Download or read book Scaling Self similarity and Intermediate Asymptotics written by G. I. Barenblatt and published by Cambridge University Press. This book was released on 1996-12-12 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.
Download or read book Similarity Self similarity and Intermediate Asymptotics written by G. I. Barenblatt and published by . This book was released on 1979 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scaling Self similarity and Intermediate Asymptotics written by Grigory Isaakovich Barenblatt and published by . This book was released on 2005 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Similarity Self Similarity and Intermediate Asymptotics written by G. Barenblatt and published by Springer. This book was released on 2013-05-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Grigorii Isaakovich Barenblatt has written an outstanding book that contains an attempt to answer the very important questions of how to under stand complex physical processes and how to interpret results obtained by numerical computations. Progress in numerical calculation brings not only great good but also notori ously awkward questions about the role of the human mind. The human partner in the interaction of a man and a computer often turns out to be the weak spot in the relationship. The problem of formulating rules and extracting ideas from vast masses of computational or experimental results remains a matter for our brains, our minds. This problem is closely connected with the recognition of patterns. It is not just a coincidence that in both the Russian and English languages the word "obvious" has two meanings-not only something easily and clearly understood, but also something immediately evident to our eyes. The identification of forms and the search for invariant relations constitute the foundation of pattern recognition; thus, we identify the similarity oflarge and small triangles, etc.
Download or read book Scaling self similarity and intermediate asymptotics Cambridge texts in applied mathematics written by G. I. Barenblatt and published by . This book was released on 2000 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scaling Self similarity and Intermediate Asymptotics written by G. I. Barenblatt and published by . This book was released on 1996 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scaling written by G. I. Barenblatt and published by Cambridge University Press. This book was released on 2003-11-13 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.
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 Phenomena in Fluid Mechanics written by G. I. Barenblatt and published by CUP Archive. This book was released on 1994-12 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the text of the inaugural lecture of Professor G. I. Barenblatt which deals with a study of scaling phenomena in several topics studied by G. I. Taylor throughout his varied career.
Download or read book Wave Asymptotics written by P. A. Martin and published by Cambridge University Press. This book was released on 1992-05-29 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers by distinguished researchers in fluid mechanics and asymptotics. The papers collected here outline the development of these topics.
Download or read book The Devil in the Details written by Robert W. Batterman and published by Oxford University Press. This book was released on 2001-11-29 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.
Download or read book Theoretical Mantle Dynamics written by Neil M. Ribe and published by Cambridge University Press. This book was released on 2018-10-04 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive, mathematically advanced treatment of the continuum mechanics of the Earth's mantle and the geodynamic models used to investigate it.
Download or read book Introduction to Symmetry Analysis Paperback with CD ROM written by Brian Cantwell and published by Cambridge University Press. This book was released on 2002-09-23 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.
Download or read book Vorticity and Incompressible Flow written by Andrew J. Majda and published by Cambridge University Press. This book was released on 2002 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
Download or read book Self Similarity and Beyond written by P.L. Sachdev and published by CRC Press. This book was released on 2019-06-13 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out. Self-Similarity and Beyond presents
Download or read book Uniqueness of Fat Tailed Self Similar Profiles to Smoluchowski s Coagulation Equation for a Perturbation of the Constant Kernel written by Sebastian Throm and published by American Mathematical Society. This book was released on 2021-09-24 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Dimensional Analysis and Self Similarity Methods for Engineers and Scientists written by Bahman Zohuri and published by Springer. This book was released on 2015-04-15 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book’s coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book’s theoretical explanations and step-by-step mathematical solutions to practical implementations.
