Approche numérique bidimensionnelle de la convection naturelle dans une enceinte fermée PDF Download

Author: Louis Philippe Wallot
Publisher:
ISBN:
Category :
Languages : fr
Pages : 226

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Book Description
L'auteur explore numériquement la route vers le chaos par convection naturelle instationnaire bidimensionnelle se développant dans une enceinte fermée contenant de l'air , de section droite carrée. La cavité est inclinée d'un angle de 15° eu égard au plan horizontal et chauffée par deux côtés opposés. Cette étude a montré que le système transite vers le chaos via trois bifurcations de Hopf surcritiques. Par augmentation du nombre de Rayleigh, l'attracteur point limite se destabilise et cède la place à un attracteur cycle limite qui, à son tour, perd sa stabilité linéaire au profit d'un attracteur tore T2. Un phénomène d'accrochage de fréquence, assez fugace, ramène ce tore à un attracteur cycle limite . Ce cycle se déstabilise, de nouveau, donnant ainsi naissance à un attracteur tore T2. Il survient un deuxième phénomène d'accrochage de fréquence à l'insue duquel l'évolution dynamique du système devient chaotique.

Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532

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Book Description
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Author: Paul Manneville
Publisher: World Scientific
ISBN: 1848163924
Category : Science
Languages : en
Pages : 456

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Book Description
This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.

Author: G. Nicolis
Publisher: Cambridge University Press
ISBN: 9780521467827
Category : Mathematics
Languages : en
Pages : 274

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Book Description
The aim of this book is to develop a unified approach to nonlinear science, which does justice to its multiple facets and to the diversity and richness of the concepts and tools developed in this field over the years. Nonlinear science emerged in its present form following a series of closely related and decisive analytic, numerical and experimental developments that took place over the past three decades. It appeals to an extremely large variety of subject areas, but, at the same time, introduces into science a new way of thinking based on a subtle interplay between qualitative and quantitative techniques, topological and metric considerations and deterministic and statistical views. Special effort has been made throughout the book to illustrate both the development of the subject and the mathematical techniques, by reference to simple models. Each chapter concludes with a set of problems. This book will be of great value to graduate students in physics, applied mathematics, chemistry, engineering and biology taking courses in nonlinear science and its applications.

Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 726

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Author: Innocent Mutabazi
Publisher: Springer
ISBN: 0387251111
Category : Science
Languages : en
Pages : 249

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Book Description
The impact of Benard's discovery on 20th century physics is crucial to any modern research area such as fluid dynamics, nonlinear dynamics, and non-equilibrium thermodynamics, just to name a few. This centenary review shows the broad scope and development including modern applications, edited and written by experts in the field.

Author: Kevin Kelly
Publisher: Basic Books
ISBN: 078674703X
Category : Science
Languages : en
Pages : 528

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Book Description
Out of Control chronicles the dawn of a new era in which the machines and systems that drive our economy are so complex and autonomous as to be indistinguishable from living things.

Author: Georg Müller
Publisher: Springer Science & Business Media
ISBN: 3642732089
Category : Science
Languages : en
Pages : 145

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Book Description
1 The content ofthis article is based on a German book version ) which appeared at the end of the year 1986. The author tried to incorporate - as far as possible - new important results published in the last year. But the literature in the field of "convection and inhomogeneities in crystal growth from the melt" has increased so much in the meantime that the reader and the collegues should make allowance for any incompleteness, also in the case that their important contributions have not been cited. This could for example hold for problems related to the Czochralski growth. But especially for this topic the reader may be refered to the forthcoming volume of this series, which contains special contributions on "Surface Tension Driven Flow in Crystal Growth Melts" by D. Schwabe and on "Convection in Czochralski Melts" by M. Mihelcic, W. Uelhoff, H. Wenzl and K. Wingerath. The preparation of this manuscript has been supported by several women whose help is gratefully acknowledged by the autor: Mrs. Gisela Neuner for the type writing, Mrs. Abigail Sanders, Mrs. Fiona Eels and especially Prof. Nancy Haegel for their help in questions of the English language and Mrs. Christa Weber for reading corrections. Also the good cooperation with the Springer Verlag, especially Mrs. Bohlen and with the managing editor of Crystals, Prof. H. C. Freyhardt, who critically read the manuscript, is acknowledged.

Author: Donald Turcotte
Publisher: Cambridge University Press
ISBN: 1107006538
Category : Science
Languages : en
Pages : 639

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Book Description
A fully updated third edition of this classic textbook, containing two new chapters on numerical modelling supported by online MATLAB® codes.

Author: James Sethna
Publisher: OUP Oxford
ISBN: 0191566217
Category : Science
Languages : en
Pages : 374

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Book Description
In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.