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Boundaries of a complex world / / Andrei Ludu
| Boundaries of a complex world / / Andrei Ludu |
| Autore | Ludu Andrei |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (372 pages) |
| Disciplina | 515.35 |
| Collana | Springer Series in Synergetics |
| Soggetto topico | Boundary value problems |
| ISBN | 3-031-07361-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface to the Second Edition -- Contents -- Acknowledgements -- Preface to the First Edition -- Part I Boundary in Arts and Humanities -- 1 Introduction -- 2 Boundary in Visual Perception and Arts -- 2.1 Is Our Visual Perception Two Dimensional or Three Dimensional? -- 2.2 Message of the Frame. Nonlineart -- 2.3 Importance of the Frame to the Image Inside -- 2.4 What Type of Mathematics Does Our Visual Brain Possess? -- 2.5 Framed Versus Non-framed -- 2.5.1 The Necessity of a Frame -- 2.5.2 Framed Paintings of Canvases -- 2.5.3 Eliminating Frame Effects -- 2.5.4 Frameless: Greek Pottery, Vermeer, and Feynman -- 2.6 Perception of Image Boundaries -- 2.6.1 Illusions and Frames -- 2.6.2 Bioinformatics -- 2.6.3 Representations of Boundaries in the Left and Right Cerebral Hemispheres -- 2.7 René Magritte and Bernhard Riemann -- 2.8 Appendix* -- 3 Boundary in Social Systems -- 3.1 Social Science Approach to Boundaries -- 3.1.1 Social and Collective Identity -- 3.1.2 Class, Ethnic, and Gender Inequality -- 3.1.3 Professions, Science, and Knowledge -- 3.1.4 Communities, National Identities, and Spatial Boundaries -- 3.2 Social Boundaries and Networks -- 3.3 Impact of Social Boundaries in Social Relations -- 3.4 Mathematical Approaches to Social Boundaries -- 3.5 Social Distance: Euclidean MetricSuperscript asterisk* -- 3.6 Social Distance: UltrametricSuperscript asterisk asterisk** -- 3.7 Social Topological BoundariesSuperscript asterisk asterisk** -- 3.8 Social Topological Patterns -- 3.8.1 Growth Models -- 3.8.2 Cooperation and Patterns -- 3.8.3 Multivariate NetworksSuperscript asterisk asterisk** -- 3.8.4 Pattern Formation in Unstable Social Systems -- 3.9 Epidemic Models with Moving Boundary -- 3.10 AppendixSuperscript asterisk asterisk** -- Part II Mathematical Language of Boundaries -- 310327_2_En_4_Chapter_OnlinePDF.
4 Boundary in Continuous Mathematics -- 4.2 Intuitive Introduction to Topology -- 4.2.1 SeparationSuperscript asterisk* -- 4.2.2 Compactness -- 4.2.3 Connectedness and Connectivity -- 4.3 Topological Boundary -- 4.4 Manifold BoundarySuperscript asterisk* -- 4.5 Forms and the Lie DerivativeSuperscript asterisk asterisk** -- 4.6 Fiber Bundles and Covariant DerivativeSuperscript asterisk asterisk** -- 4.7 Is the Lagrangian Derivative a Lie Derivative, or a Covariant Derivative? -- 4.7.1 Geometric and Physics Intuition -- 4.7.2 Mathematical ApproachSuperscript asterisk asterisk** -- 4.8 Deformation of the BoundarySuperscript asterisk* -- 4.9 Differential Topology of Boundaries. CobordismSuperscript asterisk asterisk** -- 5 Boundary in Discrete Mathematics -- 5.1 Structured Finite Sets -- 5.2 Formal Theory of Graphs* -- 5.3 Algebraic Theory and Spectra of Graphs* -- 5.3.1 Relations Between Eigenvalues and the Diameter -- 5.3.2 Relations Between Eigenvalues and Connectivity -- 5.3.3 Relations Between Eigenvalues and the Topology of a Graph -- 5.3.4 Relations Between Eigenvalues and Paths -- 5.3.5 Other Relations Between Eigenvalues -- 5.4 Graph Topology and Boundaries* -- 5.4.1 The Graph Topology and the Diameter -- 5.4.2 Embeddings -- 5.4.3 Isoperimetric Problems -- 5.4.4 Separations -- 5.4.5 Expanders -- 5.5 Algebraic Topology** -- 5.6 Classification of Continuous Structure by Discrete Criteria* -- 5.7 Triangulations and CW Complexes** -- 5.8 Connecting Discrete and Continuous -- Part III Importance of Boundary in Sciences -- 310327_2_En_6_Chapter_OnlinePDF -- 6 The Boundary in the Philosophy of Science -- 6.1 Boundaries in Epistemology -- 6.2 Triadic Classifications, Complexity, and Boundaries -- 6.3 Boundarylessness as the Philosophy of Vagueness -- 7 Networks and Their Boundaries -- 7.1 Complex Networks -- 7.2 World Networks. 