Differentiability And Fractality In Dynamics Of Physical Systems
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Differentiability And Fractality In Dynamics Of Physical Systems
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Author : Ioan Merches
language : en
Publisher: World Scientific
Release Date : 2015-08-28
Differentiability And Fractality In Dynamics Of Physical Systems written by Ioan Merches and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-28 with Science categories.
Using Cartan's differential 1-forms theory, and assuming that the motion variables depend on Euclidean invariants, certain dynamics of the material point and systems of material points are developed. Within such a frame, the Newtonian force as mass inertial interaction at the intragalactic scale, and the Hubble-type repulsive interaction at intergalactic distances, are developed.The wave-corpuscle duality implies movements on curves of constant informational energy, which implies both quantizations and dynamics of velocity limits.Analysis of motion of a charged particle in a combined field which is electromagnetic and with constant magnetism implies fractal trajectories. Mechanics of material points in a fractalic space is constructed, and various applications — fractal atom, potential well, free particle, etc. — are discussed.
Fractal Analysis
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Author : Fernando Brambila
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-07-26
Fractal Analysis written by Fernando Brambila and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-26 with Medical categories.
Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book. Here we present the use of fractal geometry, in particular, fractal analysis in two sciences: health sciences and social sciences and humanities. Part 1 is Health Science. In it, we present the latest advances in cardiovascular signs, kidney images to determine cancer growth, EEG signals, magnetoencephalography signals, and photosensitive epilepsy. We show how it is possible to produce ultrasonic lenses or even sound focusing. In Part 2, we present the use of fractal analysis in social sciences and humanities. It includes anthropology, hierarchical scaling, human settlements, language, fractal dimension of different cultures, cultural traits, and Mesoamerican complexity. And in Part 3, we present a few useful tools for fractal analysis, such as graphs and correlation, self-affine and self-similar graphs, and correlation function. It is impossible to picture today's research without fractal geometry.
Nonlinear Systems
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Author :
language : en
Publisher: BoD – Books on Demand
Release Date : 2018-07-18
Nonlinear Systems written by and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-18 with Mathematics categories.
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.
Fractional Dynamics Anomalous Transport And Plasma Science
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Author : Christos H. Skiadas
language : en
Publisher: Springer
Release Date : 2018-12-11
Fractional Dynamics Anomalous Transport And Plasma Science written by Christos H. Skiadas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-11 with Science categories.
This book collects interrelated lectures on fractal dynamics, anomalous transport and various historical and modern aspects of plasma sciences and technology. The origins of plasma science in connection to electricity and electric charges and devices leading to arc plasma are explored in the first contribution by Jean-Marc Ginoux and Thomas Cuff. The second important historic connection with plasmas was magnetism and the magnetron. Victor J. Law and Denis P. Dowling, in the second contribution, review the history of the magnetron based on the development of thermionic diode valves and related devices. In the third chapter, Christos H Skiadas and Charilaos Skiadas present and apply diffusion theory and solution strategies to a number of stochastic processes of interest. Anomalous diffusion by the fractional Fokker-Planck equation and Lévy stable processes are studied by Johan Anderson and Sara Moradi in the fourth contribution. They consider the motion of charged particles in a 3-dimensional magnetic field in the presence of linear friction and of a stochastic electric field. Analysis of low-frequency instabilities in a low-temperature magnetized plasma is presented by Dan-Gheorghe Dimitriu, Maricel Agop in the fifth chapter. The authors refer to experimental results of the Innsbruck Q-machine and provide an analytical formulation of the related theory. In chapter six, Stefan Irimiciuc, Dan-Gheorghe Dimitriu, Maricel Agop propose a theoretical model to explain the dynamics of charged particles in a plasma discharge with a strong flux of electrons from one plasma structure to another. The theory and applications of fractional derivatives in many-particle disordered large systems are explored by Z.Z. Alisultanov, A.M. Agalarov, A.A. Potapov, G.B. Ragimkhanov. In chapter eight, Maricel Agop, Alina Gavrilut ̧ and Gabriel Crumpei explore the motion of physical systems that take place on continuous but non-differentiable curves (fractal curves). Finally in the last chapter S.L. Cherkas and V.L. Kalashnikov consider the perturbations of a plasma consisting of photons, baryons, and electrons in a linearly expanding (Milne-like) universe taking into account the metric tensor and vacuum perturbations.
The Mathematical Principles Of Scale Relativity Physics
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Author : Nicolae Mazilu
language : en
Publisher: CRC Press
Release Date : 2019-09-24
The Mathematical Principles Of Scale Relativity Physics written by Nicolae Mazilu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-24 with Science categories.
