Pattern Formation At Interfaces
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| Author | : Pierre Colinet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 304 |
| Release | : 2010-03-26 |
| Genre | : Technology & Engineering |
| ISBN | : 3709101255 |
The book deals with modern methods of nonlinear stability theory applied to problems of continuous media mechanics in the presence of interfaces, with applications to materials science, chemical engineering, heat transfer technologies, as well as in combustion and other reaction-diffusion systems. Interfaces play a dominant role at small scales, and their correct modeling is therefore also crucial in the rapidly expanding fields of microfluidics and nanotechnologies. To this aim, the book combines contributions of eminent specialists in the field, with a special emphasis on rigorous and predictive approaches. Other goals of this volume are to allow the reader to identify key problems of high scientific value, and to see the similarity between a variety of seemingly different physical problems.
| Author | : L.M. Pismen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 383 |
| Release | : 2006-07-07 |
| Genre | : Science |
| ISBN | : 3540304312 |
Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.
| Author | : Rebecca B. Hoyle |
| Publisher | : Cambridge University Press |
| Total Pages | : 440 |
| Release | : 2006-03-17 |
| Genre | : Mathematics |
| ISBN | : 9780521817509 |
Fully illustrated mathematical guide to pattern formation. Includes instructive exercises and examples.
| Author | : Jian-Jun Xu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 303 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642804357 |
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 | : Agnes Buka |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 146123994X |
In the last 20 years the study of nonlinear nonequilibrium phenomena in spa tially extended systems, with particular emphasis on pattern-forming phenomena, has been one of the very active areas in physics, exhibiting interesting ramifi cations into other sciences. During this time the study of the "classic" systems, like Rayleigh-Benard convection and Taylor vortex flow in simple fluids, has also been supplemented by the study of more complex systems. Here liquid crystals have played, and are still playing, a major role. One might say that liquid crystals provide just the right amount and right kind of complexity. They are full of non linearities and give rise to new symmetry classes, which are sometimes actually simpler to deal with qualitatively, but they still allow a quantitative description of experiments in many cases. In fact one of the attractions of the field is the close contact between experimentalists and theorists. Hydrodynamic instabilities in liquid crystals had already experienced a period of intense study in the late 1960s and early 1970s, but at that time neither the ex perimental and theoretical tools nor the concepts had been developed sufficiently far to address the questions that have since been found to be of particular interest. The renewed interest is also evidenced by the fact that a new series of workshops has evolved. The first one took place in 1989 in Bayreuth and united participants from almost all groups working in pattern formation in liquid crystals.
| Author | : Geoffrey Grinstein |
| Publisher | : World Scientific |
| Total Pages | : 270 |
| Release | : 1986-08-01 |
| Genre | : Science |
| ISBN | : 9814513601 |
This volume collects several in-depth articles giving lucid discussions on new developments in statistical and condensed matter physics. Many, though not all, contributors had been in touch with the late S-K Ma. Written by some of the world's experts and originators of new ideas in the field, this book is a must for all researchers in theoretical physics. Most of the articles should be accessible to diligent graduate students and experienced readers will gain from the wealth of materials contained herein.
| Author | : H. K. Henisch |
| Publisher | : Elsevier |
| Total Pages | : 137 |
| Release | : 2014-06-28 |
| Genre | : Science |
| ISBN | : 1483296806 |
Containing illustrations, worked examples, graphs and tables, this book deals with periodic precipitation (also known as Liesegang Ring formation) in terms of mathematical models and their logical consequences, and is entirely concerned with microcomputer analysis and software development. Three distinctive periodic precipitation mechanisms are included: binary diffusion-reaction; solubility modulation, and competitive particle growth. The book provides didactic illustrations of a valuable investigational procedure, in the form of hypothetical experimentation by microcomputer. The development of appropriate software is described and the resulting programs are available separately on disk. The software (for IBM compatible microcomputers; 5 1/4 and 3 1/2 inch disks available) will be sold separately by, The Carnation Press, PO Box 101, State College, PA 16804, USA.
| Author | : Jian-Jun Xu |
| Publisher | : Springer |
| Total Pages | : 605 |
| Release | : 2017-05-23 |
| Genre | : Science |
| ISBN | : 3319526634 |
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 | : Michel C. Delfour |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 364 |
| Release | : 1998 |
| Genre | : Mathematics |
| ISBN | : 9780821805053 |
This book brings together tools that have been developed in a priori distant areas of mathematics, mechanics and physics. It provides coverage of selected contemporary problems in the areas of optimal design, mathematical models in material sciences, hysteresis, superconductivity, phase transition, crystal growth, moving boundary problems, thin shells and some of the associated numerical issues.
| Author | : Len Pismen |
| Publisher | : Springer Nature |
| Total Pages | : 402 |
| Release | : 2023-06-12 |
| Genre | : Science |
| ISBN | : 303129579X |
Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.
