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Introduction to Theoretical and Mathematical Fluid Dynamics
| Introduction to Theoretical and Mathematical Fluid Dynamics |
| Autore | Shivamoggi Bhimsen K |
| Pubbl/distr/stampa | Newark : , : John Wiley & Sons, Incorporated, , 2022 |
| Descrizione fisica | 1 online resource (578 pages) |
| ISBN |
1-119-76515-3
1-119-10151-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910632494003321 |
Shivamoggi Bhimsen K
|
||
| Newark : , : John Wiley & Sons, Incorporated, , 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear Dynamics and Chaotic Phenomena: An Introduction [[electronic resource] /] / by Bhimsen K. Shivamoggi
| Nonlinear Dynamics and Chaotic Phenomena: An Introduction [[electronic resource] /] / by Bhimsen K. Shivamoggi |
| Autore | Shivamoggi Bhimsen K |
| Edizione | [2nd ed. 2014.] |
| Pubbl/distr/stampa | Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (396 p.) |
| Disciplina | 514/.74 |
| Collana | Fluid Mechanics and Its Applications |
| Soggetto topico |
Mechanical engineering
Vibration Dynamical systems Dynamics Fluid mechanics Mechanical Engineering Vibration, Dynamical Systems, Control Engineering Fluid Dynamics |
| ISBN | 94-007-7094-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Nonlinear Ordinary Differential Equations -- 1.1 First-order Systems -- 1.1.1 Dynamical System -- 1.1.2 Lipschitz Condition -- 1.1.3 Gronwall’s Lemma -- 1.1.4 Linear Equations -- 1.1.5 Autonomous Equations -- 1.1.6 Stability of Equilibrium Points -- 1.1.6.1 Liapunov and Asymptotic Stability -- 1.1.6.2 Liapunov Function Method -- 1.1.7 Center Manifold Theorem -- 1.2 Phase-plane Analysis -- 1.3 Fully Nonlinear Evolution -- 1.4 Non-autonomous Systems -- 2 Bifurcation Theory -- 2.1 Stability and Bifurcation -- 2.2 Saddle-Node, Transcritical and Pitchfork Bifurcations -- 2.3 Hopf Bifurcation -- 2.4 Break-up of Bifurcations under Perturbations -- 2.5 Bifurcation Theory of One-Dimensional Maps -- 2.6 Appendix: The Normal Form Reduction -- 3 Hamiltonian Dynamics -- 3.1 Hamilton’s Equations -- 3.2 Phase Space -- 3.3 Canonical Transformations -- 3.4 The Hamilton-Jacobi Equation -- 3.5 Action-Angle Variables -- 3.6 Infinitesimal Canonical Transformations -- 3.7 Poisson’s Brackets -- 4 Integrable Systems -- 4.1 Separable Hamiltonian Systems -- 4.2 Integrable Systems -- 4.3 Dynamics on the Tori -- 4.4 Canonical Perturbation Theory -- 4.5 Komogorov-Arnol’d-Moser Theory -- 4.6 Breakdown of Integrability and Criteria for Transition to Chaos -- 4.6.1 Local Criteria -- 4.6.2 Local Stability vs. Global Stability -- 4.6.3 Global Criteria -- 4.7 Magnetic Island Overlap and Stochasticity in Magnetic Confinement Systems -- 4.8 Appendix: The Problem of Internal Resonance in Nonlinearly-Coupled Systems -- 5 Chaos in Conservative Systems -- 5.1 Phasse-Space Dynamics of Conservative Systems -- 5.2 Poincar´e’s Surface of Section -- 5.3 Area-preserving Mappings -- 5.4 Twist Maps -- 5.5 Tangent Maps -- 5.6 Poincar´e-Birkhoff Fixed-Point Theorem -- 5.7 Homoclinic and Heteroclinic Points -- 5.8 Quantitative Measures of Chaos -- 5.8.1 Liapunov Exponents -- 5.8.2 Kolmogorov Entropy -- 5.8.3 Autocorrelation Function -- 5.8.4 Power Spectra -- 5.9 Ergodicity and Mixing -- 5.9.1 Ergodicity -- 5.9.2 Mixing -- 