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Probabilistic Theory of Mean Field Games with Applications II : Mean Field Games with Common Noise and Master Equations / / by René Carmona, François Delarue
| Probabilistic Theory of Mean Field Games with Applications II : Mean Field Games with Common Noise and Master Equations / / by René Carmona, François Delarue |
| Autore | Carmona René |
| Edizione | [1st ed. 2018.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
| Descrizione fisica | 1 online resource (697 pages) |
| Disciplina | 530.1595 |
| Collana | Probability Theory and Stochastic Modelling |
| Soggetto topico |
Probabilities
Calculus of variations Partial differential equations Economic theory Probability Theory and Stochastic Processes Calculus of Variations and Optimal Control; Optimization Partial Differential Equations Economic Theory/Quantitative Economics/Mathematical Methods |
| ISBN | 3-319-56436-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Foreword -- Preface to Volume II -- Part I: MFGs with a Common Noise -- Optimization in a Random Environment -- MFGs with a Common Noise: Strong and Weak Solutions -- Solving MFGs with a Common Noise -- Part II: The Master Equation, Convergence, and Approximation Problems -- The Master Field and the Master Equation -- Classical Solutions to the Master Equation -- Convergence and Approximations -- Epilogue to Volume II -- Extensions for Volume II -- References -- Indices. |
| Record Nr. | UNINA-9910300116003321 |
Carmona René
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Probability and statistics in the physical sciences / / Byron P. Roe
| Probability and statistics in the physical sciences / / Byron P. Roe |
| Autore | Roe Byron P. |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2020] |
| Descrizione fisica | 1 online resource (XIII, 285 p. 54 illus., 5 illus. in color.) |
| Disciplina | 530.1595 |
| Collana | Undergraduate Texts in Physics |
| Soggetto topico |
Statistical physics
Probabilities Mathematical physics |
| ISBN | 3-030-53694-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1. Basic Probability Concepts -- Chapter 2. Some Initial Definitions -- Chapter 3. Some Results Independent of Specific Distributions -- Chapter 4. Discrete Distributions and Combinatorials -- Chapter 5. Specific Discrete Distributions -- Chapter 6. The Normal (or Gaussian) Distribution and Other Continuous Distributions -- Chapter 7. Generating Functions and Characteristic Functions -- Chapter 8. The Monte Carlo Method: Computer Simulation of Experiments -- Chapter 9. Queueing Theory and Other Probability Questions -- Chapter 10. Two-Dimensional and Multidimensional Distributions -- Chapter 11. The Central Limit Theorem -- Chapter 12. Choosing Hypotheses and Estimating Parameters from Experimental Data -- Chapter 13. Methods of Least Squares (Regression Analysis) -- Chapter 14. Inverse Probability; Confidence Limits -- Chapter 15. Curve Fitting -- Chapter 16. Fitting Data with Correlations and Constraints -- Chapter 17. Bartlett S Function; Estimating Likelihood Ratios Needed for an Experiment -- Chapter 18. Interpolating Functions and Unfolding Problems -- Chapter 19. Beyond Maximum Likelihood and Least Squares; Robust Methods -- Chapter 20. Characterization of Events -- Appendix -- Index. |
| Record Nr. | UNINA-9910427666003321 |
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Roe Byron P.
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| Cham, Switzerland : , : Springer, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Probability and statistics in the physical sciences / / Byron P. Roe
| Probability and statistics in the physical sciences / / Byron P. Roe |
| Autore | Roe Byron P. |
| Edizione | [Third edition.] |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2020] |
| Descrizione fisica | 1 online resource (XIII, 285 p. 54 illus., 5 illus. in color.) |
| Disciplina | 530.1595 |
| Collana | Undergraduate Texts in Physics |
| Soggetto topico |
Statistical physics
Probabilities Mathematical physics |
| ISBN | 3-030-53694-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chapter 1. Basic Probability Concepts -- Chapter 2. Some Initial Definitions -- Chapter 3. Some Results Independent of Specific Distributions -- Chapter 4. Discrete Distributions and Combinatorials -- Chapter 5. Specific Discrete Distributions -- Chapter 6. The Normal (or Gaussian) Distribution and Other Continuous Distributions -- Chapter 7. Generating Functions and Characteristic Functions -- Chapter 8. The Monte Carlo Method: Computer Simulation of Experiments -- Chapter 9. Queueing Theory and Other Probability Questions -- Chapter 10. Two-Dimensional and Multidimensional Distributions -- Chapter 11. The Central Limit Theorem -- Chapter 12. Choosing Hypotheses and Estimating Parameters from Experimental Data -- Chapter 13. Methods of Least Squares (Regression Analysis) -- Chapter 14. Inverse Probability; Confidence Limits -- Chapter 15. Curve Fitting -- Chapter 16. Fitting Data with Correlations and Constraints -- Chapter 17. Bartlett S Function; Estimating Likelihood Ratios Needed for an Experiment -- Chapter 18. Interpolating Functions and Unfolding Problems -- Chapter 19. Beyond Maximum Likelihood and Least Squares; Robust Methods -- Chapter 20. Characterization of Events -- Appendix -- Index. |
| Record Nr. | UNISA-996418439703316 |
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Roe Byron P.