7.3 The Shape of the Internet -- 7.4 Internet Is Its Own Boundary* -- 8 Big Data Systems -- 8.1 Data Dimensionality -- 8.2 Topology of Big Data: Persistent Homology** -- 8.3 Topology of Big Data: Regions with Holes** -- 9 Liquid Boundaries -- 9.1 Exotic Liquid Boundaries -- 9.2 Geometry of Inviscid Fluids* -- 9.3 Geometry of Viscous Fluids* -- 9.4 Soap Films with Boundary** -- 9.5 3D Drops* -- 9.6 Rotation of 3D Drops* -- 9.7 Rotation of 2D Drops* -- 9.8 Leidenfrost Drops -- 9.9 Spinning Polygons* -- 9.10 Universality in Rotating Fluid Patterns -- 9.10.1 Hollow Polygons on a Rotating Fluid Surface -- 9.10.2 Polygonal Eyewalls in Hurricanes -- 9.10.3 From the Lab to Saturn -- 9.11 Appendix: Second Fundamental Form -- 9.12 Appendix: Calculus of Variations -- 9.13 Appendix: n-Dimensional Rotating Drops -- 10 Conclusions -- 310327_2_En_BookBackmatter_OnlinePDF -- Index -- Appendix References. |
| Record Nr. | UNISA-996490349703316 |
Ludu Andrei
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Boundaries of a complex world / / Andrei Ludu
| Boundaries of a complex world / / Andrei Ludu |
| Autore | Ludu Andrei |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (372 pages) |
| Disciplina | 515.35 |
| Collana | Springer Series in Synergetics |
| Soggetto topico | Boundary value problems |
| ISBN | 3-031-07361-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface to the Second Edition -- Contents -- Acknowledgements -- Preface to the First Edition -- Part I Boundary in Arts and Humanities -- 1 Introduction -- 2 Boundary in Visual Perception and Arts -- 2.1 Is Our Visual Perception Two Dimensional or Three Dimensional? -- 2.2 Message of the Frame. Nonlineart -- 2.3 Importance of the Frame to the Image Inside -- 2.4 What Type of Mathematics Does Our Visual Brain Possess? -- 2.5 Framed Versus Non-framed -- 2.5.1 The Necessity of a Frame -- 2.5.2 Framed Paintings of Canvases -- 2.5.3 Eliminating Frame Effects -- 2.5.4 Frameless: Greek Pottery, Vermeer, and Feynman -- 2.6 Perception of Image Boundaries -- 2.6.1 Illusions and Frames -- 2.6.2 Bioinformatics -- 2.6.3 Representations of Boundaries in the Left and Right Cerebral Hemispheres -- 2.7 René Magritte and Bernhard Riemann -- 2.8 Appendix* -- 3 Boundary in Social Systems -- 3.1 Social Science Approach to Boundaries -- 3.1.1 Social and Collective Identity -- 3.1.2 Class, Ethnic, and Gender Inequality -- 3.1.3 Professions, Science, and Knowledge -- 3.1.4 Communities, National Identities, and Spatial Boundaries -- 3.2 Social Boundaries and Networks -- 3.3 Impact of Social Boundaries in Social Relations -- 3.4 Mathematical Approaches to Social Boundaries -- 3.5 Social Distance: Euclidean MetricSuperscript asterisk* -- 3.6 Social Distance: UltrametricSuperscript asterisk asterisk** -- 3.7 Social Topological BoundariesSuperscript asterisk asterisk** -- 3.8 Social Topological Patterns -- 3.8.1 Growth Models -- 3.8.2 Cooperation and Patterns -- 3.8.3 Multivariate NetworksSuperscript asterisk asterisk** -- 3.8.4 Pattern Formation in Unstable Social Systems -- 3.9 Epidemic Models with Moving Boundary -- 3.10 AppendixSuperscript asterisk asterisk** -- Part II Mathematical Language of Boundaries -- 310327_2_En_4_Chapter_OnlinePDF.
