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Author: Allen C. Pipkin Publisher: Springer Science & Business Media ISBN: 1461599709 Category : Mathematics Languages : en Pages : 190
Book Description
This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely de tailed explanation. Furthermore, much of the content of the course is in the prob lems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not given, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA~, 291(1962)) remains the best reference for proofs of theorems.
Author: Allen C. Pipkin Publisher: Springer Science & Business Media ISBN: 1461599709 Category : Mathematics Languages : en Pages : 190
Book Description
This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely de tailed explanation. Furthermore, much of the content of the course is in the prob lems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not given, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA~, 291(1962)) remains the best reference for proofs of theorems.
Author: Montgomery T. Shaw Publisher: John Wiley & Sons ISBN: 111918181X Category : Technology & Engineering Languages : en Pages : 377
Book Description
Completely revised and updated, the fourth edition of this classic text continues to offer the reader a thorough understanding of viscoelastic behavior, essential for the proper utilization of polymers. Explains principles, corresponding equations, and experimental methods with supporting real-life applications Adds coverage of measurement techniques (nano-indentation, atomic force microscopy (AFM), and diffusing wave spectroscopy (DWS)), biopolymer viscoelasticity, and the relationship between mechanical polymer properties and viscoelastic functions Has two new ections to address modern areas of viscoelastic measurement: large amplitude oscillatory shear (LAOS) and microrheology Includes problems in the text and an Instructor’s Manual (including solutions) available for adopting professors Prior edition reviews: "The book is clear written and...[is] appropriate for students in introductory undergraduate courses and for others wanting introduction to the fundamentals of the subject." (CHOICE, December 2005); "This book is invariably well written, logically organized and easy to follow...I highly recommend this book to anyone studying polymer viscoelasticity." (Polymer News, December 2005)
Author: Weih Q. Lee Publisher: John Wiley & Sons ISBN: 1394211171 Category : Technology & Engineering Languages : en Pages : 548
Book Description
APPLIED COATINGS An integrated collection of case studies providing a concise guide for professionals working with coatings materials in academia and industry In Applied Coatings: Chemistry, Formulation, and Performance, distinguished scientist Dr. Weih Q. Lee delivers an illuminating collection of case studies designed to connect various elements of applied coatings technology. Going beyond generic discussions, the author describes the fundamental chemistry, formulations, and properties of applied coating materials – including the structural and functional components of structure-property relationships – as well as the foundations of applied cure kinetics and the rheology of epoxy coatings. Each chapter is self-contained, comprehensive, and can be read individually, while the book remains technically and editorially integrated. Core themes include structure-performance relationships, formulation index driven experiment design, and consolidated thermal analysis. Readers will also find: A thorough introduction to epoxies and epoxy curing agents, including oxetanes, vinyl esters, glycidyl methacrylate (GMA), isocyanate and silicone crosslinkers, cationic catalysts, acrylate and phenol accelerators, and specialty derivatives Attentive descriptions of epoxy curing chemistry, including epoxy-phenolic, -polyamide, -active ester, and acid- or base-catalyzed systems in a broader scope Comprehensive explorations of cure kinetics and rheology, including model-free kinetics (MFK), the nth-order model covering Kissinger plots and the Borchardt—Daniels (BD) approach, the autocatalytic model, executive quantification via curve fitting of DSC (differential scanning calorimetry) exotherms, the rheology of non-reactive fluids, and the viscoelasticity of reactive coatings Practical discussions of C1S thick-film surface coatings, C2S structural lamination, liquid and powder epoxies, and phenolic coatings, including fluorene monomers, heterocyclic resins, and polymerizable derivatives Complete treatments of coating characterization, microencapsulation, epoxy hybrids and non-epoxy platforms, adhesion of applied coatings, and adhesion promotion, including reactive and functional silicones Perfect for formulation and research and development scientists and engineers at any technical level, Applied Coatings will also benefit research professors and students studying coatings, adhesives, composites, electronic materials, and more.
