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Braids and dynamics / / Jean-Luc Thiffeault
| Braids and dynamics / / Jean-Luc Thiffeault |
| Autore | Thiffeault Jean-Luc |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (147 pages) |
| Disciplina | 514.224 |
| Collana | Frontiers in applied dynamical systems |
| Soggetto topico |
Braid theory
Fluid dynamics Dynamics Dinàmica de fluids |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031047909
9783031047893 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 1.1 Motivation: Fluid Mixing -- 1.2 Taffy Pullers -- 1.3 Outline -- 2 Topological Dynamics on the Torus -- 2.1 Diffeomorphisms of the Torus -- 2.2 The Fundamental Group of a Surface -- 2.3 The Mapping Class Group of the Torus -- 2.4 Classification of MCG(T2) -- 2.4.1 Elliptic Case -- 2.4.2 Parabolic Case -- 2.4.3 Hyperbolic Case -- 2.5 Summary -- 3 Stretching with Three Rods -- 3.1 From the Torus to the Sphere -- 3.2 The Mapping Class Groups of S4 and D3 -- 3.3 Dehn Twists -- 3.4 Fluid Stirring with Three Rods -- 3.5 Taffy Pulling with Three Rods -- 3.6 Summary -- 4 Braids -- 4.1 Braids as Particle Dances -- 4.2 Algebraic Braids -- 4.3 Artin's Representation -- 4.4 Free Homotopy Representation -- 4.5 The Burau Representation -- 4.6 Summary -- 5 The Thurston-Nielsen Classification -- 5.1 Classification of Diffeomorphisms of a Surface -- 5.2 Pseudo-Anosov Maps -- 5.3 The Degree of the Dilatation -- 5.4 Summary -- 6 Topological Entropy -- 6.1 Definition -- 6.2 Word Length Growth -- 6.3 The Burau Estimate for the Dilatation -- 6.4 An Upper Bound -- 6.5 Summary -- 7 Train Tracks -- 7.1 The Figure-Eight Stirring Device -- 7.2 A Second Pseudo-Anosov Example -- 7.3 A Reducible Example -- 7.4 Finding Cancellations -- 7.5 Summary -- 8 Dynnikov Coordinates -- 8.1 Coordinates for Multicurves -- 8.2 Action of Braids on Dynnikov Coordinates (Update Rules) -- 8.2.1 Update Rules for sigmai -- 8.2.2 Update Rules for sigmaiinv -- 8.3 Max-Plus Algebra -- 8.4 Mapping Classes and Dynnikov Coordinates -- 8.4.1 Finite-Order Case -- 8.4.2 Reducible Case -- 8.4.3 Pseudo-Anosov Case -- 8.5 The Word Problem -- 8.6 Summary -- 9 The Braidlab Library -- 9.1 Setup and Getting Help -- 9.2 Braids -- 9.2.1 Basic Operations -- 9.2.2 Representation and Invariants -- 9.3 Loops -- 9.3.1 Acting on Loops with Braids.
9.3.2 Loop Coordinates for a Braid -- 9.4 Entropy and Train Tracks -- 9.4.1 Topological Entropy and Complexity -- 9.4.2 Train Track Map and Transition Matrix -- 9.5 Summary -- 10 Braids and Data Analysis -- 10.1 Braids from Closed Trajectories -- 10.1.1 Constructing a Braid from Orbit Data -- 10.1.2 An Example: Taffy Pullers -- 10.1.3 Changing the Projection Line -- 10.2 Braids from Non-closed Trajectories -- 10.2.1 Constructing a Braid from Data: An Example -- 10.2.2 Changing the Projection Line and Enforcing Closure -- 10.2.3 Finite-Time Braiding Exponent (FTBE) -- 10.3 Summary -- Derivation of Dynnikov Update Rules (Spencer A. Smith) -- A.1 Dynnikov Coordinates -- A.2 Whitehead Moves -- A.2.1 Triangulation Coordinates -- A.2.2 Whitehead Move and Update Rule -- A.3 Deriving the Update Rules -- A.3.1 Counterclockwise Switch -- A.3.2 Equivalence of Update Rules -- A.3.3 Clockwise Switch -- A.3.4 Edge Cases -- References -- Index. |
| Record Nr. | UNISA-996490347603316 |
Thiffeault Jean-Luc
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Braids and dynamics / / Jean-Luc Thiffeault
| Braids and dynamics / / Jean-Luc Thiffeault |
| Autore | Thiffeault Jean-Luc |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (147 pages) |
| Disciplina | 514.224 |
| Collana | Frontiers in applied dynamical systems |
| Soggetto topico |
Braid theory
Fluid dynamics Dynamics Dinàmica de fluids |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031047909