4 Boundary in Continuous Mathematics -- 4.2 Intuitive Introduction to Topology -- 4.2.1 SeparationSuperscript asterisk* -- 4.2.2 Compactness -- 4.2.3 Connectedness and Connectivity -- 4.3 Topological Boundary -- 4.4 Manifold BoundarySuperscript asterisk* -- 4.5 Forms and the Lie DerivativeSuperscript asterisk asterisk** -- 4.6 Fiber Bundles and Covariant DerivativeSuperscript asterisk asterisk** -- 4.7 Is the Lagrangian Derivative a Lie Derivative, or a Covariant Derivative? -- 4.7.1 Geometric and Physics Intuition -- 4.7.2 Mathematical ApproachSuperscript asterisk asterisk** -- 4.8 Deformation of the BoundarySuperscript asterisk* -- 4.9 Differential Topology of Boundaries. CobordismSuperscript asterisk asterisk** -- 5 Boundary in Discrete Mathematics -- 5.1 Structured Finite Sets -- 5.2 Formal Theory of Graphs* -- 5.3 Algebraic Theory and Spectra of Graphs* -- 5.3.1 Relations Between Eigenvalues and the Diameter -- 5.3.2 Relations Between Eigenvalues and Connectivity -- 5.3.3 Relations Between Eigenvalues and the Topology of a Graph -- 5.3.4 Relations Between Eigenvalues and Paths -- 5.3.5 Other Relations Between Eigenvalues -- 5.4 Graph Topology and Boundaries* -- 5.4.1 The Graph Topology and the Diameter -- 5.4.2 Embeddings -- 5.4.3 Isoperimetric Problems -- 5.4.4 Separations -- 5.4.5 Expanders -- 5.5 Algebraic Topology** -- 5.6 Classification of Continuous Structure by Discrete Criteria* -- 5.7 Triangulations and CW Complexes** -- 5.8 Connecting Discrete and Continuous -- Part III Importance of Boundary in Sciences -- 310327_2_En_6_Chapter_OnlinePDF -- 6 The Boundary in the Philosophy of Science -- 6.1 Boundaries in Epistemology -- 6.2 Triadic Classifications, Complexity, and Boundaries -- 6.3 Boundarylessness as the Philosophy of Vagueness -- 7 Networks and Their Boundaries -- 7.1 Complex Networks -- 7.2 World Networks. 7.3 The Shape of the Internet -- 7.4 Internet Is Its Own Boundary* -- 8 Big Data Systems -- 8.1 Data Dimensionality -- 8.2 Topology of Big Data: Persistent Homology** -- 8.3 Topology of Big Data: Regions with Holes** -- 9 Liquid Boundaries -- 9.1 Exotic Liquid Boundaries -- 9.2 Geometry of Inviscid Fluids* -- 9.3 Geometry of Viscous Fluids* -- 9.4 Soap Films with Boundary** -- 9.5 3D Drops* -- 9.6 Rotation of 3D Drops* -- 9.7 Rotation of 2D Drops* -- 9.8 Leidenfrost Drops -- 9.9 Spinning Polygons* -- 9.10 Universality in Rotating Fluid Patterns -- 9.10.1 Hollow Polygons on a Rotating Fluid Surface -- 9.10.2 Polygonal Eyewalls in Hurricanes -- 9.10.3 From the Lab to Saturn -- 9.11 Appendix: Second Fundamental Form -- 9.12 Appendix: Calculus of Variations -- 9.13 Appendix: n-Dimensional Rotating Drops -- 10 Conclusions -- 310327_2_En_BookBackmatter_OnlinePDF -- Index -- Appendix References. |
| Record Nr. | UNINA-9910595059803321 |
|
Ludu Andrei
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Boundaries of a complex world [[electronic resource] /] / by Andrei Ludu
| Boundaries of a complex world [[electronic resource] /] / by Andrei Ludu |
| Autore | Ludu Andrei |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (365 p.) |
| Disciplina | 530 |
| Collana | Springer Series in Synergetics |
| Soggetto topico |
Statistical physics
System theory Computational complexity Systems biology Ecology Physical geography Applications of Nonlinear Dynamics and Chaos Theory Complex Systems Complexity Systems Biology Theoretical Ecology/Statistics Earth System Sciences |
| ISBN | 3-662-49078-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Part I Arts and Nonlinear Systems: `Nonlineart' -- Part II Mathematical Language -- Part III Applications -- Conclusions -- References. |
| Record Nr. | UNINA-9910254623203321 |
|
Ludu Andrei
|
||
| Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Nonlinear waves and solitons on contours and closed surfaces / / Andrei Ludu