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| Cham, Switzerland : , : Springer, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Random Fields for Spatial Data Modeling : A Primer for Scientists and Engineers / Dionissios T. Hristopulos
| Random Fields for Spatial Data Modeling : A Primer for Scientists and Engineers / Dionissios T. Hristopulos |
| Autore | Hristopulos, Dionissios T. |
| Pubbl/distr/stampa | Dordrecht, : Springer, 2020 |
| Descrizione fisica | XXX, 867 p. : ill. ; 24 cm |
| Disciplina |
550(Scienze della terra e geologia - Geofisica)
003(Sistemi dinamici) 530(Fisica) 530.1595(Statistica in fisica) |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNICAMPANIA-VAN0239046 |
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Hristopulos, Dionissios T.
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| Dordrecht, : Springer, 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Vanvitelli | ||
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Regularity Theory for Mean-Field Game Systems / / by Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
| Regularity Theory for Mean-Field Game Systems / / by Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan |
| Autore | Gomes Diogo A |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (XIV, 156 p. 4 illus. in color.) |
| Disciplina | 530.1595 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Game theory
Economic theory System theory Game Theory, Economics, Social and Behav. Sciences Economic Theory/Quantitative Economics/Mathematical Methods Systems Theory, Control |
| ISBN | 3-319-38934-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Introduction -- Explicit solutions, special transformations, and further examples -- Estimates for the Hamilton-Jacobi equation -- Estimates for the Transport and Fokker-Planck equations -- The nonlinear adjoint method -- Estimates for MFGs -- A priori bounds for stationary models -- A priori bounds for time-dependent models -- A priori bounds for models with singularities -- Non-local mean-field games - existence -- Local mean-field games - existence -- References -- Index. |
| Record Nr. | UNINA-9910254083503321 |
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Gomes Diogo A
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Scale invariance : self-similarity of the physical world / / Richard N. Henriksen
| Scale invariance : self-similarity of the physical world / / Richard N. Henriksen |
| Autore | Henriksen R. N. |
| Pubbl/distr/stampa | Weinheim, Germany : , : Wiley-VCH, , 2015 |
| Descrizione fisica | 1 online resource (301 p.) |
| Disciplina | 530.1595 |
| Soggetto topico |
Scaling laws (Statistical physics)
Self-similar processes Statistical mechanics |
| ISBN |
3-527-68735-1
3-527-68734-3 3-527-68733-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Cover ""; ""Contents ""; ""Preface ""; ""Acknowledgments ""; ""Introduction ""; ""Chapter 1 Arbitrary Measures of the Physical World ""; ""1.1 Similarity ""; ""1.2 Dimensional Similarity ""; ""1.3 Physical Equations and the 'Pi' Theorem ""; ""1.4 Applications of the Pi Theorem ""
""1.4.1 Plane Pendulum """"1.4.2 Pipe Flow of a Fluid ""; ""1.4.3 Steady Motion of a Rigid Object in Viscous 'Fluid' ""; ""1.4.4 Diffusion and Self-Similarity ""; ""1.4.5 Ship Wave Drag ""; ""1.4.6 Adiabatic Gas Flow ""; ""1.4.7 Time-Dependent Adiabatic Flow "" ""1.4.8 Point Explosion in a Gaseous Medium """"1.4.9 Applications in Fundamental Physics ""; ""1.4.10 Drag on a Flexible Object in Steady Motion ""; ""1.4.11 Dimensional Analysis of Mammals ""; ""1.4.12 Trees ""; ""References ""; ""Chapter 2 Lie Groups and Scaling Symmetry "" ""2.1 The Rescaling Group """"2.1.1 Rescaling Physical Objects ""; ""2.1.2 Reconciliation with the Buckingham Pi Theorem ""; ""2.1.3 Rescaling and Self-Similarity as a Lie Algebra ""; ""2.1.4 Practical Lie Self-Similarity ""; ""2.2 Familiar Physical Examples "" ""3.2.1 Self-Similar Lorentz Boost "" |
| Record Nr. | UNINA-9910131305903321 |
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Henriksen R. N.