9783031047893 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 1.1 Motivation: Fluid Mixing -- 1.2 Taffy Pullers -- 1.3 Outline -- 2 Topological Dynamics on the Torus -- 2.1 Diffeomorphisms of the Torus -- 2.2 The Fundamental Group of a Surface -- 2.3 The Mapping Class Group of the Torus -- 2.4 Classification of MCG(T2) -- 2.4.1 Elliptic Case -- 2.4.2 Parabolic Case -- 2.4.3 Hyperbolic Case -- 2.5 Summary -- 3 Stretching with Three Rods -- 3.1 From the Torus to the Sphere -- 3.2 The Mapping Class Groups of S4 and D3 -- 3.3 Dehn Twists -- 3.4 Fluid Stirring with Three Rods -- 3.5 Taffy Pulling with Three Rods -- 3.6 Summary -- 4 Braids -- 4.1 Braids as Particle Dances -- 4.2 Algebraic Braids -- 4.3 Artin's Representation -- 4.4 Free Homotopy Representation -- 4.5 The Burau Representation -- 4.6 Summary -- 5 The Thurston-Nielsen Classification -- 5.1 Classification of Diffeomorphisms of a Surface -- 5.2 Pseudo-Anosov Maps -- 5.3 The Degree of the Dilatation -- 5.4 Summary -- 6 Topological Entropy -- 6.1 Definition -- 6.2 Word Length Growth -- 6.3 The Burau Estimate for the Dilatation -- 6.4 An Upper Bound -- 6.5 Summary -- 7 Train Tracks -- 7.1 The Figure-Eight Stirring Device -- 7.2 A Second Pseudo-Anosov Example -- 7.3 A Reducible Example -- 7.4 Finding Cancellations -- 7.5 Summary -- 8 Dynnikov Coordinates -- 8.1 Coordinates for Multicurves -- 8.2 Action of Braids on Dynnikov Coordinates (Update Rules) -- 8.2.1 Update Rules for sigmai -- 8.2.2 Update Rules for sigmaiinv -- 8.3 Max-Plus Algebra -- 8.4 Mapping Classes and Dynnikov Coordinates -- 8.4.1 Finite-Order Case -- 8.4.2 Reducible Case -- 8.4.3 Pseudo-Anosov Case -- 8.5 The Word Problem -- 8.6 Summary -- 9 The Braidlab Library -- 9.1 Setup and Getting Help -- 9.2 Braids -- 9.2.1 Basic Operations -- 9.2.2 Representation and Invariants -- 9.3 Loops -- 9.3.1 Acting on Loops with Braids.
9.3.2 Loop Coordinates for a Braid -- 9.4 Entropy and Train Tracks -- 9.4.1 Topological Entropy and Complexity -- 9.4.2 Train Track Map and Transition Matrix -- 9.5 Summary -- 10 Braids and Data Analysis -- 10.1 Braids from Closed Trajectories -- 10.1.1 Constructing a Braid from Orbit Data -- 10.1.2 An Example: Taffy Pullers -- 10.1.3 Changing the Projection Line -- 10.2 Braids from Non-closed Trajectories -- 10.2.1 Constructing a Braid from Data: An Example -- 10.2.2 Changing the Projection Line and Enforcing Closure -- 10.2.3 Finite-Time Braiding Exponent (FTBE) -- 10.3 Summary -- Derivation of Dynnikov Update Rules (Spencer A. Smith) -- A.1 Dynnikov Coordinates -- A.2 Whitehead Moves -- A.2.1 Triangulation Coordinates -- A.2.2 Whitehead Move and Update Rule -- A.3 Deriving the Update Rules -- A.3.1 Counterclockwise Switch -- A.3.2 Equivalence of Update Rules -- A.3.3 Clockwise Switch -- A.3.4 Edge Cases -- References -- Index. |
| Record Nr. | UNINA-9910592982603321 |
|
Thiffeault Jean-Luc
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Equations of motion for incompressible viscous fluids : with mixed boundary conditions / / Tujin Kim, Daomin Cao
| Equations of motion for incompressible viscous fluids : with mixed boundary conditions / / Tujin Kim, Daomin Cao |
| Autore | Kim Tujin |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (374 pages) |
| Disciplina | 515 |
| Collana | Advances in Mathematical Fluid Mechanics |
| Soggetto topico |
Dinàmica de fluids
Problemes de contorn Calculus Functions Harmonic analysis Mathematical analysis |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-78659-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466403903316 |
|
Kim Tujin
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Equations of motion for incompressible viscous fluids : with mixed boundary conditions / / Tujin Kim, Daomin Cao
| Equations of motion for incompressible viscous fluids : with mixed boundary conditions / / Tujin Kim, Daomin Cao |
| Autore | Kim Tujin |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (374 pages) |
| Disciplina | 515 |
| Collana | Advances in Mathematical Fluid Mechanics |
| Soggetto topico |
