Mathematical modeling of shock-wave processes in condensed matter : from statistical thermodynamics to control theory / / Tatiana Aleksandrovna Khantuleva

• Record Nr.: UNISA996483071703316
• Autore: Khantuleva Tatiana Aleksandrovna
• Pubbl/distr/stampa: Singapore : , : Springer, , [2022]; ©2022
• ISBN: 9789811924040; 9789811924033
• Descrizione fisica: 1 online resource (347 pages)
• Collana: Shock wave and high pressure phenomena
• Disciplina: 530.41
• Soggetti: Condensed matter
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Models of Continuum Mechanics and Their Deficiencies -- 1.1 Description of Macroscopic Systems -- Macroscopic Variables -- 1.2 Macroscopic Transport Equations -- 1.2.1 Equation of Mass Transport -- 1.2.2 Equation of Momentum Transport -- 1.2.3 Equation of Energy Transport -- 1.3 Validity of Continuum Mechanics -- 1.4 The Problem of Closure of the Transport Equations -- 1.5 Medium Models and Transient Processes -- 1.6 Averaging in Continuum Mechanics -- 1.7 Deficiencies of the Continuum Mechanics Concept -- 1.8 The Problem of a Uniform Description of the Media Motions -- 1.9 Short Review of Approaches to Extension of Continuum Mechanics -- References -- 2 Specific Features of Processes Far from Equilibrium -- 2.1 Experimental Difficulties in Studying Non-Equilibrium Processes -- 2.2 Anomalous Medium Response to Strong Impact -- 2.3 The Internal Structure Effects -- 2.4 Fluctuations, Pulsations, and Instabilities -- 2.5 Multi-Scale Energy Exchange Between Various Degrees of Freedom -- 2.6 Multi-Stage Relaxation Processes -- 2.7 Finite Speed of Disturbance Propagation and the Delay Effects -- 2.8 Influence of the Loading Duration and Inertial Effects -- 2.9 Dynamic Self-Organization of New Internal Structure in Open Systems -- 2.10 Predictive Ability of Modeling Non-Equilibrium Processes -- References -- 3 Macroscopic Description ; in Terms of Non-Equilibrium Statistical Mechanics -- 3.1 Fundamentals of Statistical Mechanics -- 3.2 Bogolyubov's Hypothesis of Attenuation of Spatiotemporal Correlations -- 3.3 Rigorous Statistical Approaches to Non-Equilibrium Processes -- 3.4 Description of Macroscopic Systems from the First Principles. Local-Equilibrium Distribution Function -- 3.5 Description of Macroscopic Systems from the First Principles. Non-equilibrium Distribution Function.; 3.6 Non-Equilibrium Statistical Operator by Zubarev -- 3.7 The Nonlocal Thermodynamic Relationships with Memory Between the Conjugate Macroscopic Fluxes and Gradients -- 3.8 Two Types of the Spatiotemporal Nonlocal Effects -- 3.9 Main Problem of Non-Equilibrium Statistical Mechanics -- 3.10 The Disadvantages and New Opportunities to Close Transport Equations for High-Rate Processes -- References -- 4 Thermodynamic Concepts Out of Equilibrium -- 4.1 Basic Concepts and Principles of Thermodynamics -- 4.2 Entropy Production in Transport Processes -- 4.3 Linear Thermodynamics of Irreversible Processes -- 4.4 Revision of the Generally Accepted Thermodynamic Concepts Out of Equilibrium -- 4.5 Thermodynamic Entropy, Information Entropy, and Information -- 4.6 Local Entropy Production Near and Far from Equilibrium -- 4.7 Total Entropy Generation and the Second Law of Thermodynamics -- 4.8 Maximum Entropy Principle by Jaynes -- 4.9 Influence of the Constraints Imposed on the System -- 4.10 Thermodynamic Temporal Evolution Out of Equilibrium -- 4.11 Self-organization of New Structures in Thermodynamics -- References -- 5 New Approach to Modeling Non-equilibrium Processes -- 5.1 Generalized Constitutive Relationships Based on Non-Equilibrium Statistical Mechanics -- 5.2 Modeling Spatiotemporal Correlation Functions -- 5.3 Temporal Stages of the Correlation Attenuation -- 5.4 Deficiencies of the Generally Accepted Models for the Media with Complicated Properties -- 5.5 Requirements to New Approach to Modeling Shock-Induced Processes -- 5.6 Foundations of New Approach to Modeling Transport Processes Far from Equilibrium -- 5.7 New Interdisciplinary Approach to Modeling Highly Non-Equilibrium Processes -- 5.8 Interrelationship Between Spatiotemporal Correlations and Dynamic Structure of the System -- 5.9 Modeling Correlation Functions in Boundary-Value Problems.; 5.10 Boundary Conditions for Nonlocal Equations -- 5.11 Discrete-Size Spectrum of the Dynamic Structure of a Bounded System -- 5.12 The Mathematical Basis for the Self-Consistent Problem Formulation -- 5.13 Distinctive Features of New Approach from Semi-Empirical Models -- References -- 6 Description of the Structure Evolution Using Methods of Control Theory of Adaptive Systems -- 6.1 Methods of Control Theory in Physics. Cybernetical Physics -- 6.2 Speed Gradient Principle by Fradkov for Non-Stationary Complex Systems -- 6.3 Description of the System Temporal Evolution at Macroscopic Level -- 6.4 Temporal Evolution of Statistical Distribution Functions -- 6.5 The System Temporal Evolution Out of Local Equilibrium on the Mesoscale -- 6.6 Internal Control on the Mesoscale Based on Speed Gradient Principle -- 6.7 Entropy Production in a Stationary State Out of Equilibrium -- 6.8 Paths of Structural Evolution and Reduction of Irreversible Losses Due to Self-Organization -- 6.9 A New Look at the Problem of Stability of Non-Equilibrium Systems -- 6.10 Influence of Feedbacks on the Paths of the System Evolution and Prediction of the Final States -- References -- 7 The Shock-Induced Planar Wave Propagation in Condensed Matter -- 7.1 Thermodynamic Properties of Solids -- 7.2 Wave Processes in Crystal Lattice -- 7.3 Elastic Properties of Solids -- 7.4 Plastic Deformation. Deficiencies of Continuum Mechanics -- 7.5 Shock Wave as a Transient ; Highly Non-equilibrium Process -- 7.6 The Integral Model for the Stress Tensor Without Separation into Elastic and Plastic Parts -- 7.7 Formulation of the Problem of the Shock-Induced Wave Propagation in Condensed Matter -- 7.8 Self-similar Quasi-Stationary Solution to the Problem -- 7.9 The Relaxation Model of the Shock-Induced Waveforms During Propagation.; 7.10 Decryption of the Information Recorded in the Experimentally Observed Waveforms -- 7.11 Comparison of the Model Waveforms with Experimental Data -- References -- 8 Evolution of Waveforms During Propagation in Solids -- 8.1 Waveforms Evolution Within the Integral Model -- 8.2 Speed-Gradient Principle for the Waveforms Evolution -- 8.3 The Waveform Evolution During Quasi-Stationary Wave Propagation -- 8.4 Paths of the Waveform Evolution and Experimental Results -- 8.5 Modeling Finite-Duration Waveforms -- 8.6 Shock-Induced Waveform as a Result of Non-monotone Relaxation -- 8.7 Entropy Production in Finite-Duration Waveforms -- 8.8 Evolution of the Waveforms During Their Propagation -- References -- 9 Abnormal Loss or Growth of the Wave Amplitude -- 9.1 Mass Velocity Dispersion and Interference of Shock Waves on the Mesoscale -- 9.2 The Shock-Induced Waveform as a Wave Packet -- 9.3 Behavior of the Mass Velocity Dispersion and the Waveform Amplitude Loss -- 9.4 Dependence of the Waveform Amplitude Loss on the Impact Velocity -- 9.5 Multi-scale Momentum and Energy Exchange in Wave Processes -- 9.6 The Shock-Induced Structure Instability -- 9.7 Self-organization of Turbulent Structures in the Entropy Well -- 9.8 Quantum Effects on the Mesoscale -- References -- 10 The Stress-Strain Relationships for the Continuous Stationary Loading -- 10.1 Stress-Strain Relationships for Continuous Quasi-Static Loading -- 10.2 The Stress-Strain Relationship for Continuous Planar Loading with Accounting Only Shear Relaxation -- 10.3 The Stress-strain Relationship for Continuous Plane High-Rate Loading -- 10.4 Reversible and Irreversible Loading-Unloading Processes -- 10.5 Entropy Production Surfaces for Various Duration Loading and Possible Evolutionary Paths -- 10.6 Probable Evolutionary Paths and Final States.; 10.7 Fundamental Difference Between Shock and Quasi-Static Loading -- References.