Falling Liquid Films / Kalliadasis, S (2012)  

Público ISBD Título : Falling Liquid Films Tipo de documento: documento electrónico Autores: Kalliadasis, S ; SpringerLink (Online service) ; Ruyer-Quil, C ; Scheid, B ; Velarde, M. G Editorial: London : Springer London Fecha de publicación: 2012 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 176 Número de páginas: XVI, 440 p Il.: online resource ISBN/ISSN/DL: 978-1-84882-367-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Applied  mathematics  Engineering  Visualization  Physics  Continuum  physics  Fluids  Applications  of  Classical  Appl.Mathematics/Computational  Methods  Fluid-  and  Aerodynamics  Theoretical,  Mathematical  Computational Clasificación: 51 Matemáticas Resumen: Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence.  Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiment is illustrated, and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of basic, underlying physics.   This monograph will appeal to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program. It will also be of use to researchers working on both applied, fundamental theoretical and experimental aspects of thin film flows, as well as engineers and technologists dealing with processes involving isothermal or heated films. This monograph is largely self-contained and no background on interfacial fluid mechanics is assumed Nota de contenido: Introduction -- Flow and heat transfer -- Primary instability -- Boundary layer approximation -- Methodologies for low Re flows -- Methodologies for moderate Re flows -- Isothermal case: 2D flow -- Isothermal case: 3D flow -- Interaction of 3D solitary waves -- Heated films -- Reactive films -- Open questions and suggestions for further research En línea: http://dx.doi.org/10.1007/978-1-84882-367-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32853 Falling Liquid Films [documento electrónico] / Kalliadasis, S ; SpringerLink (Online service) ; Ruyer-Quil, C ; Scheid, B ; Velarde, M. G . - London : Springer London, 2012 . - XVI, 440 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 176) . ISBN : 978-1-84882-367-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Applied  mathematics  Engineering  Visualization  Physics  Continuum  physics  Fluids  Applications  of  Classical  Appl.Mathematics/Computational  Methods  Fluid-  and  Aerodynamics  Theoretical,  Mathematical  Computational Clasificación: 51 Matemáticas Resumen: Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence.  Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiment is illustrated, and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of basic, underlying physics.   This monograph will appeal to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program. It will also be of use to researchers working on both applied, fundamental theoretical and experimental aspects of thin film flows, as well as engineers and technologists dealing with processes involving isothermal or heated films. This monograph is largely self-contained and no background on interfacial fluid mechanics is assumed Nota de contenido: Introduction -- Flow and heat transfer -- Primary instability -- Boundary layer approximation -- Methodologies for low Re flows -- Methodologies for moderate Re flows -- Isothermal case: 2D flow -- Isothermal case: 3D flow -- Interaction of 3D solitary waves -- Heated films -- Reactive films -- Open questions and suggestions for further research En línea: http://dx.doi.org/10.1007/978-1-84882-367-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32853

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Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles / Han, Maoan (2012)  

Público ISBD Título : Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles Tipo de documento: documento electrónico Autores: Han, Maoan ; SpringerLink (Online service) ; Yu, Pei Editorial: London : Springer London Fecha de publicación: 2012 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 181 Número de páginas: XII, 404 p Il.: online resource ISBN/ISSN/DL: 978-1-4471-2918-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Approximation  theory  Dynamics  Ergodic  Differential  equations  Computer  software  Statistical  physics  Dynamical  Systems  and  Theory  Approximations  Expansions  Ordinary  Equations  Mathematical  Software  Nonlinear Clasificación: 51 Matemáticas Resumen: Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus  is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on  the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior Nota de contenido: Hopf Bifurcation and Normal Form Computation -- Comparison of Methods for Computing Focus Values -- Application (I)—Hilbert’s 16th Problem -- Application (II)—Practical Problems -- Fundamental Theory of the Melnikov Function Method -- Limit Cycle Bifurcations Near a Center -- Limit Cycles Near a Homoclinic or Heteroclinic Loop -- Finding More Limit Cycles Using Melnikov Functions -- Limit Cycle Bifurcations in Equivariant Systems En línea: http://dx.doi.org/10.1007/978-1-4471-2918-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32723 Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles [documento electrónico] / Han, Maoan ; SpringerLink (Online service) ; Yu, Pei . - London : Springer London, 2012 . - XII, 404 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 181) . ISBN : 978-1-4471-2918-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Approximation  theory  Dynamics  Ergodic  Differential  equations  Computer  software  Statistical  physics  Dynamical  Systems  and  Theory  Approximations  Expansions  Ordinary  Equations  Mathematical  Software  Nonlinear Clasificación: 51 Matemáticas Resumen: Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus  is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on  the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior Nota de contenido: Hopf Bifurcation and Normal Form Computation -- Comparison of Methods for Computing Focus Values -- Application (I)—Hilbert’s 16th Problem -- Application (II)—Practical Problems -- Fundamental Theory of the Melnikov Function Method -- Limit Cycle Bifurcations Near a Center -- Limit Cycles Near a Homoclinic or Heteroclinic Loop -- Finding More Limit Cycles Using Melnikov Functions -- Limit Cycle Bifurcations in Equivariant Systems En línea: http://dx.doi.org/10.1007/978-1-4471-2918-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32723