| Nonlinear waves and solitons on contours and closed surfaces / / Andrei Ludu |
| Autore | Ludu Andrei |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (583 pages) |
| Disciplina | 514.32 |
| Collana | Springer Series in Synergetics |
| Soggetto topico | Compact spaces |
| ISBN |
9783031146411
9783031146404 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Symbols -- 1 Introduction -- 1.1 Intuitive Introduction to Nonlinear Waves and Solitons -- 1.2 Integrability -- 1.3 Algebraic and Geometric Approaches -- 1.4 A List of Useful Derivatives in Finite Dimensional Spaces -- References -- Part I Mathematical Prerequisites -- 2 Topology and Algebra -- 2.1 What Is Topology -- 2.1.1 Topological Spaces and Separation -- 2.1.2 Compactness and Weierstrass-Stone Theorem -- 2.1.3 Connectedness and Homotopy -- 2.1.4 Separability and Metric Spaces -- 2.2 Elements of Homology -- 2.3 Group Action -- References -- 3 Vector Fields, Differential Forms, and Derivatives -- 3.1 Manifolds and Maps -- 3.2 Differential and Vector Fields -- 3.3 Existence and Uniqueness Theorems: Differential Equation Approach -- 3.4 Existence and Uniqueness Theorems: Flow Box Approach -- 3.5 Compact Supported Vector Fields -- 3.6 Differential Forms and the Lie Derivative -- 3.7 Differential Systems, Integrability and Invariants -- 3.8 Poincaré Lemma -- 3.9 Fiber Bundles and Covariant Derivative -- 3.9.1 Principal Bundle and Frames -- 3.9.2 Connection Form and Covariant Derivative -- 3.10 Tensor Analysis -- 3.11 The Mixed Covariant Derivative -- 3.12 Curvilinear Orthogonal Coordinates -- 3.13 Special Two-Dimensional Nonlinear Orthogonal Coordinates -- 3.14 Problems -- References -- 4 The Importance of the Boundary -- 4.1 The Power of Compact Boundaries: Representation Formulas -- 4.1.1 Representation Formula for n=1: Taylor Series -- 4.1.2 Representation Formula for n=2: Cauchy Formula -- 4.1.3 Representation Formula for n=3: Green Formula -- 4.1.4 Representation Formula in General: Stokes Theorem -- 4.2 Comments and Examples -- References -- Part II Curves and Surfaces -- 5 Geometry of Curves.
5.1 Elements of Differential Geometry of Curves -- 5.2 Closed Curves -- 5.3 Curves Lying on a Surface -- 5.4 Problems -- References -- 6 Geometry of Surfaces -- 6.1 Elements of Differential Geometry of Surfaces -- 6.2 Covariant Derivative and Connections -- 6.3 Geometry of Parameterized Surfaces Embedded in mathbbR3 -- 6.3.1 Christoffel Symbols and Covariant Differentiation for Hybrid Tensors -- 6.4 Compact Surfaces -- 6.5 Surface Differential Operators -- 6.5.1 Surface Gradient -- 6.5.2 Surface Divergence -- 6.5.3 Surface Laplacian -- 6.5.4 Surface Curl -- 6.5.5 Integral Relations for Surface Differential Operators -- 6.5.6 Applications -- 6.6 Problems -- References -- 7 Motion of Curves and Solitons -- 7.1 Kinematics of Two-Dimensional Curves -- 7.2 Mapping Two-Dimensional Curve Motion into Nonlinear Integrable Systems -- 7.3 The Time Evolution of Length and Area -- 7.4 Cartan Theory of Three-Dimensional Curve Motion -- 7.5 Kinematics of Three-Dimensional Curves -- 7.6 Mapping Three-Dimensional Curve Motion into Nonlinear Integrable Systems -- 7.7 Problems -- References -- 8 Theory of Motion of Surfaces -- 8.1 Differential Geometry of Surface Motion -- 8.2 Coordinates and Velocities on a Fluid Surface -- 8.3 Kinematics of Moving Surfaces -- 8.4 Dynamics of Moving Surfaces -- 8.5 Boundary Conditions for Moving Fluid Interfaces -- 8.6 Dynamics of the Fluid Interfaces -- 8.7 Problems -- References -- Part III Solitons and Nonlinear Waves on Closed Curves and Surfaces -- 9 Kinematics of Fluids -- 9.1 Lagrangian Verses Eulerian Frames -- 9.1.1 Introduction -- 9.1.2 Geometrical Picture for Lagrangian Verses Eulerian -- 9.2 Fluid Fiber Bundle -- 9.2.1 Introduction -- 9.2.2 Motivation for a Geometrical Approach -- 9.2.3 The Fiber Bundle -- 9.2.4 Fixed Fluid Container -- 9.2.5 Free Surface Fiber Bundle. 