Chaos, Fractals and Complexity

• Autore: Bountis Tassos
• Pubblicazione: Cham : , : Springer International Publishing AG, , 2023; ©2023
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (381 pages)
• Disciplina: 003
• Altri autori: VallianatosFilippos ProvataAstero KugiumtzisDimitris KominisYannis
• Nota di contenuto: Intro -- Organization -- Preface -- Contents -- Contributors -- Chaos -- Diffusion Without Spreading of a Wave Packet in Nonlinear Random Models -- 1 Introduction -- 1.1 Difference Between Spreading and Diffusion -- 1.2 Discussion of the Boltzmann Ergodic Hypothesis -- 2 Dynamics of Hamiltonians with a Finite Number of Degrees of Freedom -- 2.1 KAM Tori in Finite Nearly Integrable Hamiltonian Systems -- 2.2 Arnold Diffusion Conjecture and Extension -- 2.3 Anti Integrable Limit -- 3 Dynamics of Hamiltonians on Infinite Lattices -- 3.1 KAM Tori in Infinite Hamiltonian Systems on Lattices with Linear Discrete Spectrum -- 3.2 Numerical Observation of KAM Tori in Large Non Integrable Hamiltonian Systems -- 4 Long Time Behavior of Wave Packets -- 4.1 A Criterion for the Long Time Behavior of a Wave Packet -- 4.2 Discussion of the Long Time Behavior of Wave Packets -- 5 Exact Results for Ding Dong Models -- 5.1 Definition -- 5.2 Regular Trajectories and a Lemma -- 5.3 Some Exact Results -- 5.4 Non Genericity of DD Models -- 6 Concluding Remarks -- References -- Nonlinear Phenomena Shaping the Structure of Spiral Galaxies -- 1 Introduction -- 2 Order and Chaos -- 2.1 Two Dimensional (2D) Models -- 2.2 Three Dimensional (3D) Models -- 3 Discussion -- References -- Phase Space Transport and Dynamical Matching in a Caldera-Type Hamiltonian System -- 1 Introduction -- 2 Hamiltonian Model -- 3 Lagrangian Descriptors in Caldera-Type Hamiltonian Systems -- 4 Numerical Results -- 5 Conclusions -- References -- The Building Blocks of Spiral Arms in Galaxies -- 1 Introduction -- 2 Spiral Arms in Grand Design Galaxies -- 2.1 The Model -- 2.2 Spiral Density Waves from Precessing Ellipses -- 3 Spiral Arms in Barred Spiral Galaxies -- 3.1 The Model -- 3.2 Manifold Spirals -- 4 Conclusion -- References -- Ordered and Chaotic Bohmian Trajectories -- 1 Introduction. ; 2 Nodal Point-X-Point Complex Mechanism -- 3 Chaos and Entanglement in Bohmian Qubits -- 4 Summary -- References -- A Brief Introduction to Quantum Chaos of Generic Systems -- 1 Introduction -- 2 Quantum Mechanics of Classically Integrable Systems -- 3 Quantum Chaos in Classically Ergodic Systems -- 4 Quantum Chaos in Generic Systems -- 4.1 The Wigner Functions -- 4.2 The Principle of Uniform Semiclassical Condensation (PUSC) of Wigner Functions -- 4.3 Spectral Statistics in the Mixed-type Systems -- 4.4 Quantum Localization of the Chaotic Eigenstates -- 5 The Poincaré-Husimi Functions in Billiards -- 6 The Phase Space Localization Measures of Chaotic Eigenstates -- 7 The Distribution of the Localization Measures -- 8 Semiclassical Limiting Approach to the Regime of PUSC -- 9 Discussion and Conclusions -- References -- Dynamics and Statistics of Weak Chaos in a 4-D Symplectic Map -- 1 Introduction -- 2 Statistical Analysis of Weak Chaos -- 3 Evidence of Weak Chaos in 4DMM Maps -- 3.1 Weak Chaos in an Example of the 4DMM Map -- 3.2 HE Cases of the 4DMM Map -- 3.3 HH Cases of the 4DMM Map -- 3.4 Close to the Instability Transition -- 4 Conclusions -- References -- Fractals -- Multifractal Analysis of SEM Images of Multiphase Materials: The Case of OPC Clinker -- 1 Introduction -- 2 Multifractal Analysis -- 3 Data -- 4 Results -- 5 Summary -- References -- Fractal Dimensional Analysis for Retinal Vascularization Images in Retinitis Pigmentosa: A Pilot Study -- 1 Introduction -- 2 A Brief Introduction to Fractal Dimension -- 3 Retinitis Pigmentosa -- 3.1 First Methodology: Digital Fundus Photography -- 3.2 Second Methodology: Optical Coherence Tomography Angiography -- 4 Discussion -- References -- Extending the Bayesian Framework from Information to Action -- 1 Introduction -- 2 Biological Versus Artificial Information Processing. ; 3 Extended Bayesian Inference: Two Modes in One Loop -- 4 Outlook and Forthcoming Experiments -- References -- Complexity -- Fokas on Medical Imaging: Analytic Reconstructions for Emission Tomography -- 1 Introduction -- 2 Radon Transform and Its Attenuated Version in Two Dimensions -- 3 Inversion of the Radon Transform in Two Dimensions -- 3.1 Fourier-Based Inversion of the Radon Transform in Two Dimensions -- 3.2 Complex Analysis Tools -- 3.3 The Inversion of the Radon Transform in Two Dimensions Without the Fourier Transform: The Fokas Approach -- 4 Inversion of the Attenuated Radon Transform in Two Dimensions -- 4.1 The Inversion of the