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Spatial Patterns

Spatial Patterns Author L.A. Peletier
ISBN-10 9781461201359
Release 2012-12-06
Pages 343
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The study of spatial patterns in extended systems, and their evolution with time, poses challenging questions for physicists and mathematicians alike. Waves on water, pulses in optical fibers, periodic structures in alloys, folds in rock formations, and cloud patterns in the sky: patterns are omnipresent in the world around us. Their variety and complexity make them a rich area of study. In the study of these phenomena an important role is played by well-chosen model equations, which are often simpler than the full equations describing the physical or biological system, but still capture its essential features. Through a thorough analysis of these model equations one hopes to glean a better under standing of the underlying mechanisms that are responsible for the formation and evolution of complex patterns. Classical model equations have typically been second-order partial differential equations. As an example we mention the widely studied Fisher-Kolmogorov or Allen-Cahn equation, originally proposed in 1937 as a model for the interaction of dispersal and fitness in biological populations. As another example we mention the Burgers equation, proposed in 1939 to study the interaction of diffusion and nonlinear convection in an attempt to understand the phenomenon of turbulence. Both of these are nonlinear second-order diffusion equations.



A Study of Heteroclinic Orbits for a Class of Fourth Order Ordinary Differential Equations

A Study of Heteroclinic Orbits for a Class of Fourth Order Ordinary Differential Equations Author Denis Bonheure
ISBN-10 9782930344751
Release 2004-01-01
Pages 217
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In qualitative theory of differential equations, an important role is played by special classes of solutions, like periodic solutions or solutions to some boundary value problems. When a system of ordinary differential equations has equilibria, i.e. constant solutions, whose stability properties are known, it is significant to search for connections between them by trajectories of solutions of the given system. These are called homoclinic or heteroclinic, according to whether they describe a loop based at one single equilibrium or they "start" and "end" at two distinct equilibria. This thesis is devoted to the study of heteroclinic solutions for a specific class of ordinary differential equations related to the Extended Fisher-Kolmogorov equation and the Swift-Hohenberg equation. These are semilinear fourth order bi-stable evolution equations which appear as mathematical models for problems arising in Mechanics, Chemistry and Biology. For such equations, the set of bounded stationary solutions is of great interest. These solve an autonomous fourth order equation. In this thesis, we focus on such equations having a variational structure. In that case, the solutions are critical points of an associated action functional defined in convenient functional spaces. We then look for heteroclinic solutions as minimizers of the action functional. Our main contributions concern existence and multiplicity results of such global and local minimizers in the case where the functional is defined from sign changing Lagrangians. The underlying idea is to impose conditions which imply a lower bound on the action over all admissible functions. We then combine classical arguments of the Calculus of Variations with careful estimates on minimizing sequences to prove the existence of a minimum.



Handbook of Differential Equations Evolutionary Equations

Handbook of Differential Equations  Evolutionary Equations Author C.M. Dafermos
ISBN-10 0080931979
Release 2008-10-06
Pages 608
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The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area - Continuation of previous volumes in the handbook series covering Evolutionary PDEs - Written by leading experts



Structural Geology

Structural Geology Author Bruce E. Hobbs
ISBN-10 9780124079335
Release 2014-11-21
Pages 680
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Structural Geology is a groundbreaking reference that introduces you to the concepts of nonlinear solid mechanics and non-equilibrium thermodynamics in metamorphic geology, offering a fresh perspective on rock structure and its potential for new interpretations of geological evolution. This book stands alone in unifying deformation and metamorphism and the development of the mineralogical fabrics and the structures that we see in the field. This reflects the thermodynamics of systems not at equilibrium within the framework of modern nonlinear solid mechanics. The thermodynamic approach enables the various mechanical, thermal, hydrological and chemical processes to be rigorously coupled through the second law of thermodynamics, invariably leading to nonlinear behavior. The book also differs from others in emphasizing the implications of this nonlinear behavior with respect to the development of the diverse, complex, even fractal, range of structures in deformed metamorphic rocks. Building on the fundamentals of structural geology by discussing the nonlinear processes that operate during the deformation and metamorphism of rocks in the Earth's crust, the book's concepts help geoscientists and graduate-level students understand how these processes control or influence the structures and metamorphic fabrics—providing applications in hydrocarbon exploration, ore mineral exploration, and architectural engineering. Authored by two of the world's foremost experts in structural geology, representing more than 70 years of experience in research and instruction Nearly 300 figures, illustrations, working examples, and photographs reinforce key concepts and underscore major advances in structural geology



Mathematics Today

Mathematics Today Author
ISBN-10 UOM:39015072631792
Release 2007
Pages
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Mathematics Today has been writing in one form or another for most of life. You can find so many inspiration from Mathematics Today also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematics Today book for free.



Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UVA:X006180726
Release 2004
Pages
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.



Advances in Differential Equations

Advances in Differential Equations Author
ISBN-10 UOM:39015059085368
Release 2004
Pages
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Advances in Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Advances in Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Advances in Differential Equations book for free.



Partial Differential Equations and Mathematical Physics

Partial Differential Equations and Mathematical Physics Author Jean Leray
ISBN-10 UOM:39015056651725
Release 2003
Pages 238
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Partial Differential Equations and Mathematical Physics has been writing in one form or another for most of life. You can find so many inspiration from Partial Differential Equations and Mathematical Physics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Partial Differential Equations and Mathematical Physics book for free.



Variational and Topological Methods in the Study of Nonlinear Phenomena

Variational and Topological Methods in the Study of Nonlinear Phenomena Author Vieri Benci
ISBN-10 UOM:39015054149623
Release 2002
Pages 131
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This volume covers recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods.A broad range of topics is covered, including: * concentration phenomena in pdes* variational methods with applications to pdes and physics* periodic solutions of odes* computational aspects in topological methods* mathematical models in biologyThough well-differentiated, the topics covered are unified through a common perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on pdes and odes. The volume will be an excellent reference text for researchers and graduate students in the above mentioned fields.Contributors: M. Clapp, M. Del Pino, M. Esteban, P. Felmer, A. Ioffe, W. Marzantowicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, E. Sere, P. Sintzoff, R. Turner, M. Willem



Energy Methods for Free Boundary Problems

Energy Methods for Free Boundary Problems Author Stanislav Nikolaevich Antont︠s︡ev
ISBN-10 UOM:39015053541721
Release 2002
Pages 329
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Energy Methods for Free Boundary Problems has been writing in one form or another for most of life. You can find so many inspiration from Energy Methods for Free Boundary Problems also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Energy Methods for Free Boundary Problems book for free.



Scientific and Technical Aerospace Reports

Scientific and Technical Aerospace Reports Author
ISBN-10 UVA:X004872562
Release 1995
Pages
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Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.



International Aerospace Abstracts

International Aerospace Abstracts Author
ISBN-10 UOM:39015034740756
Release 1986
Pages
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International Aerospace Abstracts has been writing in one form or another for most of life. You can find so many inspiration from International Aerospace Abstracts also informative, and entertaining. Click DOWNLOAD or Read Online button to get full International Aerospace Abstracts book for free.



Nuclear Science Abstracts

Nuclear Science Abstracts Author
ISBN-10 UOM:39015023544425
Release 1973
Pages
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Nuclear Science Abstracts has been writing in one form or another for most of life. You can find so many inspiration from Nuclear Science Abstracts also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Nuclear Science Abstracts book for free.



Finite Volumes for Complex Applications VIII Hyperbolic Elliptic and Parabolic Problems

Finite Volumes for Complex Applications VIII   Hyperbolic  Elliptic and Parabolic Problems Author Clément Cancès
ISBN-10 9783319573946
Release 2017-05-22
Pages 559
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This book is the second volume of proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017). It includes reviewed contributions reporting successful applications in the fields of fluid dynamics, computational geosciences, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete l evel. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is useful for researchers, PhD and master’s level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as for engineers working in numerical modeling and simulations.



Reviews in Global Analysis 1980 86 as Printed in Mathematical Reviews

Reviews in Global Analysis  1980 86 as Printed in Mathematical Reviews Author
ISBN-10 UCAL:B4342570
Release 1988
Pages 3920
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Reviews in Global Analysis 1980 86 as Printed in Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Reviews in Global Analysis 1980 86 as Printed in Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Reviews in Global Analysis 1980 86 as Printed in Mathematical Reviews book for free.



INIS Atomindeks

INIS Atomindeks Author
ISBN-10 MINN:31951D007675370
Release 1987
Pages
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Government reports annual index

Government reports annual index Author
ISBN-10 MSU:31293017238712
Release 199?
Pages
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Government reports annual index has been writing in one form or another for most of life. You can find so many inspiration from Government reports annual index also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Government reports annual index book for free.