5.9.3 Baker’s Tranformation -- 5.9.4 Lagrangian Chaos in Fluids -- 6 Chaos in Dissipative Systems -- 6.1 Phase-Space Dynamics of Dissipative Systems -- 6.2 Strange Attractors -- 6.3 Fractals -- 6.3.1 Examples of Fractals -- 6.3.2 Box-Counting Method -- 6.4 Multi-fractals -- 6.5 Analysis of Time Series Data -- 6.6 The Lorenz Attractor -- 6.6.1 Equilibrium Solutions and Their Stability -- 6.6.2 Slightly Supercritical Case -- 6.6.3 Existence of an Attractor -- 6.6.4 Chaotic Behavior of the Nonlinear Solutions -- 6.7 Period-Doubling Bifurcations -- 6.7.1 Difference Equations -- 6.7.2 The Logistic Map -- 6.8 Appendix: The Hausdorff-Besicovitch Dimension -- 6.9 Appendix: The Derivation of Lorenz’s Equations -- 6.10 Appendix: The Derivation of Universality for One-Dimensional Maps -- 7 Solitons -- 7.1 Fermi-Pasta-Ulam Recurrence -- 7.2 Korteweg-deVries Equation -- 7.3 Waves in an Anharmonic Lattice -- 7.4 Shallow Water Waves -- 7.5 Ion-acoustic Waves -- 7.6 Basic Properties of Korteweg-deVries Equation -- 7.6.1 Effect of Nonlinearity -- 7.6.2 Effect of Dispersion -- 7.6.3 Similarity Transformation -- 7.6.4 Stokes Waves: Periodic Solutions -- 7.6.5 Solitary Waves -- 7.6.6 Peridic Cnoidal Wave Solutions -- 7.6.7 Interacting Solitary Waves: Hirota’s Method -- 7.7 Inverse-Scattering Transform Method -- 7.7.1 Time Evolution of the Scattering Data -- 7.7.2 Gel’fand-Levitan-Marchenko Equation -- 7.7.3 Direct Scattering Problem -- 7.7.4 Inverse-Scattering Problem -- 7.8 Conservation Laws -- 7.9 Lax Formulation -- 7.10 B¨acklund Transformations -- 8 Singularity Analysis and the Painlev´e Property of Dynamical Systems -- 8.1 The Painlev´e Property -- 8.2 Singularity Analysis -- 8.3 The Painlev´e Property for Partial Differential Equations -- 9 Fractals and Multi-Fractals in Turbulence -- 9.1 Scale Invariance of the Navier-Stokes Equations and the Kolmogorov (1941) Theory -- 9.2 The β -model for Turbulence -- 9.3 The Multi-fractal Models -- 9.4 The Random-β Model -- 9.5 The Transition to Dissipation Range -- 9.6 Critical Phenomena Perspectives on the Turbulence Problem -- 10 Exercises -- 11 References -- 12 Index. |
| Record Nr. | UNINA-9910300399703321 |
|
Shivamoggi Bhimsen K
|
||
| Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Theoretical fluid dynamics [[electronic resource] /] / Bhimsen K. Shivamoggi
| Theoretical fluid dynamics [[electronic resource] /] / Bhimsen K. Shivamoggi |
| Autore | Shivamoggi Bhimsen K |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | New York, : John Wiley & Sons, 1998 |
| Descrizione fisica | 1 online resource (578 p.) |
| Disciplina | 532.050151 |
| Soggetto topico | Fluid dynamics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-75248-3
9786613677914 1-118-03078-8 1-118-03253-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Theoretical Fluid Dynamics; CONTENTS; Preface; Acknowledgments; Chapter 1. Review of Basic Concepts and Equations of Fluid Dynamics; 1.1 Introduction to Fluid Dynamics; Fluid Model of Systems; The Objective of Fluid Dynamics; The Fluid State; Description of the Flow Field; Volume Forces and Surface Forces; Relative Motion Near a Point; Stress-Strain Relations; Equations of Fluid Flows; The Transport Theorem; The Material Derivative; The Law of Conservation of Mass; Equation of Motion; The Energy Equation; The Equation of Vorticity; The Incompressible Fluid