9.2.6 How Does the Time Derivative of Tensors Transform from Euler to Lagrange Frame? -- 9.3 Path Lines, Stream Lines, and Particle Contours -- 9.4 Eulerian-Lagrangian Description for Moving Curves -- 9.5 The Free Surface -- 9.6 Equation of Continuity -- 9.6.1 Introduction -- 9.6.2 Solutions of the Continuity Equation on Compact Intervals -- 9.7 Problems -- References -- 10 Hydrodynamics -- 10.1 Momentum Conservation: Euler and Navier-Stokes Equations -- 10.2 Boundary Conditions -- 10.3 Circulation Theorem -- 10.4 Surface Tension -- 10.4.1 Physical Problem -- 10.4.2 Minimal Surfaces -- 10.4.3 Application -- 10.4.4 Isothermal Parametrization -- 10.4.5 Topological Properties of Minimal Surfaces -- 10.4.6 General Condition for Minimal Surfaces -- 10.4.7 Surface Tension for Almost Isothermal Parametrization -- 10.5 Special Fluids -- 10.6 Representation Theorems in Fluid Dynamics -- 10.6.1 Helmholtz Decomposition Theorem in mathbbR3 -- 10.6.2 Decomposition Formula for Transversal Isotropic Vector Fields -- 10.6.3 Solenoidal-Toroidal Decomposition Formulas -- 10.7 Problems -- References -- 11 Nonlinear Surface Waves in One Dimension -- 11.1 KdV Equation Deduction for Shallow Waters -- 11.2 Smooth Transitions Between Periodic and Aperiodic Solutions -- 11.3 Modified KdV Equation and Generalizations -- 11.4 Hydrodynamic Equations Involving Higher-Order Nonlinearities -- 11.4.1 A Compact Version for KdV -- 11.4.2 Small Amplitude Approximation -- 11.4.3 Dispersion Relations -- 11.4.4 The Full Equation -- 11.4.5 Reduction of GKdV to Other Equations and Solutions -- 11.4.6 The Finite Difference Form -- 11.5 Boussinesq Equations on a Circle -- References -- 12 Nonlinear Surface Waves in Two Dimensions -- 12.1 Geometry of Two-Dimensional Flow -- 12.2 Two-Dimensional Nonlinear Equations -- 12.3 Two-Dimensional Fluid Systems with Moving Boundary. 12.4 Oscillations in Two-Dimensional Liquid Drops -- 12.5 Contours Described by Quartic Closed Curves -- 12.6 Nonlinear Waves in Rotating Leidenfrost Drops -- References -- 13 Dynamics of Two-Dimensional Fluid in Bounded Domain via Conformal Variables (A. Chernyavsky and S. Dyachenko) -- 13.1 Introduction -- 13.2 Mechanics of Droplet and the Conformal Map -- 13.2.1 The Hamiltonian, Momentum and Angular Momentum -- 13.2.2 The Center of Mass -- 13.3 The Complex Equations of Motion -- 13.3.1 Kinematic Equation -- 13.3.2 Dynamic Condition -- 13.4 Traveling Waves Around a Disk -- 13.5 Linear Waves -- 13.6 Numerical Simulation -- 13.7 Series Solution -- 13.8 Nonlinear Waves -- 13.9 Conclusion -- References -- 14 Nonlinear Surface Waves in Three Dimensions -- 14.1 Oscillations of Inviscid Drops: The Linear Model -- 14.1.1 Drop Immersed in Another Fluid -- 14.1.2 Drop with Rigid Core -- 14.1.3 Moving Core -- 14.1.4 Drop Volume -- 14.2 Oscillations of Viscous Drops: The Linear Model -- 14.2.1 Model 1 -- 14.3 Nonlinear Three-Dimensional Oscillations of Axisymmetric Drops -- 14.3.1 Nonlinear Resonances in Drop Oscillation -- 14.4 Other Nonlinear Effects in Drop Oscillations -- 14.5 Solitons on the Surface of Liquid Drops -- 14.6 Problems -- References -- 15 Other Special Nonlinear Compact Systems -- 15.1 Solitons on Interfaces of Layered Fluid Droplet (Written by A. S. Carstea) -- 15.2 Nonlinear Compact Shapes and Collective Motion -- 15.3 The Hamiltonian Structure for Free Boundary Problems on Compact Surfaces -- References -- Part IV Physical Nonlinear Systems at Different Scales -- 16 Filaments, Chains, and Solitons -- 16.1 Vortex Filaments -- 16.1.1 Gas Dynamics Filament Model and Solitons -- 16.1.2 Special Solutions -- 16.1.3 Integration of Serret-Frenet Equations for Filaments -- 16.1.4 The Riccati Form of the Serret-Frenet Equations. 