Scale Invariance
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Scale Invariance
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Author : Annick LESNE
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-04
Scale Invariance written by Annick LESNE and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-04 with Science categories.
During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.
Scale Invariance Interfaces And Non Equilibrium Dynamics
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Author : Alan McKane
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Scale Invariance Interfaces And Non Equilibrium Dynamics written by Alan McKane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
The NATO Advanced Study Institute on "Scale Invariance, Interfaces and Non Equilibrium Dynamics" was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK from 20-30 June 1994. The topics discussed at the Institute were all concerned with the origin and nature of complex structures found far from equilibrium. Examples ranged from reaction diffusion systems and hydrodynamics through to surface growth due to deposition. A common theme was that of scale invariance due to the self-similarity of the underly ing structures. The topics that were covered can be broadly classified as pattern for mation (theoretical, computational and experimental aspects), the non-equilibrium dynamics of the growth of interfaces and other manifolds, coarsening phenomena, generic scale invariance in driven systems and the concept of self-organized critical ity. The main feature of the Institute was the four one-hour-Iong lectures given each day by invited speakers. In addition to thirty-seven of these lectures, two contributed lectures were also given. The many questions that were asked after the lectures attested to the excitement and interest that the lecturers succeeded in generating amongst the students. In addition to the discussions initiated by lectures, an im portant component of the meeting were the poster sessions, where participants were able to present their own work, which took place on three of the afternoons. The list of titles given at the end of these proceedings gives some idea of the range and scope of these posters.
Scale Invariance
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Author : Richard N. Henriksen
language : en
Publisher: John Wiley & Sons
Release Date : 2015-06-08
Scale Invariance written by Richard N. Henriksen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-08 with Science categories.
Bringing the concepts of dimensional analysis, self-similarity, and fractal dimensions together in a logical and self-contained manner, this book reveals the close links between modern theoretical physics and applied mathematics. The author focuses on the classic applications of self-similar solutions within astrophysical systems, with some general theory of self-similar solutions, so as to provide a framework for researchers to apply the principles across all scientific disciplines. He discusses recent advances in theoretical techniques of scaling while presenting a uniform technique that encompasses these developments, as well as applications to almost any branch of quantitative science. The result is an invaluable reference for active scientists, featuring examples of dimensions and scaling in condensed matter physics, astrophysics, fluid mechanics, and general relativity, as well as in mathematics and engineering.
Scale Invariance And Beyond
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Author : B. Dubrulle
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-09
Scale Invariance And Beyond written by B. Dubrulle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-09 with Science categories.
This book is an excellent introduction to the concept of scale invariance, which is a growing field of research with wide applications. It describes where and how symmetry under scale transformation (and its various forms of partial breakdown) can be used to analyze solutions of a problem without the need to explicitly solve it. The first part gives descriptions of tools and concepts; the second is devoted to recent attempts to go beyond the invariance or symmetry breaking, to discuss causes and consequences, and to extract useful information about the system. Examples are carefully worked out in fields as diverse as condensed matter physics, population dynamics, earthquake physics, turbulence, cosmology and finance.
Scale Invariance And Beyond
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Author : B. Dubrulle
language : en
Publisher:
Release Date : 1997
Scale Invariance And Beyond written by B. Dubrulle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Fractals categories.
Broken Scale Invariance And The Light Cone
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Author :
language : en
Publisher:
Release Date : 1971
Broken Scale Invariance And The Light Cone written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Nuclear reactions categories.
Scale Invariance
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Author : Richard N. Henriksen
language : en
Publisher: John Wiley & Sons
Release Date : 2015-02-13
Scale Invariance written by Richard N. Henriksen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-13 with Science categories.
Bringing the concepts of dimensional analysis, self-similarity, and fractal dimensions together in a logical and self-contained manner, this book reveals the close links between modern theoretical physics and applied mathematics. The author focuses on the classic applications of self-similar solutions within astrophysical systems, with some general theory of self-similar solutions, so as to provide a framework for researchers to apply the principles across all scientific disciplines. He discusses recent advances in theoretical techniques of scaling while presenting a uniform technique that encompasses these developments, as well as applications to almost any branch of quantitative science. The result is an invaluable reference for active scientists, featuring examples of dimensions and scaling in condensed matter physics, astrophysics, fluid mechanics, and general relativity, as well as in mathematics and engineering.
Scale Dependence And Scale Invariance In Hydrology
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Author : Garrison Sposito
language : en
Publisher: Cambridge University Press
Release Date : 1998-10-22
Scale Dependence And Scale Invariance In Hydrology written by Garrison Sposito and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-22 with Science categories.
Leading hydrologists present their views on the role of scale effects in hydrologic phenomena occurring in a range of field settings.
Introduction To Conformal Invariance And Its Applications To Critical Phenomena
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Author : Philippe Christe
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-11
Introduction To Conformal Invariance And Its Applications To Critical Phenomena written by Philippe Christe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-11 with Science categories.
The history of critical phenomena goes back to the year 1869 when Andrews discovered the critical point of carbon dioxide, located at about 31°C and 73 atmospheres pressure. In the neighborhood ofthis point the carbon dioxide was observed to become opalescent, that is, light is strongly scattered. This is nowadays interpreted as comingfrom the strong fluctuations of the system close to the critical point. Subsequently, a wide varietyofphysicalsystems were realized to display critical points as well. Ofparticular importance was the observation of a critical point in ferromagnetic iron by Curie. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and may even extend to the quark-gluon plasmaand the early universe as a whole. Early theoretical investigationstried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations and culminating in Landau's general theory of critical phenomena. In a dramatic development, Onsager's exact solutionofthe two-dimensional Ising model made clear the important role of the critical fluctuations. Their role was taken into account in the subsequent developments leading to the scaling theories of critical phenomena and the renormalization group. These developements have achieved a precise description of the close neighborhood of the critical point and results are often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is today emphasized.
Scaling Fractals And Wavelets
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Author : Patrice Abry
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-01
Scaling Fractals And Wavelets written by Patrice Abry and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-01 with Mathematics categories.
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.