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| Weinheim, Germany : , : Wiley-VCH, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Scale invariance : self-similarity of the physical world / / Richard N. Henriksen
| Scale invariance : self-similarity of the physical world / / Richard N. Henriksen |
| Autore | Henriksen R. N. |
| Pubbl/distr/stampa | Weinheim, Germany : , : Wiley-VCH, , 2015 |
| Descrizione fisica | 1 online resource (301 p.) |
| Disciplina | 530.1595 |
| Soggetto topico |
Scaling laws (Statistical physics)
Self-similar processes Statistical mechanics |
| ISBN |
3-527-68735-1
3-527-68734-3 3-527-68733-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Cover ""; ""Contents ""; ""Preface ""; ""Acknowledgments ""; ""Introduction ""; ""Chapter 1 Arbitrary Measures of the Physical World ""; ""1.1 Similarity ""; ""1.2 Dimensional Similarity ""; ""1.3 Physical Equations and the 'Pi' Theorem ""; ""1.4 Applications of the Pi Theorem ""
""1.4.1 Plane Pendulum """"1.4.2 Pipe Flow of a Fluid ""; ""1.4.3 Steady Motion of a Rigid Object in Viscous 'Fluid' ""; ""1.4.4 Diffusion and Self-Similarity ""; ""1.4.5 Ship Wave Drag ""; ""1.4.6 Adiabatic Gas Flow ""; ""1.4.7 Time-Dependent Adiabatic Flow "" ""1.4.8 Point Explosion in a Gaseous Medium """"1.4.9 Applications in Fundamental Physics ""; ""1.4.10 Drag on a Flexible Object in Steady Motion ""; ""1.4.11 Dimensional Analysis of Mammals ""; ""1.4.12 Trees ""; ""References ""; ""Chapter 2 Lie Groups and Scaling Symmetry "" ""2.1 The Rescaling Group """"2.1.1 Rescaling Physical Objects ""; ""2.1.2 Reconciliation with the Buckingham Pi Theorem ""; ""2.1.3 Rescaling and Self-Similarity as a Lie Algebra ""; ""2.1.4 Practical Lie Self-Similarity ""; ""2.2 Familiar Physical Examples "" ""3.2.1 Self-Similar Lorentz Boost "" |
| Record Nr. | UNINA-9910828806903321 |
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Henriksen R. N.
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| Weinheim, Germany : , : Wiley-VCH, , 2015 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Scaling / Grigory Isaakovich Barenblatt
| Scaling / Grigory Isaakovich Barenblatt |
| Autore | Barenblatt, Grigory Isaakovich |
| Pubbl/distr/stampa | Cambridge : Cambridge University Press, 2003 |
| Descrizione fisica | xiv, 171 p. : ill. ; 24 cm |
| Disciplina | 530.1595 |
| Collana | Cambridge texts in applied mathematics |
| Soggetto topico | Scaling laws (Statistical physics) |
| ISBN | 0521533945 |
| Classificazione |
AMS 00A73
LC QC174.85.S34B373 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991002519499707536 |
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Barenblatt, Grigory Isaakovich
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| Cambridge : Cambridge University Press, 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Scaling laws in dynamical systems / / Edson Denis Leonel
| Scaling laws in dynamical systems / / Edson Denis Leonel |
| Autore | Leonel Edson Denis |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (258 pages) |
| Disciplina | 530.1595 |
| Collana | Nonlinear physical science |
| Soggetto topico | Scaling laws (Statistical physics) |