The Mathematical Principles of Scale Relativity Physics: The Concept of Interpretation explores and builds upon the principles of Laurent Nottale’s scale relativity. The authors address a variety of problems encountered by researchers studying the dynamics of physical systems. It explores Madelung fluid from a wave mechanics point of view, showing that confinement and asymptotic freedom are the fundamental laws of modern natural philosophy. It then probes Nottale’s scale transition description, offering a sound mathematical principle based on continuous group theory. The book provides a comprehensive overview of the matter to the reader via a generalization of relativity, a theory of colors, and classical electrodynamics. Key Features: Develops the concept of scale relativity interpreted according to its initial definition enticed by the birth of wave and quantum mechanics Provides the fundamental equations necessary for interpretation of matter, describing the ensembles of free particles according to the concepts of confinement and asymptotic freedom Establishes a natural connection between the Newtonian forces and the Planck’s law from the point of view of space and time scale transition: both are expressions of invariance to scale transition The work will be of great interest to graduate students, doctoral candidates, and academic researchers working in mathematics and physics.
Advances In Epidemiological Modeling And Control Of Viruses
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Author : Hemen Dutta
language : en
Publisher: Elsevier
Release Date : 2023-01-06
Advances In Epidemiological Modeling And Control Of Viruses written by Hemen Dutta and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-06 with Medical categories.
Advances in Epidemiological Modeling and Control of Viruses covers recent and advanced research works in the field of epidemiological modeling, with special emphasis on new strategies to control the occurrence and reoccurrence of viruses. The models included in this book can be used to study the dynamics of different viruses, searching for control measures, and epidemic models under various effects and environments. This book covers different models and methods of modeling, including data-driven approaches. The authors and editors are experienced researchers, and each chapter has been designed to provide readers with leading-edge information on topics discussed. - Includes models to describe global and local dynamics of various viruses - Provides readers with control strategies for occurrence and reoccurrence of viruses - Includes epidemic models under various effects and environments - Provides readers with a robust set of mathematical tools and techniques for epidemiological modeling
Atomicity Through Fractal Measure Theory
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Author : Alina Gavriluţ
language : en
Publisher: Springer Nature
Release Date : 2019-11-02
Atomicity Through Fractal Measure Theory written by Alina Gavriluţ and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-02 with Mathematics categories.
This book presents an exhaustive study of atomicity from a mathematics perspective in the framework of multi-valued non-additive measure theory. Applications to quantum physics and, more generally, to the fractal theory of the motion, are highlighted. The study details the atomicity problem through key concepts, such as the atom/pseudoatom, atomic/nonatomic measures, and different types of non-additive set-valued multifunctions. Additionally, applications of these concepts are brought to light in the study of the dynamics of complex systems. The first chapter prepares the basics for the next chapters. In the last chapter, applications of atomicity in quantum physics are developed and new concepts, such as the fractal atom are introduced. The mathematical perspective is presented first and the discussion moves on to connect measure theory and quantum physics through quantum measure theory. New avenues of research, such as fractal/multifractal measure theory with potential applications in life sciences, are opened.
13th Chaotic Modeling And Simulation International Conference
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Author : Christos H. Skiadas
language : en
Publisher: Springer Nature
Release Date : 2021-12-14
13th Chaotic Modeling And Simulation International Conference written by Christos H. Skiadas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-14 with Mathematics categories.
Gathering the proceedings of the 13th CHAOS2020 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies.
Advances In Laser Produced Plasmas Research
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Author : Maricel Agop
language : en
Publisher: MDPI
Release Date : 2021-01-21
Advances In Laser Produced Plasmas Research written by Maricel Agop and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-21 with Computers categories.
The world of laser matter interaction has known great and rapid advancements in the last few years, with a considerable increase in the number of both experimental and theoretical studies. The classical paradigm used to describe the dynamics of laser produced plasmas has been challenged by new peculiar phenomena observed experimentally, like plasma particles’ oscillations, plume splitting and self-structuring behavior during the expansion of the ejected particles. The use of multiple complementary techniques has become a requirement nowadays, as different aspects can be showcased by specific experimental approaches. To balance these non-linear effects and still remain tributary to the classical theoretical, views on laser produced plasma dynamics novel theoretical models that cover the two sides of the ablation plasma (differentiability and non-differentiability) still need to be developed. Plasma is a strongly nonlinear dynamic system, with many degrees of freedom and other symmetries, favorable for the development of ordered structures, instabilities and transitions (from ordered to chaotic states). In such contexts, we showcased research based on global and local symmetries, complexity and invariance. This special number highlighted exciting new phenomena related to laser produced plasma dynamics with the implementation of theoretical models, towards understanding the complex reality of laser matter interaction.
Progress In Relativity
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Author : Calin Gheorghe Buzea
language : en
Publisher: BoD – Books on Demand
Release Date : 2020-06-17
Progress In Relativity written by Calin Gheorghe Buzea and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-17 with Science categories.
This volume deals with extensions of special relativity, general relativity, and their applications in relation to intragalactic and extragalactic dynamics. The book comprises chapters authored by various researchers and edited by an expert active in the relativity research area. It provides a thorough overview of the latest research efforts by international authors on relativity, opening new possible research paths for further novel developments.