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Piecewise-smooth Dynamical Systems / SpringerLink (Online service) ; Laurea, Mario di Bernardo ; Champneys, Alan R ; Budd, Christopher J ; Kowalczyk, Piotr (2008)  

Público ISBD Título : Piecewise-smooth Dynamical Systems : Theory and Applications Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Laurea, Mario di Bernardo ; Champneys, Alan R ; Budd, Christopher J ; Kowalczyk, Piotr Editorial: London : Springer London Fecha de publicación: 2008 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 163 Número de páginas: XXII, 482 p Il.: online resource ISBN/ISSN/DL: 978-1-84628-708-4 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Dynamics  Ergodic  theory  Applied  mathematics  Engineering  Vibration  Dynamical  systems  Control  engineering  Robotics  Mechatronics  Electrical  Systems  and  Theory  Control,  Robotics,  Vibration,  Systems,  Applications  of Clasificación: 51 Matemáticas Resumen: Traditional analysis of dynamical systems has restricted its attention to smooth problems, but it has become increasingly clear that there are distinctive phenomena unique to discontinuous systems that can be analyzed mathematically but which fall outside the usual methodology for smooth dynamical systems. The primary purpose of this book is to present a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction asserts the ubiquity of such models with examples drawn from mechanics, electronics, control theory and physiology. The main thrust is to classify complex behavior via bifurcation theory in a systematic yet applicable way. The key concept is that of a discontinuity-induced bifurcation, which generalizes diverse phenomena such as grazing, border-collision, sliding, chattering and the period-adding route to chaos. The results are presented in an informal style and illustrated with copious examples, both theoretical and experimental. Aimed at a wide audience of applied mathematicians, engineers and scientists at the early postgraduate level, the book assumes only the standard background of basic calculus and linear algebra for most of the presentation and will be an indispensable resource for students and researchers. The inclusion of a comprehensive bibliography and many open questions will also serve as a stimulus for future research Nota de contenido: Qualitative theory of non-smooth dynamical systems -- Border-collision in piecewise-linear continuous maps -- Bifurcations in general piecewise-smooth maps -- Boundary equilibrium bifurcations in flows -- Limit cycle bifurcations in impacting systems -- Limit cycle bifurcations in piecewise-smooth flows -- Sliding bifurcations in Filippov systems -- Further applications and extensions En línea: http://dx.doi.org/10.1007/978-1-84628-708-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34296 Piecewise-smooth Dynamical Systems : Theory and Applications [documento electrónico] / SpringerLink (Online service) ; Laurea, Mario di Bernardo ; Champneys, Alan R ; Budd, Christopher J ; Kowalczyk, Piotr . - London : Springer London, 2008 . - XXII, 482 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 163) . ISBN : 978-1-84628-708-4 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Dynamics  Ergodic  theory  Applied  mathematics  Engineering  Vibration  Dynamical  systems  Control  engineering  Robotics  Mechatronics  Electrical  Systems  and  Theory  Control,  Robotics,  Vibration,  Systems,  Applications  of Clasificación: 51 Matemáticas Resumen: Traditional analysis of dynamical systems has restricted its attention to smooth problems, but it has become increasingly clear that there are distinctive phenomena unique to discontinuous systems that can be analyzed mathematically but which fall outside the usual methodology for smooth dynamical systems. The primary purpose of this book is to present a coherent framework for understanding the dynamics of piecewise-smooth and hybrid systems. An informal introduction asserts the ubiquity of such models with examples drawn from mechanics, electronics, control theory and physiology. The main thrust is to classify complex behavior via bifurcation theory in a systematic yet applicable way. The key concept is that of a discontinuity-induced bifurcation, which generalizes diverse phenomena such as grazing, border-collision, sliding, chattering and the period-adding route to chaos. The results are presented in an informal style and illustrated with copious examples, both theoretical and experimental. Aimed at a wide audience of applied mathematicians, engineers and scientists at the early postgraduate level, the book assumes only the standard background of basic calculus and linear algebra for most of the presentation and will be an indispensable resource for students and researchers. The inclusion of a comprehensive bibliography and many open questions will also serve as a stimulus for future research Nota de contenido: Qualitative theory of non-smooth dynamical systems -- Border-collision in piecewise-linear continuous maps -- Bifurcations in general piecewise-smooth maps -- Boundary equilibrium bifurcations in flows -- Limit cycle bifurcations in impacting systems -- Limit cycle bifurcations in piecewise-smooth flows -- Sliding bifurcations in Filippov systems -- Further applications and extensions En línea: http://dx.doi.org/10.1007/978-1-84628-708-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34296

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