| ISBN | 981-16-3544-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Contents -- List of Figures -- List of Tables -- 1 Introduction -- 1.1 Initial Concepts -- 1.2 Summary -- 2 One-Dimensional Mappings -- 2.1 Introduction -- 2.2 The Concept of Stability -- 2.2.1 Asymptotically Stable Fixed Point -- 2.2.2 Neutral Stability -- 2.2.3 Unstable Fixed Point -- 2.3 Fixed Points to the Logistic Map -- 2.4 Bifurcations -- 2.4.1 Transcritical Bifurcation -- 2.4.2 Period Doubling Bifurcation -- 2.4.3 Tangent Bifurcation -- 2.5 Summary -- 2.6 Exercises -- 3 Some Dynamical Properties for the Logistic Map -- 3.1 Convergence to the Stationary State -- 3.1.1 Transcritical Bifurcation -- 3.1.2 Period Doubling Bifurcation -- 3.1.3 Route to Chaos via Period Doubling -- 3.1.4 Tangent Bifurcation -- 3.2 Lyapunov Exponent -- 3.3 Summary -- 3.4 Exercises -- 4 The Logistic-Like Map -- 4.1 The Mapping -- 4.2 Transcritical Bifurcation -- 4.2.1 Analytical Approach to Obtain α, β, z and δ -- 4.2.2 Critical Exponents for the Period Doubling Bifurcation -- 4.3 Extensions to Other Mappings -- 4.3.1 Hassell Mapping -- 4.3.2 Maynard Mapping -- 4.4 Summary -- 4.5 Exercises -- 5 Introduction to Two Dimensional Mappings -- 5.1 Linear Mappings -- 5.2 Nonlinear Mappings -- 5.3 Applications of Two Dimensional Mappings -- 5.3.1 Hénon Map -- 5.3.2 Lyapunov Exponents -- 5.3.3 Ikeda Map -- 5.4 Summary -- 5.5 Exercises -- 6 A Fermi Accelerator Model -- 6.1 Fermi-Ulam Model -- 6.1.1 Jacobian Matrix for the Indirect Collisions -- 6.1.2 Jacobian Matrix for the Direct Collisions -- 6.1.3 Fixed Points -- 6.1.4 Phase Space -- 6.1.5 Phase Space Measure Preservation -- 6.2 A Simplified Version of the Fermi-Ulam Model -- 6.3 Scaling Properties for the Chaotic Sea -- 6.4 Localization of the First Invariant Spanning Curve -- 6.5 The Regime of Growth -- 6.6 Summary -- 6.7 Exercises -- 7 Dissipation in the Fermi-Ulam Model.
7.1 Dissipation via Inelastic Collisions -- 7.1.1 Jacobian Matrix for the Direct Collisions -- 7.1.2 Jacobian Matrix for the Indirect Collisions -- 7.1.3 The Phase Space -- 7.1.4 Fixed Points -- 7.1.5 Construction of the Manifolds -- 7.1.6 Transient and Manifold Crossings Determination -- 7.1.7 Determining the Exponent δ from the Eigenvalues of the Saddle Point -- 7.2 Dissipation by Drag Force -- 7.2.1 Drag Force of the Type F=-tildeηv -- 7.2.2 Drag Force of the Type F=pmtildeηv2 -- 7.2.3 Drag Force of the Type F=-tildeηvγ -- 7.3 Summary -- 7.4 Exercises -- 8 Dynamical Properties for a Bouncer Model -- 8.1 The Model -- 8.2 Complete Version of the Bouncer Model -- 8.2.1 Successive Collisions -- 8.2.2 Indirect Collisions -- 8.2.3 Jacobian Matrix -- 8.2.4 The Phase Space -- 8.3 A Simplified Version of the Bouncer Model -- 8.4 Numerical Investigation on the Simplified Version -- 8.5 Approximation of Continuum Time -- 8.6 Summary -- 8.7 Exercises -- 9 Localization of Invariant Spanning Curves -- 9.1 The Standard Mapping -- 9.2 Localization of the Curves -- 9.3 Rescale in the Phase Space -- 9.4 Summary -- 9.5 Exercises -- 10 Chaotic Diffusion in Non-Dissipative Mappings -- 10.1 A Family of Discrete Mappings -- 10.2 Dynamical Properties for the Chaotic Sea: A Phenomenological Description -- 10.3 A Semi Phenomenological Approach -- 10.4 Determination of the Probability via the Solution of the Diffusion Equation -- 10.5 Summary -- 10.6 Exercises -- 11 Scaling on a Dissipative Standard Mapping -- 11.1 The Model -- 11.2 A Solution for the Diffusion Equation -- 11.3 Specific Limits -- 11.4 Summary -- 11.5 Exercises -- 12 Introduction to Billiard Dynamics -- 12.1 The Billiard -- 12.1.1 The Circle Billiard -- 12.1.2 The Elliptical Billiard -- 12.1.3 The Oval Billiard -- 12.2 Summary -- 12.3 Exercises -- 13 Time Dependent Billiards -- 13.1 The Billiard. 