Hamiltonian Formulation of Fluid-Flow ProblemsHamiltonian Dynamics of Continuous Systems; Three-Dimensional Incompressible Flows; 1.2 Surface Tension; Capillary Rises in Liquids; 1.3 A Program for Analysis of the Governing Equations; Chapter 2. Dynamics of Inviscid Incompressible Fluid Flows; 2.1 Fluid Kinematics and Dynamics; Stream Function; Equations of Motion; Integrals of Motion; Capillary Waves on a Spherical Drop; Cavitation; Rates of Change of Material Integrals; Irrotational Flow; Simple-Flow Patterns; The Source Flow; The Doublet Flow; The Vortex Flow; Doublet in a Uniform Stream Uniform Flow Past a Circular Cylinder with Circulation2.2 The Complex-Variable Method; The Complex Potential; Conformal Mapping of Flows; Hydrodynamic Images; Principles of Free-Streamline Flow; Schwartz-Christoffel Transformation; Hodograph Method; 2.3 Three-Dimensional Irrotational Flows; Special Singular Solutions; The Source Flow; The Doublet Flow; d'Alembert's Paradox; Image of a Source in a Sphere; Flow Past an Arbitrary Body; Unsteady Flows; Added Mass of Bodies Moving Through a Fluid; 2.4 Vortex Flows; Vortex Tubes; Induced Velocity Field; Biot-Savart's Law; Vortex Ring Hill's Spherical VortexVortex Sheet; The Vortex Breakdown: Brooke Benjamin's Theory; 2.5 Rotating Flows; Governing Equations and Elementary Results; Taylor-Proudman Theorem; Propagation of Waves in a Rotating Fluid; Plane Inertial Waves; Forced Wavemotion in a Rotating Fluid; The Elliptic Case; The Hyperbolic Case; Slow Motion Along the Axis of Rotation; Rossby Waves; 2.6 Water Waves; Governing Equations; Surface Waves in a Semi-infinite Liquid; Surface Waves in a Liquid Layer of Finite Depth; Shallow-Water Waves; Water Waves Generated by an Initial Displacement Over a Localized Region Water Waves Generated by a Finite Train of Harmonic WavesWaves on a Steady Stream; One-Dimensional Gravity Waves; One-Dimensional Capillary-Gravity Waves; Ship Waves; Gravity Waves in a Rotating Fluid; Theory of Tides; Nonlinear Shallow Water Waves; Solitary Waves; Periodic Cnoidal Waves; Interacting Solitary Waves; Stokes Waves; Modulational Instability and Envelope Solitons; Nonlinear Resonant Three-Wave Interactions of Capillary-Gravity Waves; Second-Harmonic Resonance; Hydraulic Jump; 2.7 Applications to Aerodynamics; Airfoil Theory: Method of Complex Variables Force and Moments on an Arbitrary Body |
| Record Nr. | UNINA-9910133453403321 |
|
Shivamoggi Bhimsen K
|
||
| New York, : John Wiley & Sons, 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Theoretical fluid dynamics [[electronic resource] /] / Bhimsen K. Shivamoggi
| Theoretical fluid dynamics [[electronic resource] /] / Bhimsen K. Shivamoggi |
| Autore | Shivamoggi Bhimsen K |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | New York, : John Wiley & Sons, 1998 |
| Descrizione fisica | 1 online resource (578 p.) |
| Disciplina | 532.050151 |
| Soggetto topico | Fluid dynamics |
| ISBN |
1-280-75248-3