16.2 Soliton Solutions on the Vortex Filament -- 16.2.1 Constant Torsion Vortex Filaments -- 16.2.2 Vortex Filaments and the Nonlinear Schrödinger Equation -- 16.3 Closed Curves Solitons -- 16.4 Nonlinear Dynamics of Stiff Chains -- 16.5 Problems -- References -- 17 Solitons on the Boundaries of Microscopic Systems -- 17.1 Solitons as Elementary Particles -- 17.2 Quantization of Solitons on a Closed Contour and Instantons -- 17.3 Clusters as Solitary Waves on the Nuclear Surface -- 17.4 Nonlinear Schrödinger Equation Solitons on Quantum … -- 17.5 Solitons and Quasimolecular Structure -- 17.6 Soliton Model for Heavy Emitted Nuclear Clusters -- 17.7 Quintic Nonlinear Schrödinger Equation for Nuclear Cluster Decay -- 17.8 Contour Solitons in the Quantum Hall Liquid -- References -- 18 Nonlinear Contour Dynamics in Macroscopic Systems -- 18.1 Plasma Vortex -- 18.1.1 Effective Surface Tension in Magnetohydrodynamics and Plasma Systems -- 18.1.2 Trajectories in Magnetic Field Configurations -- 18.1.3 Magnetic Surfaces in Static Equilibrium -- 18.2 Elastic Spheres -- 18.3 Curvature Dependent Nonlinear Diffusion on Closed Surfaces -- 18.4 Nonlinear Evolution of Oscillation Modes in Neutron Stars -- References -- 19 Mathematical Appendix -- 19.1 Differentiable Manifolds -- 19.2 Riccati Equation -- 19.3 Special Functions -- 19.4 One-Soliton Solutions for the KdV, MKdV, and Their Combination -- 19.5 Scaling and Nonlinear Dispersion Relations1 -- References -- Index. |
| Record Nr. | UNISA-996499864303316 |
|
Ludu Andrei
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Nonlinear waves and solitons on contours and closed surfaces / / Andrei Ludu
| Nonlinear waves and solitons on contours and closed surfaces / / Andrei Ludu |
| Autore | Ludu Andrei |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (583 pages) |
| Disciplina | 514.32 |
| Collana | Springer Series in Synergetics |
| Soggetto topico | Compact spaces |
| ISBN |
9783031146411
9783031146404 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Preface to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- Symbols -- 1 Introduction -- 1.1 Intuitive Introduction to Nonlinear Waves and Solitons -- 1.2 Integrability -- 1.3 Algebraic and Geometric Approaches -- 1.4 A List of Useful Derivatives in Finite Dimensional Spaces -- References -- Part I Mathematical Prerequisites -- 2 Topology and Algebra -- 2.1 What Is Topology -- 2.1.1 Topological Spaces and Separation -- 2.1.2 Compactness and Weierstrass-Stone Theorem -- 2.1.3 Connectedness and Homotopy -- 2.1.4 Separability and Metric Spaces -- 2.2 Elements of Homology -- 2.3 Group Action -- References -- 3 Vector Fields, Differential Forms, and Derivatives -- 3.1 Manifolds and Maps -- 3.2 Differential and Vector Fields -- 3.3 Existence and Uniqueness Theorems: Differential Equation Approach -- 3.4 Existence and Uniqueness Theorems: Flow Box Approach -- 3.5 Compact Supported Vector Fields -- 3.6 Differential Forms and the Lie Derivative -- 3.7 Differential Systems, Integrability and Invariants -- 3.8 Poincaré Lemma -- 3.9 Fiber Bundles and Covariant Derivative -- 3.9.1 Principal Bundle and Frames -- 3.9.2 Connection Form and Covariant Derivative -- 3.10 Tensor Analysis -- 3.11 The Mixed Covariant Derivative -- 3.12 Curvilinear Orthogonal Coordinates -- 3.13 Special Two-Dimensional Nonlinear Orthogonal Coordinates -- 3.14 Problems -- References -- 4 The Importance of the Boundary -- 4.1 The Power of Compact Boundaries: Representation Formulas -- 4.1.1 Representation Formula for n=1: Taylor Series -- 4.1.2 Representation Formula for n=2: Cauchy Formula -- 4.1.3 Representation Formula for n=3: Green Formula -- 4.1.4 Representation Formula in General: Stokes Theorem -- 4.2 Comments and Examples -- References -- Part II Curves and Surfaces -- 5 Geometry of Curves.
