Interfacial Wave Theory Of Pattern Formation
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Interfacial Wave Theory Of Pattern Formation
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Author : Jian-Jun Xu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Interfacial Wave Theory Of Pattern Formation written by Jian-Jun Xu 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 2012-12-06 with Science categories.
For the last several years, the study of interfacial instability and pattern formation phenomena has preoccupied many researchers in the broad area of nonlinear science. These phenomena occur in a variety of dynamical sys tems far from equilibrium. In many practically very important physical sys tems some fascinating patterns are always displayed at the interface between solid and liquid or between two liquids. Two prototypes of these phenomena are dendrite growth in solidification and viscous fingering in a Hele-Shaw cell. These two phenomena occur in completely different scientific fields, but both are described by similar nonlinear free boundary problems of partial differential-equation systems; the boundary conditions on the interface for both cases contain a curvature operator involving the surface tension, which is nonlinear. Moreover, both cases raise the same challenging theoretical is sues, interfacial instability mechanisms and pattern selection, and it is now found that these issues can be solved by the same analytical approach. Thus, these two phenomena are regarded as special examples of a class of nonlinear pattern formation phenomena in nature, and they are the prominent topics of the new interdisciplinary field of nonlinear science. This research monograph is based on a series of lectures I have given at McGill University, Canada (1993-1994), Northwestern Poly technical In stitute, China (1994), Aachen University, Germany (1994), and the CRM summer school at Banff, Alberta, Canada (1995).
Interfacial Wave Theory Of Pattern Formation In Solidification
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Author : Jian-Jun Xu
language : en
Publisher: Springer
Release Date : 2017-05-23
Interfacial Wave Theory Of Pattern Formation In Solidification written by Jian-Jun Xu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-23 with Science categories.
This comprehensive work explores interfacial instability and pattern formation in dynamic systems away from the equilibrium state in solidification and crystal growth. Further, this significantly expanded 2nd edition introduces and reviews the progress made during the last two decades. In particular, it describes the most prominent pattern formation phenomena commonly observed in material processing and crystal growth in the framework of the previously established interfacial wave theory, including free dendritic growth from undercooled melt, cellular growth and eutectic growth in directional solidification, as well as viscous fingering in Hele-Shaw flow. It elucidates the key problems, systematically derives their mathematical solutions by pursuing a unified, asymptotic approach, and finally carefully examines these results by comparing them with the available experimental results. The asymptotic approach described here will be useful for the investigation of pattern formation phenomena occurring in a much broader class of inhomogeneous dynamical systems. In addition, the results on global stability and selection mechanisms of pattern formation will be of particular interest to researchers working on material processing and crystal growth. The stability mechanisms of a curved front and the pattern formation have been fundamental subjects in the areas of condensed-matter physics, materials science, crystal growth, and fluid mechanics for some time now. This book offers a stimulating and insightful introduction for all physicists, engineers and applied mathematicians working in the fields of soft condensed-matter physics, materials science, mechanical and chemical engineering, fluid dynamics, and nonlinear sciences.
Interfacial Wave Theory Of Pattern Formation In Solidification
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Author : Jian-Jun Xu
language : en
Publisher:
Release Date : 2017
Interfacial Wave Theory Of Pattern Formation In Solidification written by Jian-Jun Xu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Chemical engineering categories.
Interfacial Wave Theory Of Pattern Formation
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Author : Jian-Jun Xu
language : en
Publisher:
Release Date : 1997-12-16
Interfacial Wave Theory Of Pattern Formation written by Jian-Jun Xu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-12-16 with categories.
Complex Symmetries
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Author : György Darvas
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Complex Symmetries written by György Darvas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts. Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts. The contributions in this volume analyse selected examples (not limited to geometric symmetries). These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts. The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.
Theory Of Solidification
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Author : Stephen H. Davis
language : en
Publisher: Cambridge University Press
Release Date : 2001-10-08
Theory Of Solidification written by Stephen H. Davis 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 2001-10-08 with Science categories.
The processes of freezing and melting were present at the beginnings of the Earth and continue to dominate the natural and industrial worlds. The solidification of a liquid or the melting of a solid involves a complex interplay of many physical effects. This 2001 book presents in a systematic way the field of continuum solidification theory based on instability phenomena. An understanding of the physics is developed by using examples of increasing complexity with the object of creating a deep physical insight applicable to more complex problems. Applied mathematicians, engineers, physicists, and materials scientists will all find this volume of interest.
Advances In Mechanics And Mathematics
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Author : David Yang Gao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Advances In Mechanics And Mathematics written by David Yang Gao 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 2013-11-11 with Science categories.
Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications. This volume, AMMA 2002, includes two parts with three articles by four subject experts. Part 1 deals with nonsmooth static and dynamic systems. A systematic mathematical theory for multibody dynamics with unilateral and frictional constraints and a brief introduction to hemivariational inequalities together with some new developments in nonsmooth semi-linear elliptic boundary value problems are presented. Part 2 provides a comprehensive introduction and the latest research on dendritic growth in fluid mechanics, one of the most profound and fundamental subjects in the area of interfacial pattern formation, a commonly observed phenomenon in crystal growth and solidification processes.
Free Boundary Problems Involving Solids
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Author : J M Chadam
language : en
Publisher: CRC Press
Release Date : 1993-02-22
Free Boundary Problems Involving Solids written by J M Chadam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-02-22 with Mathematics categories.
This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined.
Nonlinear Waves And Solitons On Contours And Closed Surfaces
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Author : Andrei Ludu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-09
Nonlinear Waves And Solitons On Contours And Closed Surfaces written by Andrei Ludu 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 2007-09-09 with Science categories.
The present volume is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such as closed curves and surfaces and other domain contours. The first part of the book introduces the mathematical concept required for treating the manifolds considered. An introduction to the theory of motion of curves and surfaces is given. The second and third parts discuss the modeling of various physical solitons on compact systems.
Patterns And Interfaces In Dissipative Dynamics
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Author : L.M. Pismen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-07
Patterns And Interfaces In Dissipative Dynamics written by L.M. Pismen 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 2006-07-07 with Science categories.
Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium is a paradigmatic case of emergent behaviour associated with complex systems. It is encountered in a great variety of settings, both in nature and technology, and has numerous applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. Nature creates its variety of forms through spontaneous pattern formation and self-assembly, and this strategy is likely to be imitated by future biomorphic technologies. This book is a first-hand account by one of the leading players in this field, which gives in-depth descriptions of analytical methods elucidating the complex evolution of nonlinear dissipative systems, and brings the reader to the forefront of current research. The introductory chapter on the theory of dynamical systems is written with a view to applications of its powerful methods to spatial and spatio-temporal patterns. It is followed by two chapters treating moving interfaces, based largely on reaction-diffusion and phase-separating systems. The following two chapters on amplitude equations for patterns and waves describe universal phenomena generated by representative equations which can be derived for a variety of non-equilibrium systems originating in fluid mechanics, physical chemistry or nonlinear optics. This book addresses graduate students and non-specialists from the many related areas of applied mathematics, physical chemistry, chemical engineering and biology, as well as the seasoned scientist in search of a modern source of reference.