9786613677914 1-118-03078-8 1-118-03253-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Theoretical Fluid Dynamics; CONTENTS; Preface; Acknowledgments; Chapter 1. Review of Basic Concepts and Equations of Fluid Dynamics; 1.1 Introduction to Fluid Dynamics; Fluid Model of Systems; The Objective of Fluid Dynamics; The Fluid State; Description of the Flow Field; Volume Forces and Surface Forces; Relative Motion Near a Point; Stress-Strain Relations; Equations of Fluid Flows; The Transport Theorem; The Material Derivative; The Law of Conservation of Mass; Equation of Motion; The Energy Equation; The Equation of Vorticity; The Incompressible Fluid
Hamiltonian Formulation of Fluid-Flow ProblemsHamiltonian Dynamics of Continuous Systems; Three-Dimensional Incompressible Flows; 1.2 Surface Tension; Capillary Rises in Liquids; 1.3 A Program for Analysis of the Governing Equations; Chapter 2. Dynamics of Inviscid Incompressible Fluid Flows; 2.1 Fluid Kinematics and Dynamics; Stream Function; Equations of Motion; Integrals of Motion; Capillary Waves on a Spherical Drop; Cavitation; Rates of Change of Material Integrals; Irrotational Flow; Simple-Flow Patterns; The Source Flow; The Doublet Flow; The Vortex Flow; Doublet in a Uniform Stream Uniform Flow Past a Circular Cylinder with Circulation2.2 The Complex-Variable Method; The Complex Potential; Conformal Mapping of Flows; Hydrodynamic Images; Principles of Free-Streamline Flow; Schwartz-Christoffel Transformation; Hodograph Method; 2.3 Three-Dimensional Irrotational Flows; Special Singular Solutions; The Source Flow; The Doublet Flow; d'Alembert's Paradox; Image of a Source in a Sphere; Flow Past an Arbitrary Body; Unsteady Flows; Added Mass of Bodies Moving Through a Fluid; 2.4 Vortex Flows; Vortex Tubes; Induced Velocity Field; Biot-Savart's Law; Vortex Ring Hill's Spherical VortexVortex Sheet; The Vortex Breakdown: Brooke Benjamin's Theory; 2.5 Rotating Flows; Governing Equations and Elementary Results; Taylor-Proudman Theorem; Propagation of Waves in a Rotating Fluid; Plane Inertial Waves; Forced Wavemotion in a Rotating Fluid; The Elliptic Case; The Hyperbolic Case; Slow Motion Along the Axis of Rotation; Rossby Waves; 2.6 Water Waves; Governing Equations; Surface Waves in a Semi-infinite Liquid; Surface Waves in a Liquid Layer of Finite Depth; Shallow-Water Waves; Water Waves Generated by an Initial Displacement Over a Localized Region Water Waves Generated by a Finite Train of Harmonic WavesWaves on a Steady Stream; One-Dimensional Gravity Waves; One-Dimensional Capillary-Gravity Waves; Ship Waves; Gravity Waves in a Rotating Fluid; Theory of Tides; Nonlinear Shallow Water Waves; Solitary Waves; Periodic Cnoidal Waves; Interacting Solitary Waves; Stokes Waves; Modulational Instability and Envelope Solitons; Nonlinear Resonant Three-Wave Interactions of Capillary-Gravity Waves; Second-Harmonic Resonance; Hydraulic Jump; 2.7 Applications to Aerodynamics; Airfoil Theory: Method of Complex Variables Force and Moments on an Arbitrary Body |
| Record Nr. | UNINA-9910830542503321 |
|
Shivamoggi Bhimsen K
|
||
| New York, : John Wiley & Sons, 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Theoretical fluid dynamics [[electronic resource] /] / Bhimsen K. Shivamoggi
| Theoretical fluid dynamics [[electronic resource] /] / Bhimsen K. Shivamoggi |
| Autore | Shivamoggi Bhimsen K |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | New York, : John Wiley & Sons, 1998 |
| Descrizione fisica | 1 online resource (578 p.) |
