Download or read book Singular Phenomena and Scaling in Mathematical Models written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.
Download or read book Singularities Formation Structure and Propagation written by J. Eggers and published by Cambridge University Press. This book was released on 2015-09-10 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.
Download or read book Extended Abstracts Spring 2018 written by Andrei Korobeinikov and published by Springer Nature. This book was released on 2019-09-03 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains extended abstracts outlining selected presentations delivered by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2018 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), dedicated to the mathematical theory and applications of the multiple scale systems, the systems with hysteresis and general trends in the dynamical systems theory. The workshop was jointly organized by the Centre de Recerca Matemàtica (CRM), Barcelona, and the Collaborative Research Center 910, Berlin, and held at the Centre de Recerca Matemàtica in Bellaterra, Barcelona, from May 28th to June 1st, 2018. This was the ninth workshop continuing a series of biennial meetings started in Ireland in 2002, and the second workshop of this series held at the CRM. Earlier editions of the workshops in this series were held in Cork, Pechs, Suceava, Lutherstadt and Berlin. The collection includes brief research articles reporting new results, descriptions of preliminary work, open problems, and the outcome of work in groups initiated during the workshop. Topics include analysis of hysteresis phenomena, multiple scale systems, self-organizing nonlinear systems, singular perturbations and critical phenomena, as well as applications of the hysteresis and the theory of singularly perturbed systems to fluid dynamics, chemical kinetics, cancer modeling, population modeling, mathematical economics, and control. The book is intended for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active research areas.
Download or read book Conformal Invariance and Critical Phenomena written by Malte Henkel and published by Springer Science & Business Media. This book was released on 1999-04-16 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are also reviewed.
Download or read book Lie Group Analysis of Differential Equations written by Ranis Ibragimov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-03-04 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is focused on physical interpretation and visualization of the obtained invariant solutions for nonlinear mathematical modeling of atmospheric and ocean waves. This volume represents a unique blend of analytical and numerical methods complemented by the author's developments in ocean and atmospheric sciences and it is meant for researchers and graduate students interested in applied mathematics and mathematical modeling.
Download or read book Mathematical Modelling of Waves in Multi Scale Structured Media written by Alexander B. Movchan and published by CRC Press. This book was released on 2017-11-09 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.
Download or read book Scaling Self similarity and Intermediate Asymptotics written by Grigory Isaakovich Barenblatt and published by Cambridge University Press. This book was released on 1996-12-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Classical examples of scaling phenomena are presented. It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics). It is explained why the dimensional analysis as a rule is insufficient for establishing self-similarity and constructing scaling variables. Important examples of scaling phenomena for which the dimensional analysis is insufficient (self-similarities of the second kind) are presented and discussed. A close connection of intermediate asymptotics and self-similarities of the second kind with a fundamental concept of theoretical physics, the renormalization group, is explained and discussed. Numerous examples from various fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, flow in porous strata, atmospheric and oceanic phenomena are presented for which the ideas of scaling, intermediate asymptotics, self-similarity and renormalization group were of decisive value in modeling.
Download or read book Scaling written by Grigory Isaakovich Barenblatt and published by Cambridge University Press. This book was released on 2003-11-13 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from dimensional analysis and physical similarity, G. Barenblatt describes the art of discovering scaling laws. He demonstrates the concepts of intermediate asymptotics and the renormalization group as natural consequences of self-similarity and shows how and when these tools can tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used independently by biologists, chemists, astronomers, engineers and geoscientists.
Download or read book Multiscale Problems in Science and Technology written by Nenad Antonic and published by Springer Science & Business Media. This book was released on 2011-06-27 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The International conference on Multiscale problems in science and technol ogy; Challenges to mathematical analysis and applications brought together mathematicians working on multiscale techniques (homogenisation, singular perturbation) and specialists from applied sciences who use these techniques. Our idea was that mathematicians could contribute to solving problems in the emerging applied disciplines usually overlooked by them and that specialists from applied sciences could pose new challenges for multiscale problems. Numerous problems in natural sciences contain multiple scales: flows in complex heterogeneous media, many particles systems, composite media, etc. Mathematically, we are led to study of singular homogenisation limits and the procedure is called upscaling or homogenisation. The processes to be up scaled are usually described by differential equations. For simple cases, when the differential equation is linear and the heterogeneities are periodic some progress has been made. However, most natural phenomena are described by nonlinear differential equations in a random nonhomogeneous medium and, despite an intensive development in recent years, there are many open problems. The objective of the conference was to bring together leading special ists from Europe and the United States and to discuss new challenges in this quickly developing field. Topics of the conference were Nonlinear Partial Differential Equations and Applied Analysis, with direct applications to the modeling in Material Sciences, Petroleum Engineering and Hydrodynamics.