Author: Eberhard Zeidler Publisher: Springer Science & Business Media ISBN: 1461208211 Category : Mathematics Languages : en Pages : 417
Book Description
The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications. The book addresses undergraduates and beginning graduates of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The books approach is to attempt to determine the most important applications. These concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws, the quark model, and gauge theory in elementary particle physics. The presentation is self-contained and requires only that readers be familiar with some basic facts of calculus.
Author: C. Corduneanu Publisher: CRC Press ISBN: 1482287420 Category : Mathematics Languages : en Pages : 515
Book Description
This volume comprises selected papers presented at the Volterra Centennial Symposium and is dedicated to Volterra and the contribution of his work to the study of systems - an important concept in modern engineering. Vito Volterra began his study of integral equations at the end of the nineteenth century and this was a significant development in th
Author: Miklos Farkas Publisher: Springer Science & Business Media ISBN: 1475742118 Category : Mathematics Languages : en Pages : 585
Book Description
A summary of the most important results in the existence and stability of periodic solutions for ordinary differential equations achieved in the twentieth century, along with relevant applications. It differs from standard classical texts on non-linear oscillations in that it also contains linear theory; theorems are proved with mathematical rigor; and, besides the classical applications such as Van der Pol's, Linard's and Duffing's equations, most applications come from biomathematics. For graduate and Ph.D students in mathematics, physics, engineering, and biology, and as a standard reference for use by researchers in the field of dynamical systems and their applications.
Author: Jianhong Wu Publisher: Springer Science & Business Media ISBN: 1461240506 Category : Mathematics Languages : en Pages : 441
Book Description
Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.
Author: Derek F. Lawden Publisher: Springer Science & Business Media ISBN: 147573980X Category : Mathematics Languages : en Pages : 349
Book Description
The subject matter of this book formed the substance of a mathematical se am which was worked by many of the great mathematicians of the last century. The mining metaphor is here very appropriate, for the analytical tools perfected by Cauchy permitted the mathematical argument to penetra te to unprecedented depths over a restricted region of its domain and enabled mathematicians like Abel, Jacobi, and Weierstrass to uncover a treasurehouse of results whose variety, aesthetic appeal, and capacity for arousing our astonishment have not since been equaled by research in any other area. But the circumstance that this theory can be applied to solve problems arising in many departments of science and engineering graces the topic with an additional aura and provides a powerful argument for including it in university courses for students who are expected to use mathematics as a tool for technological investigations in later life. Unfortunately, since the status of university staff is almost wholly determined by their effectiveness as research workers rather than as teachers, the content of undergraduate courses tends to reflect those academic research topics which are currently popular and bears little relationship to the future needs of students who are themselves not destined to become university teachers. Thus, having been comprehensively explored in the last century and being undoubtedly difficult .
Author: P.A. Lagerstrom Publisher: Springer Science & Business Media ISBN: 1475719906 Category : Mathematics Languages : en Pages : 263
Book Description
Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular perturba tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed further. Examples which required too sophis ticated and involved calculations, or advanced knowledge of a special field, are not treated; for instance, to the author's regret some very interesting applications to fluid mechanics had to be omitted for this reason. Artificial mathematical examples introduced to show some exotic or unexpected behavior are omitted, except when they are analytically simple and are needed to illustrate mathematical phenomena important for realistic problems. Problems of numerical analysis are not discussed.
Author: Martin Golubitsky Publisher: Springer Science & Business Media ISBN: 146125034X Category : Mathematics Languages : en Pages : 480
Book Description
This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.
Author: Allen C. Pipkin
Author: Allen C. Pipkin
Author: Montgomery T. Shaw
Author: Weih Q. Lee
Author: Eberhard Zeidler
Author: C. Corduneanu
Author: Miklos Farkas
Author: Jianhong Wu
Author: Derek F. Lawden
Author: P.A. Lagerstrom
Author: Martin Golubitsky