Attenuated Radon Transform in Two Dimensions Without the Fourier Transform: The Fokas Approach -- 4.2 A Novel Method for the Inversion of the Attenuated Radon Transform in Two Dimensions -- References -- Inverse EEG Problem, Minimization and Numerical Solutions -- 1 Neurophysiology of EEG -- 2 The Importance of EEG -- 3 Head Model -- 4 Basic Equations for the EEG Formulation -- 5 Configuration of the Numerical Solution -- 6 Future Work -- References -- Traveling Waves in Flowing Sand: The Dynamical Systems Approach -- 1 Introduction -- 2 Steady Uniform Flow and the Monoclinal Flood Wave -- 3 One Equation to Rule All Traveling Waveforms -- 3.1 Focusing on Traveling Wave Solutions -- 3.2 Non-dimensional Form -- 4 Dynamical Systems Approach -- 5 From Monoclinal Waves to Roll Waves -- 5.1 Stage 1: The Monoclinal Wave -- 5.2 Stage 2: The Undular Bore -- 5.3 Stage 3: Roll Waves -- 6 Conclusion -- References -- Identifying Discrete Breathers Using Convolutional Neural Networks -- 1 Introduction -- 2 Creation of Breather and Phonon Samples -- 3 Machine Learning Training Process and Results -- 4 Conclusions -- References -- Subthreshold Oscillations in Multiplex Leaky Integrate-and-Fire Networks with Nonlocal Interactions. ; 1 Introduction -- 2 The Model -- 2.1 The Coupled LIF Dynamics in the Multiplex -- 2.2 Kuramoto Order Parameter -- 3 Results -- 3.1 Subthreshold Oscillations -- 4 Conclusions and Open Problems -- References -- Networks' Modulation: How Different Structural Network Properties Affect the Global Synchronization of Coupled Kuramoto Oscillators -- 1 Introduction -- 2 Methods and Materials -- 2.1 Connectivity Measurements -- 2.2 Neural Networks as Graphs -- 2.3 The Kuramoto Model -- 3 Results -- 4 Summary and Discussion -- References -- Neural Correlates of Human-Machine Trust in Autonomous Vehicles Context -- 1 Introduction -- 2 Understanding Trust-in-Automation -- 2.1 Cognitive Component -- 2.2 Affective Component -- 2.3 Behavioural Component -- 3 Psychological and Cognitive Factors of Trust Between Drivers and AVs -- 4 Current Approaches to Objective Trust Measures Using Brain Signals -- 4.1 Approaches Based on EEG -- 4.2 Approaches Based on fNIRS -- 5 Conclusions and Future Directions -- References -- Fokas and Mathematics -- High-Order Localized Wave Solutions of the New (3+1)-Dimensional Kadomtsev-Petviashvili Equation -- 1 Introduction -- 2 Soliton Solutions of the (3+1)-Dimensional KP Equation -- 3 Rational Solutions of the (3+1)-Dimensional KP Equation -- 4 Semi-rational Solutions of the (3+1)-Dimensional KP Equation -- 5 Discussion -- References -- Progress in Initial-Boundary Value Problems for Nonlinear Evolution Equations and the Fokas Method -- 1 Introduction -- 2 Initial-Boundary Value Problems via the Fokas Method -- 3 A Higher Dispersion KdV on the Half-Line -- References -- Instabilities of Linear Evolution PDEs via the Fokas Method -- 1 Introduction -- 2 The Equation tu+xxxu=0 -- 3 The Equation tu-xxxu=0 -- 4 Conclusion -- References -- Fokas Diagonalization -- 1 Introduction -- 1.1 The Classical Spectral Transform Method. ; 1.2 Derivation of Transforms -- 1.3 Example Problems -- 1.4 A More General Spectral Transform Method -- 2 Results -- 2.1 Half Line Neumann Problem for the Stokes Equation -- 2.2 Finite Interval Problem for the Heat Equation with a Nonlocal Condition -- 2.3 Half Line Dirichlet Problem for the Linearized BBM Equation -- 3 Conclusion -- 3.1 On Pedagogy -- References -- A Novel Difference-Integral Equation Satisfied Asymptotically by the Riemann Zeta Function -- 1 Introduction -- 2 Review of Some of the Results of ch22F -- 3 Computation of 3 and 4 -- 4 Sketch of the Derivation of (1.1) -- 5 Numerical Evidence -- References -- The Role of Periodicity in the Solution of Third Order Boundary Value Problems -- 1 Introduction -- 2 A Motivating Example and the Unified Transform of Fokas -- 3 Non-periodic Boundary Value Problems -- 3.1 Uncoupled BC of Dirichlet Type -- 3.2 Mixed BC of Dirichlet Type -- 3.3 Coupled BC: Pseudo-periodic -- 3.4 An Outlier: Quasi-periodic BC -- References -- The Fokas Method for the Well-posedness of Nonlinear Dispersive Equations in Domains with a Boundary -- 1 Introduction -- 2 Inverse Scattering for Linear Equations: Rediscovering the Fourier Transform -- 3 A Novel Approach for the Well-posedness of IBVPs -- References -- Athanassios S. Fokas: A Renaissance Scientist -- Athanassios S. Fokas: A Renaissance Scientist -- References -- Author Index.
• Titolo autorizzato: Chaos, Fractals and Complexity
• ISBN: 3-031-37404-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910746294503321
• Lo trovi qui: Univ. Federico II
• Serie: Springer Proceedings in Complexity Series