Download or read book Multiple Time Scale Dynamics written by Christian Kuehn and published by Springer. This book was released on 2015-02-25 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Download or read book Mathematics Applied to Deterministic Problems in the Natural Sciences written by C. C. Lin and published by SIAM. This book was released on 1988-12-01 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers.
Download or read book Extended Abstracts Summer 2016 written by Andrei Korobeinikov and published by Springer. This book was released on 2018-11-27 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains extended abstracts outlining selected presentations given by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2016 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), which was dedicated to the mathematical theory and applications of multiple scale systems and systems with hysteresis, and held at the Centre de Recerca Matemàtica (CRM) in Barcelona from June 13th to 17th, 2016. The collection includes brief research articles on new results, preliminary work, open problems, and the outcomes of group work initiated during the workshop. The book addresses multiple scale phenomena, singular perturbations, phase transitions, and hysteresis phenomena occurring in mathematical, physical, economic, engineering and information systems. Its scope includes both new results in the theory of hysteresis, singularly perturbed systems and dynamical systems in general; and applications to the physical, chemical, biological, microbiological, economic, and engineering sciences, such as: elasto-plasticity and mechanical structures, damage processes, magnetic materials, photonics and optoelectronics, energy storage systems, hydrology, biology, semiconductor lasers, and shock phenomena in economic modeling. Given its breadth of coverage, the book offers a valuable resource for established researchers, as well as for PhD and postdoctoral students who want to learn more about the latest advances in these highly active research areas.
Download or read book Scaling Self similarity and Intermediate Asymptotics written by Grigory Isaakovich Barenblatt and published by Cambridge University Press. This book was released on 1996-12-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Classical examples of scaling phenomena are presented. It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics). It is explained why the dimensional analysis as a rule is insufficient for establishing self-similarity and constructing scaling variables. Important examples of scaling phenomena for which the dimensional analysis is insufficient (self-similarities of the second kind) are presented and discussed. A close connection of intermediate asymptotics and self-similarities of the second kind with a fundamental concept of theoretical physics, the renormalization group, is explained and discussed. Numerous examples from various fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, flow in porous strata, atmospheric and oceanic phenomena are presented for which the ideas of scaling, intermediate asymptotics, self-similarity and renormalization group were of decisive value in modeling.
Download or read book Control and Dynamic Systems V38 Advances in Aeronautical Systems written by C.T. Leonides and published by Academic Press. This book was released on 2012-12-02 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Aeronautical Systems shows that real-time simulation of aeronautical systems is fundamental in the analysis, design, and testing of today's increasingly complex aeronautical systems. Perhaps more important is the fact that simulation, including 3-D vision and motion simulation techniques, is an essential element in pilot training for both commercial and military aircraft. An essential characteristic of all modern aeronautical systems is their avionics system, which is composed of many elements, in particular sensor systems. This book comprises eight chapters, with the first focusing on aircraft automatic flight control system with model inversion. The following chapters then discuss information systems for supporting design of complex human-machine systems and formulation of a minimum variance deconvolution technique for compensation of pneumatic distortion in pressure-sensing devices. Other chapters cover synthesis and validation of feedback guidance laws for air-to-air interceptions; multistep matrix integrators for real-time simulation; the role of image interpretation in tracking and guidance; continuous time parameter estimation: analysis via a limiting ordinary differential equation; and in-flight alignment of inertial navigation systems. This book will be of interest to practitioners in the fields of engineering and aeronautics.
Download or read book Nonlinear Time Scale Systems in Standard and Nonstandard Forms written by Anshu Narang-Siddarth and published by SIAM. This book was released on 2014-01-01 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces key concepts for systematically controlling engineering systems that possess interacting phenomena occurring at widely different speeds. The aim is to present the reader with control techniques that extend the benefits of model reduction of singular perturbation theory to a larger class of nonlinear dynamical systems. New results and relevant background are presented through insightful examples that cover a wide range of applications from different branches of engineering. This book is unique because it: presents a new perspective on existing control methods and thus broadens their application to a larger class of nonlinear dynamical systems; discusses general rather than problem-specific developments to certain applications or disciplines in order to provide control engineers with useful analytical tools ; addresses new control problems using singular perturbation methods, including closed-form results for control of nonminimum phase systems.
Download or read book Annales de la facult des sciences de Toulouse written by and published by . This book was released on 1979 with total page 878 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scaling Fractals and Wavelets written by Patrice Abry and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.
