Fractional Calculus View Of Complexity

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Fractional Calculus View Of Complexity

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Author : Bruce J. West
language : en
Publisher: CRC Press
Release Date : 2016-01-05

Fractional Calculus View Of Complexity written by Bruce J. West and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-05 with Mathematics categories.

This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many

Nature S Patterns And The Fractional Calculus

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Author : Bruce J. West
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11

Nature S Patterns And The Fractional Calculus written by Bruce J. West and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.

Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus

Fractional Calculus And Its Applications In Physics

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Author : Dumitru Baleanu
language : en
Publisher: Frontiers Media SA
Release Date : 2019-11-15

Fractional Calculus And Its Applications In Physics written by Dumitru Baleanu and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-15 with categories.

Basic Theory

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Author : Anatoly Kochubei
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-02-19

Basic Theory written by Anatoly Kochubei and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-19 with Mathematics categories.

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Crucial Events Why Are Catastrophes Never Expected

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Author : Bruce J West
language : en
Publisher: World Scientific
Release Date : 2021-05-12

Crucial Events Why Are Catastrophes Never Expected written by Bruce J West and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-12 with Science categories.

A nonsimple (complex) system indicates a mix of crucial and non-crucial events, with very different statistical properties. It is the crucial events that determine the efficiency of information exchange between complex networks. For a large class of nonsimple systems, crucial events determine catastrophic failures - from heart attacks to stock market crashes.This interesting book outlines a data processing technique that separates the effects of the crucial from those of the non-crucial events in nonsimple time series extracted from physical, social and living systems. Adopting an informal conversational style, without sacrificing the clarity necessary to explain, the contents will lead the reader through concepts such as fractals, complexity and randomness, self-organized criticality, fractional-order differential equations of motion, and crucial events, always with an eye to helping to interpret what mathematics usually does in the development of new scientific knowledge.Both researchers and novitiate will find Crucial Events useful in learning more about the science of nonsimplicity.

Nonlinear Nonlocal And Fractional Turbulence

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Author : Peter William Egolf
language : en
Publisher: Springer Nature
Release Date : 2020-04-02

Nonlinear Nonlocal And Fractional Turbulence written by Peter William Egolf and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-02 with Science categories.

Experts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local theories of turbulence have been published. Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available. This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure. Considerations involve anomalous diffusion (Lévy flights), fractal geometry (fractal-β, bi-fractal and multi-fractal model) and fractional dynamics. Examples include a new ‘law of the wall’ and a generalization of Kraichnan’s energy-enstrophy spectrum that is in harmony with non-extensive and non-equilibrium thermodynamics (Tsallis thermodynamics) and experiments. Furthermore, the presented theories of turbulence reveal critical and cooperative phenomena in analogy with phase transitions in other physical systems, e.g., binary fluids, para-ferromagnetic materials, etc.; the two phases of turbulence identifying the laminar streaks and coherent vorticity-rich structures. This book is intended, apart from fluids specialists, for researchers in physics, as well as applied and numerical mathematics, who would like to acquire knowledge about alternative approaches involved in the analytical and numerical treatment of turbulence.

Unifying Themes In Complex Systems X

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Author : Dan Braha
language : en
Publisher: Springer Nature
Release Date : 2021-06-14

Unifying Themes In Complex Systems X written by Dan Braha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-14 with Mathematics categories.

The International Conference on Complex Systems (ICCS) offers a unique interdisciplinary venue for researchers from the physical and biological sciences, social sciences, psychology and cognitive science, engineering, medicine, human systems, and global systems. This proceedings volume gathers selected papers from the conference. The New England Complex Systems Institute (NECSI) has been instrumental in the development of complex systems science and its applications. NECSI pursues research, education, knowledge dissemination, and community development efforts around the world to promote the study of complex systems and its application for the benefit of society. NECSI hosts the International Conference on Complex Systems and publishes the NECSI Book.

Contemporary Computational Mathematics A Celebration Of The 80th Birthday Of Ian Sloan

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Author : Josef Dick
language : en
Publisher: Springer
Release Date : 2018-05-23

Contemporary Computational Mathematics A Celebration Of The 80th Birthday Of Ian Sloan written by Josef Dick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-23 with Mathematics categories.

This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

Fractional Calculus

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Author : Dingyü Xue
language : en
Publisher: Springer Nature
Release Date : 2024-05-03

Fractional Calculus written by Dingyü Xue and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-03 with Technology & Engineering categories.

Fractional calculus and its applications are fascinating research areas in many engineering disciplines. This book is a comprehensive collection of research from the author's group, which is one of the most active in the fractional calculus community worldwide and is the birthplace of one of the four MATLAB toolboxes in fractional calculus, the FOTF Toolbox. The book presents high-precision solution algorithms for a variety of fractional-order differential equations, including nonlinear, delay, and boundary value equations. Currently, there are no other universal solvers available for the latter two types of equations. Through this book, readers can systematically study the mathematics and solution methods in the field of fractional calculus and apply these concepts to different engineering fields, particularly control systems engineering. This book is a translation of an original German edition. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.

Towards Tree Level Evapotranspiration Estimation With Small Uavs In Precision Agriculture

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Author : Haoyu Niu
language : en
Publisher: Springer Nature
Release Date : 2022-10-27

Towards Tree Level Evapotranspiration Estimation With Small Uavs In Precision Agriculture written by Haoyu Niu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with Technology & Engineering categories.

Estimating evapotranspiration (ET) has been one of the most critical research areas in agriculture because of water scarcity, the growing population, and climate change. The accurate estimation and mapping of ET are necessary for crop water management. Traditionally, researchers use water balance, soil moisture, weighing lysimeters, or an energy balance approach, such as Bowen ratio or eddy covariance towers to estimate ET. However, these ET methods are point-specific or area-weighted measurements and cannot be extended to a large scale. On the other hand, while remote sensing is able to provide spatially distributed measurements, the spatial resolution of multispectral satellite images is often not enough for crops with clumped canopy structures, such as trees and vines. Unmanned aerial vehicles (UAVs) can mitigate these spatial and temporal limitations. Lightweight cameras and sensors can be mounted on the UAVs and take high-resolution images. Unlike satellite imagery, the spatial resolution of the UAV images can be at the centimeter-level. UAVs can also fly on-demand, which provides high temporal imagery. This book examines the different UAV-based approaches of ET estimation. Models and algorithms, such as mapping evapotranspiration at high resolution with internalized calibration (METRIC), the two-source energy balance (TSEB) model, and machine learning (ML) are discussed. It also covers the challenges and opportunities for UAVs in ET estimation, with the final chapters devoted to new ET estimation methods and their potential applications for future research.