13.1.1 The LRA Conjecture -- 13.2 The Time Dependent Elliptical Billiard -- 13.3 The Oval Billiard -- 13.4 Summary -- 13.5 Exercises -- 14 Suppression of Fermi Acceleration in the Oval Billiard -- 14.1 The Model and the Mapping -- 14.2 Results for the Case of Fpropto-V -- 14.3 Results for the Case of FproptopmV2 -- 14.4 Results for the Case of Fpropto-Vδ -- 14.5 Summary -- 14.6 Exercises -- 15 A Thermodynamic Model for Time Dependent Billiards -- 15.1 Motivation -- 15.2 Heat Transference -- 15.3 The Billiard Formalism -- 15.3.1 Stationary Estate -- 15.3.2 Dynamical Regime -- 15.3.3 Numerical Simulations -- 15.3.4 Average Velocity over n -- 15.3.5 Critical Exponents -- 15.3.6 Distribution of Velocities -- 15.4 Connection Between the Two Formalism -- 15.5 Summary -- 15.6 Exercises -- Appendix A Expressions for the Coefficients j -- Appendix B Change of Referential Frame -- B.1 Introduction -- B.2 Elastic Collisions -- B.3 Inelastic Collisions -- Appendix C Solution of the Diffusion Equation -- C.1 Introduction -- Appendix D Heat Flow Equation -- D.1 Introduction -- Appendix E Connection Between t and n in a Time Dependent Oval Billiard -- E.1 Introduction -- Appendix F Solution of the Integral to Obtain the Relation Between n and t in the Time Dependent Oval Billiard -- F.1 Introduction -- Appendix Bibliography. |
| Record Nr. | UNINA-9910494562303321 |
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Leonel Edson Denis
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| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Scaling laws in dynamical systems / / Edson Denis Leonel
| Scaling laws in dynamical systems / / Edson Denis Leonel |
| Autore | Leonel Edson Denis |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (258 pages) |
| Disciplina | 530.1595 |
| Collana | Nonlinear physical science |
| Soggetto topico | Scaling laws (Statistical physics) |
| ISBN | 981-16-3544-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Contents -- List of Figures -- List of Tables -- 1 Introduction -- 1.1 Initial Concepts -- 1.2 Summary -- 2 One-Dimensional Mappings -- 2.1 Introduction -- 2.2 The Concept of Stability -- 2.2.1 Asymptotically Stable Fixed Point -- 2.2.2 Neutral Stability -- 2.2.3 Unstable Fixed Point -- 2.3 Fixed Points to the Logistic Map -- 2.4 Bifurcations -- 2.4.1 Transcritical Bifurcation -- 2.4.2 Period Doubling Bifurcation -- 2.4.3 Tangent Bifurcation -- 2.5 Summary -- 2.6 Exercises -- 3 Some Dynamical Properties for the Logistic Map -- 3.1 Convergence to the Stationary State -- 3.1.1 Transcritical Bifurcation -- 3.1.2 Period Doubling Bifurcation -- 3.1.3 Route to Chaos via Period Doubling -- 3.1.4 Tangent Bifurcation -- 3.2 Lyapunov Exponent -- 3.3 Summary -- 3.4 Exercises -- 4 The Logistic-Like Map -- 4.1 The Mapping -- 4.2 Transcritical Bifurcation -- 4.2.1 Analytical Approach to Obtain α, β, z and δ -- 4.2.2 Critical Exponents for the Period Doubling Bifurcation -- 4.3 Extensions to Other Mappings -- 4.3.1 Hassell Mapping -- 4.3.2 Maynard Mapping -- 4.4 Summary -- 4.5 Exercises -- 5 Introduction to Two Dimensional Mappings -- 5.1 Linear Mappings -- 5.2 Nonlinear Mappings -- 5.3 Applications of Two Dimensional Mappings -- 5.3.1 Hénon Map -- 5.3.2 Lyapunov Exponents -- 5.3.3 Ikeda Map -- 5.4 Summary -- 5.5 Exercises -- 6 A Fermi Accelerator Model -- 6.1 Fermi-Ulam Model -- 6.1.1 Jacobian Matrix for the Indirect Collisions -- 6.1.2 Jacobian Matrix for the Direct Collisions -- 6.1.3 Fixed Points -- 6.1.4 Phase Space -- 6.1.5 Phase Space Measure Preservation -- 6.2 A Simplified Version of the Fermi-Ulam Model -- 6.3 Scaling Properties for the Chaotic Sea -- 6.4 Localization of the First Invariant Spanning Curve -- 6.5 The Regime of Growth -- 6.6 Summary -- 6.7 Exercises -- 7 Dissipation in the Fermi-Ulam Model.
