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Author : Jian-Jun Xu
Publisher : Unknown
Page : 591 pages
File Size : 45,6 Mb
Release : 2017
Category : Chemical engineering
ISBN : 3319526642
Author : Jian-Jun Xu
Publisher : Unknown
Page : 312 pages
File Size : 48,9 Mb
Release : 1997-12-16
Category : Electronic
ISBN : 3642804365
Author : Jian-Jun Xu
Publisher : Springer
Page : 591 pages
File Size : 40,6 Mb
Release : 2017-05-23
Category : Science
ISBN : 9783319526638
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.
Author : Jian-Jun Xu
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 48,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475737097
Convective flow in the liquid phase is always present in a realistic process of freezing and melting and may significantly affect the dynamics and results of the process. The study of the interplay of growth and convection flow during the solidification has been an important subject in the broad fields of materials science, condensed matter physics, fluid physics, micro-gravity science, etc. The present book is concerned with the dynamics of free dendritic growth with convective flow in the melt. It systematically presents the results obtained in terms of a unified asymptotic approach in the framework of the interfacial wave (IFW) theory. In particular, the book explores the effect of the various types of convection flow on the selection and pattern formation of dendritic growth based on the global stability analysis.
Author : Jian-Jun Xu
Publisher : Springer Science & Business Media
Page : 303 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642804359
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).
Author : Stephen H. Davis
Publisher : Cambridge University Press
Page : 406 pages
File Size : 49,5 Mb
Release : 2001-10-08
Category : Science
ISBN : 1139429639
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.
Author : V. Lakshmikantham
Publisher : Walter de Gruyter
Page : 930 pages
File Size : 49,8 Mb
Release : 1996
Category : Mathematics
ISBN : 311013215X
Author : Klaus Kassner
Publisher : World Scientific
Page : 268 pages
File Size : 50,5 Mb
Release : 1996-07-04
Category : Science
ISBN : 9789814502764
This book reviews the current state of the theory of pattern formation by a liquid-solid interface during crystal growth. It gives a pedagogical introduction to the subject, including experimental results, mathematical modeling and linear stability analysis. After highlighting the success of the theory in resolving the selection problem of dendritic growth, various new directions of research are presented in which progress has been made recently. These are the formation of nondendritic seaweed-like structures, growth of lamellar eutectics and rapid solidification. The interplay between analytic methods on the one hand (scaling arguments, asymptotic analysis, similarity equation, Sivashinsky singular expansion) and numerical calculations on the other (Newton method, dynamical schemes) is emphasized.
Author : György Darvas
Publisher : Springer Nature
Page : 262 pages
File Size : 52,5 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030880590
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.
Author : David Yang Gao,Raymond W. Ogden
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 53,5 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781475744354
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.
Author : Peter Ehrhard,David S. Riley,Paul H. Steen
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 48,7 Mb
Release : 2013-03-14
Category : Science
ISBN : 9789401598071
Crystal growth, casting, soldering, welding, high-energy surface treatment, nuclear safety systems and geophysical flows are just a few examples where solidification and convection occur together. These processes are interactive on micro- and macroscales: flow affects the distribution of heat and species and hence the freezing process, while solidification evolves flow boundaries, as in crusting, for example, and hence can radically alter the convection. Mathematical modellers, experimentalists and applied scientists were invited to this colloquium with the aim of consolidating our understanding of such interactions, of identifying key outstanding issues, and of developing new approaches in this important area of fundamental research. Both invited and contributed papers focus on both fundamental and technologically relevant problems.
Author : J M Chadam,Helen Rasmussen
Publisher : CRC Press
Page : 264 pages
File Size : 54,8 Mb
Release : 1993-02-22
Category : Mathematics
ISBN : 0582087678
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.
Author : Tomasz A. Kowalewski,Dominique Gobin
Publisher : Springer
Page : 277 pages
File Size : 41,5 Mb
Release : 2014-05-04
Category : Technology & Engineering
ISBN : 9783709127643
This unique volume offers a review of state-of-the-art modelling methods of phase change problems, numerical and experimental methods used in the field. It combines the experience of theoreticians with those using numerical tools for modelling problems of solidification.
Author : Anonim
Publisher : Unknown
Page : 730 pages
File Size : 42,8 Mb
Release : 1993
Category : Aeronautics
ISBN : STANFORD:36105002745771
Author : Nabeel Zahran Al-Rawahi
Publisher : Unknown
Page : 292 pages
File Size : 40,5 Mb
Release : 2002
Category : Electronic
ISBN : UOM:39015055166741