Dinàmica de fluids
Problemes de contorn Calculus Functions Harmonic analysis Mathematical analysis |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-78659-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910503002103321 |
|
Kim Tujin
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometry, mechanics, and control in action for the falling cat / / Toshihiro Iwai
| Geometry, mechanics, and control in action for the falling cat / / Toshihiro Iwai |
| Autore | Iwai Toshihiro |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (193 pages) |
| Disciplina | 532.05 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Fluid dynamics
Geometric function theory Dinàmica de fluids Teoria geomètrica de funcions |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-0688-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466549303316 |
|
Iwai Toshihiro
|
||
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Geometry, mechanics, and control in action for the falling cat / / Toshihiro Iwai
| Geometry, mechanics, and control in action for the falling cat / / Toshihiro Iwai |
| Autore | Iwai Toshihiro |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (193 pages) |
| Disciplina | 532.05 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Fluid dynamics
Geometric function theory Dinàmica de fluids Teoria geomètrica de funcions |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-0688-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910483590003321 |
|
Iwai Toshihiro
|
||
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Laplacian growth on branched Riemann surfaces / / Bjö Gustafsson and Yu-Lin Lin
| Laplacian growth on branched Riemann surfaces / / Bjö Gustafsson and Yu-Lin Lin |
| Autore | Gustafsson Björn <1947-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (163 pages) : illustrations |
| Disciplina | 532.053 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Fluid dynamics
Geometric function theory Dinàmica de fluids Teoria geomètrica de funcions |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-69863-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 General Background -- 1.2 Loss of Univalence, Several Scenarios -- 1.3 On the Construction of a Branched Riemann Surface -- 1.4 Moment Coordinates and the String Equation -- 1.5 Outlooks to Physics -- 1.6 Acknowledgements -- 2 The Polubarinova-Galin and Löwner-Kufarev Equations -- 2.1 Basic Set Up in the Univalent Case -- 2.2 Dynamics and Subordination -- 2.3 The Polubarinova-Galin Versus the Löwner-Kufarev Equation -- 3 Weak Solutions and Balayage -- 3.1 Weak Formulation of the Polubarinova-Galin Equation -- 3.2 Weak Solutions in Terms of Balayage -- 3.3 Inverse Balayage -- 3.4 More General Laplacian Evolutions -- 3.5 Regularity of the Boundary via the Exponential Transform -- 3.6 The Resultant and the Elimination Function -- 4 Weak and Strong Solutions on Riemann Surfaces -- 4.1 Laplacian Growth on Manifolds -- 4.2 Examples -- 4.3 The Riemann Surface Solution Pulled Back to the Unit Disk -- 4.4 Compatibility Between Balayage and Covering Maps -- 5 Global Simply Connected Weak Solutions -- 5.1 Statement of Result, and Two Lemmas -- 5.2 Statement of Conjecture, and Partial Proofs -- 5.3 Discussion -- 6 General Structure of Rational Solutions -- 6.1 Introduction -- 6.2 Direct Approach -- 6.3 Approach via Quadrature Identities -- 7 Examples -- 7.1 Examples: Several Evolutions of a Cardioid -- 7.1.1 The Univalent Solution -- 7.1.2 A Non-univalent Solution of the Polubarinova-Galin Equation -- 7.1.3 A Non-univalent Solution of the Löwner-Kufarev Equation -- 7.1.4 A Solution for the Suction Case -- 7.2 Injection Versus Suction in a Riemann Surface Setting -- 8 Moment Coordinates and the String Equation -- 8.1 The Polubarinova-Galin Equation as a String Equation -- 8.2 The String Equation for Univalent Conformal Maps -- 8.3 Intuition and Physical Interpretation in the Non-univalent Case.
