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Nonlinear PDE's, Dynamics and Continuum Physics

2000 Mathematics
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Release : 2000
Genre : Mathematics
Kind : eBook
Book Rating : 529/5 ( reviews)

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Book Synopsis Nonlinear PDE's, Dynamics and Continuum Physics by : J. L. Bona

Download or read book Nonlinear PDE's, Dynamics and Continuum Physics written by J. L. Bona. This book was released on 2000. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the refereed proceedings of the conference on Nonlinear Partial Differential Equations, Dynamics and Continuum Physics which was held at Mount Holyoke College in Massachusetts, from July 19th to July 23rd, 1998. Models examined derive from a wide range of applications, including elasticity, thermoviscoelasticity, granular media, fluid dynamics, gas dynamics and conservation laws. Mathematical topics include existence theory and stability/instability of traveling waves, asymptotic behavior of solutions to nonlinear wave equations, effects of dissipation, mechanisms of blow-up, well-posedness and regularity, and fractal solutions. The text will be of interest to graduate students and researchers working in nonlinear partial differential equations and applied mathematics.

Computational Reality

2016-10-22 Science
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Release : 2016-10-22
Genre : Science
Kind : eBook
Book Rating : 448/5 ( reviews)

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Book Synopsis Computational Reality by : Bilen Emek Abali

Download or read book Computational Reality written by Bilen Emek Abali. This book was released on 2016-10-22. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of continuum mechanics for mechanical, thermodynamical, and electrodynamical systems. It shows how to obtain governing equations and it applies them by computing the reality. It uses only open-source codes developed under the FEniCS project and includes codes for 20 engineering applications from mechanics, fluid dynamics, applied thermodynamics, and electromagnetism. Moreover, it derives and utilizes the constitutive equations including coupling terms, which allow to compute multiphysics problems by incorporating interactions between primitive variables, namely, motion, temperature, and electromagnetic fields. An engineering system is described by the primitive variables satisfying field equations that are partial differential equations in space and time. The field equations are mostly coupled and nonlinear, in other words, difficult to solve. In order to solve the coupled, nonlinear system of partial differential equations, the book uses a novel collection of open-source packages developed under the FEniCS project. All primitive variables are solved at once in a fully coupled fashion by using finite difference method in time and finite element method in space.

Energy Methods for Free Boundary Problems

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Energy Methods for Free Boundary Problems by : S.N. Antontsev

Download or read book Energy Methods for Free Boundary Problems written by S.N. Antontsev. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: This book is an integrated account of modern developments in energy methods for the study of free boundary problems in partial differential equations. The theory presented has particular relevance to a number of physical applications, including heat conduction, surface and underground water flow, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, and semiconductors. The work is divided into two parts. The first part is an exposition of the methods of several general classes of nonlinear equations and systems. Part two presents applications to the theory. `Energy Methods for Free Boundary Problems' will appeal to applied mathematicians and graduate students whose research is in partial differential equations, nonlinear analysis, and continuum mechanics. Applications to a number of different problems arising in continuum mechanics (fluid dynamics) are presented making this book of equal interest to physicists and engineers as well.

Nonlinear Wave Dynamics

2013-04-17 Technology & Engineering
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Release : 2013-04-17
Genre : Technology & Engineering
Kind : eBook
Book Rating : 910/5 ( reviews)

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Book Synopsis Nonlinear Wave Dynamics by : J. Engelbrecht

Download or read book Nonlinear Wave Dynamics written by J. Engelbrecht. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

Nonlinear Dynamics

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 884/5 ( reviews)

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Book Synopsis Nonlinear Dynamics by : Muthusamy Lakshmanan

Download or read book Nonlinear Dynamics written by Muthusamy Lakshmanan. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.

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