Elliptic Systems Of Phase Transition Type PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Elliptic Systems Of Phase Transition Type PDF full book. Access full book title Elliptic Systems Of Phase Transition Type.
| Author | : Nicholas D. Alikakos |
| Publisher | : Springer |
| Total Pages | : 343 |
| Release | : 2019-01-21 |
| Genre | : Mathematics |
| ISBN | : 3319905724 |
Download Elliptic Systems of Phase Transition Type Book in PDF, ePub and Kindle
This book focuses on the vector Allen-Cahn equation, which models coexistence of three or more phases and is related to Plateau complexes – non-orientable objects with a stratified structure. The minimal solutions of the vector equation exhibit an analogous structure not present in the scalar Allen-Cahn equation, which models coexistence of two phases and is related to minimal surfaces. The 1978 De Giorgi conjecture for the scalar problem was settled in a series of papers: Ghoussoub and Gui (2d), Ambrosio and Cabré (3d), Savin (up to 8d), and del Pino, Kowalczyk and Wei (counterexample for 9d and above). This book extends, in various ways, the Caffarelli-Córdoba density estimates that played a major role in Savin's proof. It also introduces an alternative method for obtaining pointwise estimates. Key features and topics of this self-contained, systematic exposition include: • Resolution of the structure of minimal solutions in the equivariant class, (a) for general point groups, and (b) for general discrete reflection groups, thus establishing the existence of previously unknown lattice solutions. • Preliminary material beginning with the stress-energy tensor, via which monotonicity formulas, and Hamiltonian and Pohozaev identities are developed, including a self-contained exposition of the existence of standing and traveling waves. • Tools that allow the derivation of general properties of minimizers, without any assumptions of symmetry, such as a maximum principle or density and pointwise estimates. • Application of the general tools to equivariant solutions rendering exponential estimates, rigidity theorems and stratification results. This monograph is addressed to readers, beginning from the graduate level, with an interest in any of the following: differential equations – ordinary or partial; nonlinear analysis; the calculus of variations; the relationship of minimal surfaces to diffuse interfaces; or the applied mathematics of materials science.
| Author | : Marianna Chatzakou |
| Publisher | : Springer Nature |
| Total Pages | : 187 |
| Release | : 2024 |
| Genre | : Differential equations, Partial |
| ISBN | : 3031567323 |
Download Modern Problems in PDEs and Applications Book in PDF, ePub and Kindle
The principal aim of the volume is gathering all the contributions given by the speakers (mini courses) and some of the participants (short talks) of the summer school "Modern Problems in PDEs and Applications" held at the Ghent Analysis and PDE Center from 23 August to 2 September 2023. The school was devoted to the study of new techniques and approaches for solving partial differential equations, which can either be considered or arise from the physical point of view or the mathematical perspective. Both sides are extremely important since theories and methods can be developed independently, aiming to gather each other in a common objective. The aim of the summer school was to progress and advance in the problems considered. Note that real-world problems and their applications are classical study trends in physical or mathematical modelling. The summer school was organised in a friendly atmosphere and synergy, and it was an excellent opportunity to promote and encourage the development of the subject in the community.
| Author | : Tian Ma |
| Publisher | : Springer Nature |
| Total Pages | : 757 |
| Release | : 2019-11-08 |
| Genre | : Mathematics |
| ISBN | : 3030292606 |
Download Phase Transition Dynamics Book in PDF, ePub and Kindle
This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields. This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity). Reviews of first edition: “The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. ... The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences.” (Carlo Bianca, Mathematical Reviews, December, 2014) “This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. ... The book is a very useful literature not only for the professionals in the field of dynamic systems and phase transitions but also for graduate students due to its interdisciplinary coverage and state-of-the-art level.” (Vladimir Čadež, zbMATH, Vol. 1285, 2014)
| Author | : Pierluigi Colli |
| Publisher | : World Scientific |
| Total Pages | : 321 |
| Release | : 2006 |
| Genre | : Science |
| ISBN | : 9812774297 |
Download Dissipative Phase Transitions Book in PDF, ePub and Kindle
Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects. Contents: Mathematical Models Including a Hysteresis Operator (T Aiki); Modelling Phase Transitions via an Entropy Equation: Long-Time Behavior of the Solutions (E Bonetti); Global Solution to a One Dimensional Phase Transition Model with Strong Dissipation (G Bonfanti & F Luterotti); A Global in Time Result for an Integro-Differential Parabolic Inverse Problem in the Space of Bounded Functions (F Colombo et al.); Weak Solutions for Stefan Problems with Convections (T Fukao); Memory Relaxation of the One-Dimensional CahnOCoHilliard Equation (S Gatti et al.); Mathematical Models for Phase Transition in Materials with Thermal Memory (G Gentili & C Giorgi); Hysteresis in a First Order Hyperbolic Equation (J Kopfovi); Approximation of Inverse Problems Related to Parabolic Integro-Differential Systems of Caginalp Type (A Lorenzi & E Rocca); Gradient Flow Reaction/Diffusion Models in Phase Transitions (J Norbury & C Girardet); New Existence Result for a 3-D Shape Memory Model (I Pawlow & W M Zajaczkowski); Analysis of a 1-D Thermoviscoelastic Model with Temperature-Dependent Viscosity (R Peyroux & U Stefanelli); Global Attractor for the Weak Solutions of a Class of Viscous Cahn-Hilliard Equations (R Rossi); Stability for Phase Field Systems Involving Indefinite Surface Tension Coefficients (K Shirakawa); Geometric Features of p -Laplace Phase Transitions (E Valdinoci). Readership: Applied mathematicians and researchers in analysis and differential equations."
