Mean Field Theories And Dual Variation Mathematical Structures Of The Mesoscopic Model
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Mean Field Theories And Dual Variation Mathematical Structures Of The Mesoscopic Model
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Author : Takashi Suzuki
language : en
Publisher: Springer
Release Date : 2015-11-19
Mean Field Theories And Dual Variation Mathematical Structures Of The Mesoscopic Model written by Takashi Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-19 with Mathematics categories.
Mean field approximation has been adopted to describe macroscopic phenomena from microscopic overviews. It is still in progress; fluid mechanics, gauge theory, plasma physics, quantum chemistry, mathematical oncology, non-equilibirum thermodynamics. spite of such a wide range of scientific areas that are concerned with the mean field theory, a unified study of its mathematical structure has not been discussed explicitly in the open literature. The benefit of this point of view on nonlinear problems should have significant impact on future research, as will be seen from the underlying features of self-assembly or bottom-up self-organization which is to be illustrated in a unified way. The aim of this book is to formulate the variational and hierarchical aspects of the equations that arise in the mean field theory from macroscopic profiles to microscopic principles, from dynamics to equilibrium, and from biological models to models that arise from chemistry and physics.
Non Local Partial Differential Equations For Engineering And Biology
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Author : Nikos I. Kavallaris
language : en
Publisher: Springer
Release Date : 2017-11-28
Non Local Partial Differential Equations For Engineering And Biology written by Nikos I. Kavallaris and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-28 with Technology & Engineering categories.
This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.
Vortex Dynamics
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Author : İlkay Bakırtaş
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-09-28
Vortex Dynamics written by İlkay Bakırtaş 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 2022-09-28 with Science categories.
This book discusses vortex dynamics theory from physics, mathematics, and engineering perspectives. It includes nine chapters that cover a variety of research results related to vortex dynamics including nonlinear optics, fluid dynamics, and plasma physics.
Applied Analysis Mathematics For Science Technology Engineering Third Edition
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Author : Takashi Suzuki
language : en
Publisher: World Scientific
Release Date : 2022-04-28
Applied Analysis Mathematics For Science Technology Engineering Third Edition written by Takashi Suzuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-28 with Mathematics categories.
This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the integration of ODEs, inverse Strum Liouville problems, interface vanishing of the Maxwell system, method of gradient inequality, diffusion geometry, mathematical oncology. Several descriptions on the analysis of Smoluchowski-Poisson equation in two space dimension are corrected and extended, to ensure quantized blowup mechanism of this model, particularly, the residual vanishing both in blowup solution in finite time with possible collision of sub-collapses and blowup solutions in infinite time without it.
Vortex Structures In Fluid Dynamic Problems
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Author : Hector Perez-De-Tejada
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-03-01
Vortex Structures In Fluid Dynamic Problems written by Hector Perez-De-Tejada 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 2017-03-01 with Science categories.
The contents of the book cover topics on vortex dynamics in a variety of flow problems and describe observational measurements and their interpretation. The book contains 13 chapters that first include vortices in the earth and planetary sciences related to vortices in the Venus plasma wake and also on tropical cyclones and on rotating shallow water in the earth's atmosphere. Vortices in fluid problems include airplane wake vortices, vorticity evolution in free-shear flows, together with axisymmetric flows with swirl, as well as thermal conductivities in fluid layers. Vortices in relativistic fluids, in magnetic disks, solitons and vortices, and relaxation for point vortices were also examined. Other chapters describe conditions in a vortex bioreactor and in vortex yarn structures.
Shape Memory Alloys
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Author : Farzad Ebrahimi
language : en
Publisher: BoD – Books on Demand
Release Date : 2017-09-20
Shape Memory Alloys written by Farzad Ebrahimi 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 2017-09-20 with Technology & Engineering categories.
This book is a result of contributions of experts from international scientific community working in different aspects of shape memory alloys (SMAs) and reports on the state-of-the-art research and development findings on this topic through original and innovative research studies. Through its five chapters, the reader will have access to works related to ferromagnetic SMAs, while it introduces some specific applications like development of faster SMA actuators and application of nanostructural SMAs in medical devices. The book contains up-to-date publications of leading experts, and the edition is intended to furnish valuable recent information to the professionals involved in shape memory alloys analysis and applications. The text is addressed not only to researchers but also to professional engineers, students, and other experts in a variety of disciplines, both academic and industrial, seeking to gain a better understanding of what has been done in the field recently and what kind of open problems are in this area.
Semilinear Elliptic Equations
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Author : Takashi Suzuki
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-12
Semilinear Elliptic Equations written by Takashi Suzuki 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 2020-10-12 with Mathematics categories.
This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.
Mean Field Theories And Dual Variation A Mathematical Profile Emerged In The Nonlinear Hierarchy Atlantis Studies In Mathematics For Engineering And Science
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Author : T. Suzuki
language : en
Publisher:
Release Date : 2008
Mean Field Theories And Dual Variation A Mathematical Profile Emerged In The Nonlinear Hierarchy Atlantis Studies In Mathematics For Engineering And Science written by T. Suzuki and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality†according to the PDE weak solutions and “hierarchy†for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowskiâ€"Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.
Insights In Computational Neuroscience
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Author : Si Wu
language : en
Publisher: Frontiers Media SA
Release Date : 2023-04-11
Insights In Computational Neuroscience written by Si Wu 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 2023-04-11 with Science categories.
Information Based Methods For Neuroimaging Analyzing Structure Function And Dynamics
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Author : Jesus M. Cortés
language : en
Publisher: Frontiers Media SA
Release Date : 2015-05-07
Information Based Methods For Neuroimaging Analyzing Structure Function And Dynamics written by Jesus M. Cortés 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 2015-05-07 with Neurosciences. Biological psychiatry. Neuropsychiatry categories.
The aim of this Research Topic is to discuss the state of the art on the use of Information-based methods in the analysis of neuroimaging data. Information-based methods, typically built as extensions of the Shannon Entropy, are at the basis of model-free approaches which, being based on probability distributions rather than on specific expectations, can account for all possible non-linearities present in the data in a model-independent fashion. Mutual Information-like methods can also be applied on interacting dynamical variables described by time-series, thus addressing the uncertainty reduction (or information) in one variable by conditioning on another set of variables. In the last years, different Information-based methods have been shown to be flexible and powerful tools to analyze neuroimaging data, with a wide range of different methodologies, including formulations-based on bivariate vs multivariate representations, frequency vs time domains, etc. Apart from methodological issues, the information bit as a common unit represents a convenient way to open the road for comparison and integration between different measurements of neuroimaging data in three complementary contexts: Structural Connectivity, Dynamical (Functional and Effective) Connectivity, and Modelling of brain activity. Applications are ubiquitous, starting from resting state in healthy subjects to modulations of consciousness and other aspects of pathophysiology. Mutual Information-based methods have provided new insights about common-principles in brain organization, showing the existence of an active default network when the brain is at rest. It is not clear, however, how this default network is generated, the different modules are intra-interacting, or disappearing in the presence of stimulation. Some of these open-questions at the functional level might find their mechanisms on their structural correlates. A key question is the link between structure and function and the use of structural priors for the understanding of the functional connectivity measures. As effective connectivity is concerned, recently a common framework has been proposed for Transfer Entropy and Granger Causality, a well-established methodology originally based on autoregressive models. This framework can open the way to new theories and applications. This Research Topic brings together contributions from researchers from different backgrounds which are either developing new approaches, or applying existing methodologies to new data, and we hope it will set the basis for discussing the development and validation of new Information-based methodologies for the understanding of brain structure, function, and dynamics.