| Disciplina | 532.050151 |
| Soggetto topico | Fluid dynamics |
| ISBN |
1-280-75248-3
9786613677914 1-118-03078-8 1-118-03253-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Theoretical Fluid Dynamics; CONTENTS; Preface; Acknowledgments; Chapter 1. Review of Basic Concepts and Equations of Fluid Dynamics; 1.1 Introduction to Fluid Dynamics; Fluid Model of Systems; The Objective of Fluid Dynamics; The Fluid State; Description of the Flow Field; Volume Forces and Surface Forces; Relative Motion Near a Point; Stress-Strain Relations; Equations of Fluid Flows; The Transport Theorem; The Material Derivative; The Law of Conservation of Mass; Equation of Motion; The Energy Equation; The Equation of Vorticity; The Incompressible Fluid
Hamiltonian Formulation of Fluid-Flow ProblemsHamiltonian Dynamics of Continuous Systems; Three-Dimensional Incompressible Flows; 1.2 Surface Tension; Capillary Rises in Liquids; 1.3 A Program for Analysis of the Governing Equations; Chapter 2. Dynamics of Inviscid Incompressible Fluid Flows; 2.1 Fluid Kinematics and Dynamics; Stream Function; Equations of Motion; Integrals of Motion; Capillary Waves on a Spherical Drop; Cavitation; Rates of Change of Material Integrals; Irrotational Flow; Simple-Flow Patterns; The Source Flow; The Doublet Flow; The Vortex Flow; Doublet in a Uniform Stream Uniform Flow Past a Circular Cylinder with Circulation2.2 The Complex-Variable Method; The Complex Potential; Conformal Mapping of Flows; Hydrodynamic Images; Principles of Free-Streamline Flow; Schwartz-Christoffel Transformation; Hodograph Method; 2.3 Three-Dimensional Irrotational Flows; Special Singular Solutions; The Source Flow; The Doublet Flow; d'Alembert's Paradox; Image of a Source in a Sphere; Flow Past an Arbitrary Body; Unsteady Flows; Added Mass of Bodies Moving Through a Fluid; 2.4 Vortex Flows; Vortex Tubes; Induced Velocity Field; Biot-Savart's Law; Vortex Ring Hill's Spherical VortexVortex Sheet; The Vortex Breakdown: Brooke Benjamin's Theory; 2.5 Rotating Flows; Governing Equations and Elementary Results; Taylor-Proudman Theorem; Propagation of Waves in a Rotating Fluid; Plane Inertial Waves; Forced Wavemotion in a Rotating Fluid; The Elliptic Case; The Hyperbolic Case; Slow Motion Along the Axis of Rotation; Rossby Waves; 2.6 Water Waves; Governing Equations; Surface Waves in a Semi-infinite Liquid; Surface Waves in a Liquid Layer of Finite Depth; Shallow-Water Waves; Water Waves Generated by an Initial Displacement Over a Localized Region Water Waves Generated by a Finite Train of Harmonic WavesWaves on a Steady Stream; One-Dimensional Gravity Waves; One-Dimensional Capillary-Gravity Waves; Ship Waves; Gravity Waves in a Rotating Fluid; Theory of Tides; Nonlinear Shallow Water Waves; Solitary Waves; Periodic Cnoidal Waves; Interacting Solitary Waves; Stokes Waves; Modulational Instability and Envelope Solitons; Nonlinear Resonant Three-Wave Interactions of Capillary-Gravity Waves; Second-Harmonic Resonance; Hydraulic Jump; 2.7 Applications to Aerodynamics; Airfoil Theory: Method of Complex Variables Force and Moments on an Arbitrary Body |
| Record Nr. | UNINA-9910840979603321 |
|
Shivamoggi Bhimsen K
|
||
| New York, : John Wiley & Sons, 1998 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||