| Author | : K.-H. Hoffmann |
| Publisher | : Birkhäuser |
| Total Pages | : 390 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034882742 |
Download Ginzburg-Landau Phase Transition Theory and Superconductivity Book in PDF, ePub and Kindle
This monograph compiles, rearranges, and refines recent research results in the complex G-L theory with or without immediate applications to the theory of superconductivity. An authoritative reference for applied mathematicians, theoretical physicists and engineers interested in the quantitative description of superconductivity using Ginzburg-Landau theory.
| Author | : Institute for Computer Applications in Science and Engineering. (ICASE) |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 1999 |
| Genre | : |
| ISBN | : |
Download A Gas-kinetic Method for Hyperbolic-elliptic Equations and Its Application in Two-phase Fluid Flow Book in PDF, ePub and Kindle
| Author | : Barbara L. Keyfitz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 297 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461390494 |
Download Nonlinear Evolution Equations That Change Type Book in PDF, ePub and Kindle
This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshop focussed on prob lems of ill-posedness and change of type which arise in modeling flows in porous materials, viscoelastic fluids and solids and phase changes. We thank the Coordinat ing Committee: James Glimm, Daniel Joseph, Barbara Lee Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the workshop organizers, Barbara Lee Keyfitz and Michael Shearer, for their efforts in bringing together many of the major figures in those research fields in which theories for nonlinear evolution equations that change type are being developed. A vner Friedman Willard Miller, J r. ix PREFACE During the winter and spring quarters of the 1988/89 IMA Program on Non linear Waves, the issue of change of type in nonlinear partial differential equations appeared frequently. Discussion began with the January 1989 workshop on Two Phase Waves in Fluidized Beds, Sedimentation and Granular Flow; some of the papers in the proceedings of that workshop present strategies designed to avoid the appearance of change of type in models for multiphase fluid flow.
| Author | : Augusto Visintin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 334 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461240786 |
Download Models of Phase Transitions Book in PDF, ePub and Kindle
... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/:" "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple ... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX
| Author | : T. Riste |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 456 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 9401119082 |
Download Phase Transitions and Relaxation in Systems with Competing Energy Scales Book in PDF, ePub and Kindle
Systems with competing energy scales are widespread and exhibit rich and subtle behaviour, although their systematic study is a relatively recent activity. This text presents lectures given at a NATO Advanced Study Institute reviewing the current knowledge and understanding of this fascinating subject, particularly with regard to phase transitions and dynamics, at an advanced tutorial level. Both general and specific aspects are considered, with competitions having several origins; differences in intrinsic interactions, interplay between intrinsic and extrinsic effects, such as geometry and disorder; irreversibility and non-equilibration. Among the specific physical application areas are supercooled liquids and glasses, high-temperature superconductors, flux or vortex pinning and motion, charge density waves, domain growth and coarsening, and electron solidification.
| Author | : Boris M. Smirnov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 249 |
| Release | : 2007-10-24 |
| Genre | : Science |
| ISBN | : 3540715142 |
Download Phase Transitions of Simple Systems Book in PDF, ePub and Kindle
This monograph develops a unified microscopic basis for phases and phase changes of bulk matter and small systems, based on classical physics. It describes the thermodynamics of ensembles of particles and explains phase transition in gaseous and liquid systems. The origins are derived from simple but physically relevant models of how transitions occur between rigid and fluid states, of how phase equilibria arise, and how they differ for small and large systems.