8.4 An Example -- 8.4.1 General Case -- 8.4.2 First Subcase -- 8.4.3 Second Subcase -- 8.5 Moment Evolutions in Terms of Poisson Brackets -- 9 Hamiltonian Descriptions of General Laplacian Evolutions -- 9.1 Lie Derivatives and Interior Multiplication -- 9.2 Laplacian Evolutions -- 9.3 Schwarz Potentials and Generating Functions -- 9.4 Multitime Hamiltonians -- 10 The String Equation for Some Rational Functions -- 10.1 The String Equation on Quadrature Riemann Surfaces -- 10.2 The String Equation for Polynomials -- 10.3 Evolution of a Third Degree Polynomial with RealCoefficients -- 10.4 An Example by Ullemar -- Glossary -- References -- Index. |
| Record Nr. | UNINA-9910483493103321 |
|
Gustafsson Björn <1947->
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Laplacian growth on branched Riemann surfaces / / Bjö Gustafsson and Yu-Lin Lin
| Laplacian growth on branched Riemann surfaces / / Bjö Gustafsson and Yu-Lin Lin |
| Autore | Gustafsson Björn <1947-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (163 pages) : illustrations |
| Disciplina | 532.053 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Fluid dynamics
Geometric function theory Dinàmica de fluids Teoria geomètrica de funcions |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-69863-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 General Background -- 1.2 Loss of Univalence, Several Scenarios -- 1.3 On the Construction of a Branched Riemann Surface -- 1.4 Moment Coordinates and the String Equation -- 1.5 Outlooks to Physics -- 1.6 Acknowledgements -- 2 The Polubarinova-Galin and Löwner-Kufarev Equations -- 2.1 Basic Set Up in the Univalent Case -- 2.2 Dynamics and Subordination -- 2.3 The Polubarinova-Galin Versus the Löwner-Kufarev Equation -- 3 Weak Solutions and Balayage -- 3.1 Weak Formulation of the Polubarinova-Galin Equation -- 3.2 Weak Solutions in Terms of Balayage -- 3.3 Inverse Balayage -- 3.4 More General Laplacian Evolutions -- 3.5 Regularity of the Boundary via the Exponential Transform -- 3.6 The Resultant and the Elimination Function -- 4 Weak and Strong Solutions on Riemann Surfaces -- 4.1 Laplacian Growth on Manifolds -- 4.2 Examples -- 4.3 The Riemann Surface Solution Pulled Back to the Unit Disk -- 4.4 Compatibility Between Balayage and Covering Maps -- 5 Global Simply Connected Weak Solutions -- 5.1 Statement of Result, and Two Lemmas -- 5.2 Statement of Conjecture, and Partial Proofs -- 5.3 Discussion -- 6 General Structure of Rational Solutions -- 6.1 Introduction -- 6.2 Direct Approach -- 6.3 Approach via Quadrature Identities -- 7 Examples -- 7.1 Examples: Several Evolutions of a Cardioid -- 7.1.1 The Univalent Solution -- 7.1.2 A Non-univalent Solution of the Polubarinova-Galin Equation -- 7.1.3 A Non-univalent Solution of the Löwner-Kufarev Equation -- 7.1.4 A Solution for the Suction Case -- 7.2 Injection Versus Suction in a Riemann Surface Setting -- 8 Moment Coordinates and the String Equation -- 8.1 The Polubarinova-Galin Equation as a String Equation -- 8.2 The String Equation for Univalent Conformal Maps -- 8.3 Intuition and Physical Interpretation in the Non-univalent Case.
8.4 An Example -- 8.4.1 General Case -- 8.4.2 First Subcase -- 8.4.3 Second Subcase -- 8.5 Moment Evolutions in Terms of Poisson Brackets -- 9 Hamiltonian Descriptions of General Laplacian Evolutions -- 9.1 Lie Derivatives and Interior Multiplication -- 9.2 Laplacian Evolutions -- 9.3 Schwarz Potentials and Generating Functions -- 9.4 Multitime Hamiltonians -- 10 The String Equation for Some Rational Functions -- 10.1 The String Equation on Quadrature Riemann Surfaces -- 10.2 The String Equation for Polynomials -- 10.3 Evolution of a Third Degree Polynomial with RealCoefficients -- 10.4 An Example by Ullemar -- Glossary -- References -- Index. |
| Record Nr. | UNISA-996466561903316 |
|
Gustafsson Björn <1947->
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Motion of a drop in an incompressible fluid / / I.V. Denisova, V.A. Solonnikov
| Motion of a drop in an incompressible fluid / / I.V. Denisova, V.A. Solonnikov |
| Autore | Denisova I. V. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (319 pages) |
| Disciplina | 532.05 |
| Collana | Advances in Mathematical Fluid Mechanics |
| Soggetto topico |
Fluid dynamics
Fluid dynamics - Mathematics Boundary value problems Dinàmica de fluids Problemes de contorn |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-70053-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466404503316 |
|
Denisova I. V.
|
||
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Motion of a drop in an incompressible fluid / / I.V. Denisova, V.A. Solonnikov
| Motion of a drop in an incompressible fluid / / I.V. Denisova, V.A. Solonnikov |
| Autore | Denisova I. V. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (319 pages) |
| Disciplina | 532.05 |
| Collana | Advances in Mathematical Fluid Mechanics |
| Soggetto topico |
Fluid dynamics
Fluid dynamics - Mathematics Boundary value problems Dinàmica de fluids Problemes de contorn |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-70053-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910502632203321 |
|
Denisova I. V.
|
||
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