7.1 Dissipation via Inelastic Collisions -- 7.1.1 Jacobian Matrix for the Direct Collisions -- 7.1.2 Jacobian Matrix for the Indirect Collisions -- 7.1.3 The Phase Space -- 7.1.4 Fixed Points -- 7.1.5 Construction of the Manifolds -- 7.1.6 Transient and Manifold Crossings Determination -- 7.1.7 Determining the Exponent δ from the Eigenvalues of the Saddle Point -- 7.2 Dissipation by Drag Force -- 7.2.1 Drag Force of the Type F=-tildeηv -- 7.2.2 Drag Force of the Type F=pmtildeηv2 -- 7.2.3 Drag Force of the Type F=-tildeηvγ -- 7.3 Summary -- 7.4 Exercises -- 8 Dynamical Properties for a Bouncer Model -- 8.1 The Model -- 8.2 Complete Version of the Bouncer Model -- 8.2.1 Successive Collisions -- 8.2.2 Indirect Collisions -- 8.2.3 Jacobian Matrix -- 8.2.4 The Phase Space -- 8.3 A Simplified Version of the Bouncer Model -- 8.4 Numerical Investigation on the Simplified Version -- 8.5 Approximation of Continuum Time -- 8.6 Summary -- 8.7 Exercises -- 9 Localization of Invariant Spanning Curves -- 9.1 The Standard Mapping -- 9.2 Localization of the Curves -- 9.3 Rescale in the Phase Space -- 9.4 Summary -- 9.5 Exercises -- 10 Chaotic Diffusion in Non-Dissipative Mappings -- 10.1 A Family of Discrete Mappings -- 10.2 Dynamical Properties for the Chaotic Sea: A Phenomenological Description -- 10.3 A Semi Phenomenological Approach -- 10.4 Determination of the Probability via the Solution of the Diffusion Equation -- 10.5 Summary -- 10.6 Exercises -- 11 Scaling on a Dissipative Standard Mapping -- 11.1 The Model -- 11.2 A Solution for the Diffusion Equation -- 11.3 Specific Limits -- 11.4 Summary -- 11.5 Exercises -- 12 Introduction to Billiard Dynamics -- 12.1 The Billiard -- 12.1.1 The Circle Billiard -- 12.1.2 The Elliptical Billiard -- 12.1.3 The Oval Billiard -- 12.2 Summary -- 12.3 Exercises -- 13 Time Dependent Billiards -- 13.1 The Billiard. 13.1.1 The LRA Conjecture -- 13.2 The Time Dependent Elliptical Billiard -- 13.3 The Oval Billiard -- 13.4 Summary -- 13.5 Exercises -- 14 Suppression of Fermi Acceleration in the Oval Billiard -- 14.1 The Model and the Mapping -- 14.2 Results for the Case of Fpropto-V -- 14.3 Results for the Case of FproptopmV2 -- 14.4 Results for the Case of Fpropto-Vδ -- 14.5 Summary -- 14.6 Exercises -- 15 A Thermodynamic Model for Time Dependent Billiards -- 15.1 Motivation -- 15.2 Heat Transference -- 15.3 The Billiard Formalism -- 15.3.1 Stationary Estate -- 15.3.2 Dynamical Regime -- 15.3.3 Numerical Simulations -- 15.3.4 Average Velocity over n -- 15.3.5 Critical Exponents -- 15.3.6 Distribution of Velocities -- 15.4 Connection Between the Two Formalism -- 15.5 Summary -- 15.6 Exercises -- Appendix A Expressions for the Coefficients j -- Appendix B Change of Referential Frame -- B.1 Introduction -- B.2 Elastic Collisions -- B.3 Inelastic Collisions -- Appendix C Solution of the Diffusion Equation -- C.1 Introduction -- Appendix D Heat Flow Equation -- D.1 Introduction -- Appendix E Connection Between t and n in a Time Dependent Oval Billiard -- E.1 Introduction -- Appendix F Solution of the Integral to Obtain the Relation Between n and t in the Time Dependent Oval Billiard -- F.1 Introduction -- Appendix Bibliography. |
| Record Nr. | UNISA-996466731803316 |
|
Leonel Edson Denis
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| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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