5.1 Elements of Differential Geometry of Curves -- 5.2 Closed Curves -- 5.3 Curves Lying on a Surface -- 5.4 Problems -- References -- 6 Geometry of Surfaces -- 6.1 Elements of Differential Geometry of Surfaces -- 6.2 Covariant Derivative and Connections -- 6.3 Geometry of Parameterized Surfaces Embedded in mathbbR3 -- 6.3.1 Christoffel Symbols and Covariant Differentiation for Hybrid Tensors -- 6.4 Compact Surfaces -- 6.5 Surface Differential Operators -- 6.5.1 Surface Gradient -- 6.5.2 Surface Divergence -- 6.5.3 Surface Laplacian -- 6.5.4 Surface Curl -- 6.5.5 Integral Relations for Surface Differential Operators -- 6.5.6 Applications -- 6.6 Problems -- References -- 7 Motion of Curves and Solitons -- 7.1 Kinematics of Two-Dimensional Curves -- 7.2 Mapping Two-Dimensional Curve Motion into Nonlinear Integrable Systems -- 7.3 The Time Evolution of Length and Area -- 7.4 Cartan Theory of Three-Dimensional Curve Motion -- 7.5 Kinematics of Three-Dimensional Curves -- 7.6 Mapping Three-Dimensional Curve Motion into Nonlinear Integrable Systems -- 7.7 Problems -- References -- 8 Theory of Motion of Surfaces -- 8.1 Differential Geometry of Surface Motion -- 8.2 Coordinates and Velocities on a Fluid Surface -- 8.3 Kinematics of Moving Surfaces -- 8.4 Dynamics of Moving Surfaces -- 8.5 Boundary Conditions for Moving Fluid Interfaces -- 8.6 Dynamics of the Fluid Interfaces -- 8.7 Problems -- References -- Part III Solitons and Nonlinear Waves on Closed Curves and Surfaces -- 9 Kinematics of Fluids -- 9.1 Lagrangian Verses Eulerian Frames -- 9.1.1 Introduction -- 9.1.2 Geometrical Picture for Lagrangian Verses Eulerian -- 9.2 Fluid Fiber Bundle -- 9.2.1 Introduction -- 9.2.2 Motivation for a Geometrical Approach -- 9.2.3 The Fiber Bundle -- 9.2.4 Fixed Fluid Container -- 9.2.5 Free Surface Fiber Bundle. 9.2.6 How Does the Time Derivative of Tensors Transform from Euler to Lagrange Frame? -- 9.3 Path Lines, Stream Lines, and Particle Contours -- 9.4 Eulerian-Lagrangian Description for Moving Curves -- 9.5 The Free Surface -- 9.6 Equation of Continuity -- 9.6.1 Introduction -- 9.6.2 Solutions of the Continuity Equation on Compact Intervals -- 9.7 Problems -- References -- 10 Hydrodynamics -- 10.1 Momentum Conservation: Euler and Navier-Stokes Equations -- 10.2 Boundary Conditions -- 10.3 Circulation Theorem -- 10.4 Surface Tension -- 10.4.1 Physical Problem -- 10.4.2 Minimal Surfaces -- 10.4.3 Application -- 10.4.4 Isothermal Parametrization -- 10.4.5 Topological Properties of Minimal Surfaces -- 10.4.6 General Condition for Minimal Surfaces -- 10.4.7 Surface Tension for Almost Isothermal Parametrization -- 10.5 Special Fluids -- 10.6 Representation Theorems in Fluid Dynamics -- 10.6.1 Helmholtz Decomposition Theorem in mathbbR3 -- 10.6.2 Decomposition Formula for Transversal Isotropic Vector Fields -- 10.6.3 Solenoidal-Toroidal Decomposition Formulas -- 10.7 Problems -- References -- 11 Nonlinear Surface Waves in One Dimension -- 11.1 KdV Equation Deduction for Shallow Waters -- 11.2 Smooth Transitions Between Periodic and Aperiodic Solutions -- 11.3 Modified KdV Equation and Generalizations -- 11.4 Hydrodynamic Equations Involving Higher-Order Nonlinearities -- 11.4.1 A Compact Version for KdV -- 11.4.2 Small Amplitude Approximation -- 11.4.3 Dispersion Relations -- 11.4.4 The Full Equation -- 11.4.5 Reduction of GKdV to Other Equations and Solutions -- 11.4.6 The Finite Difference Form -- 11.5 Boussinesq Equations on a Circle -- References -- 12 Nonlinear Surface Waves in Two Dimensions -- 12.1 Geometry of Two-Dimensional Flow -- 12.2 Two-Dimensional Nonlinear Equations -- 12.3 Two-Dimensional Fluid Systems with Moving Boundary. 