Exercises at the ends of chapters or sections
Solutions to selected exercises in the book
Detailed Illustrations
Kiyohiro Ikeda is a Professor in the Department of Civil Engineering, Graduate School of Engineering at Tohoku University. Kazuo Murota is a Professor in the Department of Mathematical Informatics, Graduate School of Information Science and Technology at University of Tokyo.
Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.|The ?rst edition of this book was published in 2002 for an audience of applied mathematicians and engineers. The response to the ?rst edition, represented by sev eral book reviews, has been most heartening. Accordingly, the second edition of this book maintains its major framework and serves as an expanded revision of our previous work. In the second edition, the theoretical backgrounds of group representation the ory are strengthened and made self contained, in response to a request of a book reviewer and students of the authors. Based on these strengthened backgrounds, a theory and a numerical procedure on block diagonalization are presented. Among a number of methodologies, block diagonalization analysis has come to be acknowl edged as a systematic and rigorous procedure for symmetry exploitation for the following two purposes: - Gain better insight into bifurcation behaviors via blockwise singularity detection. - Enhance the computational e?ciency and accuracy of the numerical analysis.
Overview of Book.- Imperfect Behavior at Simple Critical Points.- Critical Points and Local Behavior.- Imperfection Sensitivity Laws.- Worst Imperfection (I).- Random Imperfection (I).- Experimentally Observed Bifurcation Diagrams.- Imperfect Bifurcation of Symmetric Systems.- Group-Theoretic Bifurcation Theory.- Bifurcation Behavior of Dn-Equivariant Systems.- Worst Imperfection (II).- Random Imperfection (II).- Deillegalscription and Computation of Bifurcation Behaviors.- Efficient Transformation for Block-Diagonalization.- Modeling of Bifurcation Phenomena.- Bifurcation of Cylindrical Sand Specimens.- Echelon-Mode Formation.- Bifurcation of Steel Specimens.- Flower Patterns on Honeycomb Structures.- Answers to Problems.
This book provides a modern static imperfect bifurcation theory applicable to bifurcation phenomena of physical and engineering problems and fills the gap between the mathematical theory and engineering practice.
Systematic methods based on asymptotic, probabilistic, and group theoretic standpoints are used to examine experimental and computational data from numerous examples, such as soil, sand, kaolin, honeycomb, and domes. For mathematicians, static bifurcation theory for finite-dimensional systems, as well as its applications for practical problems, is illuminated by numerous examples. Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory.
This third edition strengthens group representation and group-theoretic bifurcation theory. Several large scale applications have been included in association with the progress of computational powers. Problems and answers have been provided.
Review of First Edition:
"The book is unique in considering the experimental identification of material-dependent bifurcations in structures such as sand, Kaolin (clay), soil and concrete shells. ... These are studied statistically. ... The book is an excellent source of practical applications for mathematicians working in this field. ... A short set of exercises at the end of each chapter makes the book more useful as a text. The book is well organized and quite readable for non-specialists."
Henry W. Haslach, Jr., Mathematical Reviews, 2003
This illustrated book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes).
This book provides a modern static imperfect bifurcation theory applicable to bifurcation phenomena of physical and engineering problems and fills the gap between the mathematical theory and engineering practice.
Systematic methods based on asymptotic, probabilistic, and group theoretic standpoints are used to examine experimental and computational data from numerous examples, such as soil, sand, kaolin, honeycomb, and domes. For mathematicians, static bifurcation theory for finite-dimensional systems, as well as its applications for practical problems, is illuminated by numerous examples. Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory.
This third edition strengthens group representation and group-theoretic bifurcation theory. Several large scale applications have been included in association with the progress of computational powers. Problems and answers have been provided.
Review of First Edition:
"The book is unique in considering the experimental identification of material-dependent bifurcations in structures such as sand, Kaolin (clay), soil and concrete shells. ... These are studied statistically. ... The book is an excellent source of practical applications for mathematicians working in this field. ... A short set of exercises at the end of each chapter makes the book more useful as a text. The book is well organized and quite readable for non-specialists."
Henry W. Haslach, Jr., Mathematical Reviews, 2003
Über den Autor
Kiyohiro Ikeda is a Professor in the Department of Civil Engineering, Graduate School of Engineering at Tohoku University. Kazuo Murota is a Professor in the Department of Mathematical Informatics, Graduate School of Information Science and Technology at University of Tokyo.
Inhaltsverzeichnis
Overview of Book.- Imperfect Behavior at Simple Critical Points.- Critical Points and Local Behavior.- Imperfection Sensitivity Laws.- Worst Imperfection (I).- Random Imperfection (I).- Experimentally Observed Bifurcation Diagrams.- Imperfect Bifurcation of Symmetric Systems.- Group-Theoretic Bifurcation Theory.- Bifurcation Behavior of Dn-Equivariant Systems.- Worst Imperfection (II).- Random Imperfection (II).- Deillegalscription and Computation of Bifurcation Behaviors.- Efficient Transformation for Block-Diagonalization.- Modeling of Bifurcation Phenomena.- Bifurcation of Cylindrical Sand Specimens.- Echelon-Mode Formation.- Bifurcation of Steel Specimens.- Flower Patterns on Honeycomb Structures.- Answers to Problems.
Klappentext
This book provides a modern static imperfect bifurcation theory applicable to bifurcation phenomena of physical and engineering problems and fills the gap between the mathematical theory and engineering practice.
Systematic methods based on asymptotic, probabilistic, and group theoretic standpoints are used to examine experimental and computational data from numerous examples, such as soil, sand, kaolin, honeycomb, and domes. For mathematicians, static bifurcation theory for finite-dimensional systems, as well as its applications for practical problems, is illuminated by numerous examples. Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory.
This third edition strengthens group representation and group-theoretic bifurcation theory. Several large scale applications have been included in association with the progress of computational powers. Problems and answers have been provided.
Review of First Edition:
"The book is unique in considering the experimental identification of material-dependent bifurcations in structures such as sand, Kaolin (clay), soil and concrete shells. ¿ These are studied statistically. ¿ The book is an excellent source of practical applications for mathematicians working in this field. ¿ A short set of exercises at the end of each chapter makes the book more useful as a text. The book is well organized and quite readable for non-specialists."
Henry W. Haslach, Jr., Mathematical Reviews, 2003
Exercises at the ends of chapters or sections
Solutions to selected exercises in the book
Detailed Illustrations
