlinear systems. The first section consists of eight chapters that focus on nonlinear dynamic modeling and analysis techniques, while the next section is composed of five chapters that center on state estimation methods and stability analysis for nonlinear systems.

Fractal Analysis

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ISBN: 9781789854336 9781789854343 Year: Pages: 112 DOI: 10.5772/intechopen.74876 Language: English
Publisher: IntechOpen
Subject: Mathematics
Added to DOAB on : 2019-10-03 07:51:53

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The aim of this book is to show some applications of fractal analysis in the fields of sciences. The first chapter introduces the readers to the book, while the second chapter shows the methods and challenges of fractal analysis of time-series data sets. The third chapter demonstrates fractal geometry as an attractive choice for miniaturized planar microwave filter design. The fourth chapter presents fractal antennas for wearable applications. The objective of the fifth chapter is to show some Parrondian games in discrete dynamic systems, while the last chapter reveals fractal structures of carbon nanotube system arrays.

Towards an embodied science of intersubjectivity: Widening the scope of social understanding research

Authors: ---
Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889195299 Year: Pages: 413 DOI: 10.3389/978-2-88919-529-9 Language: English
Publisher: Frontiers Media SA
Subject: Psychology --- Science (General)
Added to DOAB on : 2015-12-10 11:59:06
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An important amount of research effort in psychology and neuroscience over the past decades has focused on the problem of social cognition. This problem is understood as how we figure out other minds, relying only on indirect manifestations of other people's intentional states, which are assumed to be hidden, private and internal. Research on this question has mostly investigated how individual cognitive mechanisms achieve this task. A shift in the internalist assumptions regarding intentional states has expanded the research focus with hypotheses that explore the role of interactive phenomena and interpersonal histories and their implications for understanding individual cognitive processes. This interactive expansion of the conceptual and methodological toolkit for investigating social cognition, we now propose, can be followed by an expansion into wider and deeply-related research questions, beyond (but including) that of social cognition narrowly construed. Our social lives are populated by different kinds of cognitive and affective phenomena that are related to but not exhausted by the question of how we figure out other minds. These phenomena include acting and perceiving together, verbal and non-verbal engagement, experiences of (dis-)connection, management of relations in a group, joint meaning-making, intimacy, trust, conflict, negotiation, asymmetric relations, material mediation of social interaction, collective action, contextual engagement with socio-cultural norms, structures and roles, etc. These phenomena are often characterized by a strong participation by the cognitive agent in contrast with the spectatorial stance typical of social cognition research. We use the broader notion of embodied intersubjectivity to refer to this wider set of phenomena. This Research Topic aims to investigate relations between these different issues, to help lay strong foundations for a science of intersubjectivity – the social mind writ large. To contribute to this goal, we encouraged contributions in psychology, neuroscience, psychopathology, philosophy, and cognitive science that address this wider scope of intersubjectivity by extending the range of explanatory factors from purely individual to interactive, from observational to participatory.

Complexity, Criticality and Computation (C³)

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ISBN: 9783038425144 9783038425151 Year: Pages: VI, 262 DOI: 10.3390/books978-3-03842-515-1 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General)
Added to DOAB on : 2017-10-02 11:37:22
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Complex systems is a new approach to science, engineering, health and management that studies how relationships between parts give rise to the collective emergent behaviours of the entire system, and how the system interacts with its environment.A system can be thought of as complex if its dynamics cannot be easily predicted, or explained, as a linear summation of the individual dynamics of its components. In other words, the many constituent microscopic parts bring about macroscopic phenomena that cannot be understood by considering a single part alone (“the whole is more than the sum of the parts”). There is a growing awareness that complexity is strongly related to criticality: the behaviour of dynamical spatiotemporal systems at an order/disorder phase transition where scale invariance prevails.Complex systems can also be viewed as distributed information-processing systems. Consciousness emerging from neuronal activity and interactions, cell behaviour resultant from gene regulatory networks and swarming behaviour are all examples of global system behaviour emerging as a result of the local interactions of the individuals (neurons, genes, animals). Can these interactions be seen as a generic computational process? This question shapes the special issue, linking computation to complexity and criticality.

Mathematical Modelling in Engineering & Human Behaviour 2018

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ISBN: 9783038978046 / 9783038978053 Year: Pages: 196 DOI: 10.3390/books978-3-03897-805-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-06-26 10:09:00
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This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.

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