12.4 Oscillations in Two-Dimensional Liquid Drops -- 12.5 Contours Described by Quartic Closed Curves -- 12.6 Nonlinear Waves in Rotating Leidenfrost Drops -- References -- 13 Dynamics of Two-Dimensional Fluid in Bounded Domain via Conformal Variables (A. Chernyavsky and S. Dyachenko) -- 13.1 Introduction -- 13.2 Mechanics of Droplet and the Conformal Map -- 13.2.1 The Hamiltonian, Momentum and Angular Momentum -- 13.2.2 The Center of Mass -- 13.3 The Complex Equations of Motion -- 13.3.1 Kinematic Equation -- 13.3.2 Dynamic Condition -- 13.4 Traveling Waves Around a Disk -- 13.5 Linear Waves -- 13.6 Numerical Simulation -- 13.7 Series Solution -- 13.8 Nonlinear Waves -- 13.9 Conclusion -- References -- 14 Nonlinear Surface Waves in Three Dimensions -- 14.1 Oscillations of Inviscid Drops: The Linear Model -- 14.1.1 Drop Immersed in Another Fluid -- 14.1.2 Drop with Rigid Core -- 14.1.3 Moving Core -- 14.1.4 Drop Volume -- 14.2 Oscillations of Viscous Drops: The Linear Model -- 14.2.1 Model 1 -- 14.3 Nonlinear Three-Dimensional Oscillations of Axisymmetric Drops -- 14.3.1 Nonlinear Resonances in Drop Oscillation -- 14.4 Other Nonlinear Effects in Drop Oscillations -- 14.5 Solitons on the Surface of Liquid Drops -- 14.6 Problems -- References -- 15 Other Special Nonlinear Compact Systems -- 15.1 Solitons on Interfaces of Layered Fluid Droplet (Written by A. S. Carstea) -- 15.2 Nonlinear Compact Shapes and Collective Motion -- 15.3 The Hamiltonian Structure for Free Boundary Problems on Compact Surfaces -- References -- Part IV Physical Nonlinear Systems at Different Scales -- 16 Filaments, Chains, and Solitons -- 16.1 Vortex Filaments -- 16.1.1 Gas Dynamics Filament Model and Solitons -- 16.1.2 Special Solutions -- 16.1.3 Integration of Serret-Frenet Equations for Filaments -- 16.1.4 The Riccati Form of the Serret-Frenet Equations. 16.2 Soliton Solutions on the Vortex Filament -- 16.2.1 Constant Torsion Vortex Filaments -- 16.2.2 Vortex Filaments and the Nonlinear Schrödinger Equation -- 16.3 Closed Curves Solitons -- 16.4 Nonlinear Dynamics of Stiff Chains -- 16.5 Problems -- References -- 17 Solitons on the Boundaries of Microscopic Systems -- 17.1 Solitons as Elementary Particles -- 17.2 Quantization of Solitons on a Closed Contour and Instantons -- 17.3 Clusters as Solitary Waves on the Nuclear Surface -- 17.4 Nonlinear Schrödinger Equation Solitons on Quantum … -- 17.5 Solitons and Quasimolecular Structure -- 17.6 Soliton Model for Heavy Emitted Nuclear Clusters -- 17.7 Quintic Nonlinear Schrödinger Equation for Nuclear Cluster Decay -- 17.8 Contour Solitons in the Quantum Hall Liquid -- References -- 18 Nonlinear Contour Dynamics in Macroscopic Systems -- 18.1 Plasma Vortex -- 18.1.1 Effective Surface Tension in Magnetohydrodynamics and Plasma Systems -- 18.1.2 Trajectories in Magnetic Field Configurations -- 18.1.3 Magnetic Surfaces in Static Equilibrium -- 18.2 Elastic Spheres -- 18.3 Curvature Dependent Nonlinear Diffusion on Closed Surfaces -- 18.4 Nonlinear Evolution of Oscillation Modes in Neutron Stars -- References -- 19 Mathematical Appendix -- 19.1 Differentiable Manifolds -- 19.2 Riccati Equation -- 19.3 Special Functions -- 19.4 One-Soliton Solutions for the KdV, MKdV, and Their Combination -- 19.5 Scaling and Nonlinear Dispersion Relations1 -- References -- Index. |
| Record Nr. | UNINA-9910624313903321 |
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Ludu Andrei
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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The Application of Mathematics to Physics and Nonlinear Science
| The Application of Mathematics to Physics and Nonlinear Science |
| Autore | Ludu Andrei |
| Pubbl/distr/stampa | MDPI - Multidisciplinary Digital Publishing Institute, 2020 |
| Descrizione fisica | 1 electronic resource (122 p.) |
| Soggetto non controllato |
diffusion
viral infection non-Newtonian fluid convergence Navier–Stokes–Voigt equations existence Lyapunov functional Faedo–Galerkin approximations probability distribution strong solutions stability multigrid method parabolic equations long-time behavior Fokker–Planck equation viscoelastic models Cauchy problem unconditionally gradient stable scheme uniqueness existence and uniqueness theorem continuum spectrum pulse equation Stokes operator Lagrangian scheme Cahn–Hilliard equation Feller equation |
| ISBN | 3-03928-727-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910404088203321 |
|
Ludu Andrei
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||
| MDPI - Multidisciplinary Digital Publishing Institute, 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||