From Kinetic Theory to Turbulence Modeling: The Legacy of Carlo Cercignani

Preface
Contents
About the Editors
The ``Divertissements'' of Carlo Cercignani
Appendix
References
Tensorial Turbulent Viscosity Model for LES: Properties and Applications
1 Equations
2 A priori tests
3 Boundary layer
4 Rayleigh–Bénard
5 Conclusions
References
FPU Model and Toda Model: A Survey, a View
1 Introduction
1.1 FPU in a Nutshell
1.2 The Search for an Underlying Integrable Dynamics
1.3 Different Phenomena at Different Time Scales
2 The Long-Time Motion Across Toda Tori
3 Investigating the FPU State
3.1 Scalings Laws from the Dynamics
3.2 Scaling Laws from Toda Actions
3.3 A Conclusion?
References
Half-Space Problems for the Boltzmann Equation of Multicomponent Mixtures
1 Kinetic Half-Space Problem for Mixtures
2 Discrete Velocity Models for Mixtures
3 Half-Space Problem for the Full Boltzmann Equation
3.1 Brief Outline of Main Steps of the Proof of Theorem 2
References
BGK Model for a Mixture with Two Reversible Reactions
1 Introduction
2 Physical Setting and Kinetic Approach
3 BGK Model
4 Conclusions
References
On a Class of Self-Similar Solutions of the Boltzmann Equation
1 Introduction
2 Statement of the Problem
3 Eigenvalue Problem for Matrices
4 Main Results
5 Conclusions
References
The Einstein Classical Program, the Wheeler-Feynman Reabsorption and Kirchhoff's Law
1 Introduction
2 The Wheeler-Feynman Approach to the Electrodynamics of Charges in Bulk: The Idea of a Reabsorption or Cancellation Making Undamped Motions Possible
2.1 The Dirac-Wheeler-Feynman Equations of Motion
2.1.1 Conceptual Problems for the Dirac Equation: The Idea of Wheeler and Feynman
3 The Reabsorption Property, or Cancellation, as the Main Content of the Wheeler-Feynman Electrodynamics for Matter in Bulk
3.1 First Step: The Oseen Identity
3.1.1 A Global Formulation: The Wheeler-Feynman Identity Inspired to Dirac's Radiation Field
3.1.2 A Further Little Step: A Sufficient Condition for the Reabsorption Property, as an Uncorrelation Property of the ``material'' Electric Current
4 The Wheeler-Feynman Reabsorption Property Checked in Particular Models: The Case of Ionic Crystals
4.1 The Ionic Crystals Model
4.1.1 Proof of the Wheeler-Feynman Identity, and the Existence of Dispersion Relations
4.1.2 Existence of Polaritons
5 Conclusion
References
Reabsorption and Density Limit in Magnetized Plasmas Through a First-Principles Toy Model
1 Introduction
2 The Model, and Its Analytic Solution Through Normal Modes
2.1 The Model
2.1.1 Analytic Treatment Through Normal Modes
2.1.2 The Wheeler–Feynman Identity as Guaranteeing the Existence of a Dispersion Relation
2.1.3 Evidence for the Density-Induced Instability, and Estimate of a Density Limit
3 Conclusion
References
Kinetic Effects in Non-ideal, Two-Phase Shear Flows
1 Introduction
2 The Enskog–Vlasov Model
2.1 Simplified Moment Approximation of the Linearized EV Equation
3 Test Problem Formulation
4 Numerical Results
4.1 Ideal Vapor Phase and Comparison with BE
4.2 Non-Ideal Vapor Phase
5 Conclusions
References
The Cercignani Conjecture About a Classical Zero-Point Energy, and Its Confirmation for Ionic Crystals
1 Introduction
2 The Ionic Crystal Model
3 The Computed Spectra
4 Discussion of the Results
5 Conclusions
References
Turbulence Without Fluctuations
1 Introduction
2 Fluctuation-Conditioned Turbulence
3 Turbulence Without Fluctuations
4 Conclusions
References
An Ellipsoidal-Statistical (ES) Model for a Polyatomic Gas with Temperature-Dependent Specific Heats
1 Introduction
2 ES Model for a Gas with Temperature-Dependent Specific Heats
3 Basic Properties
4 Navier–Stokes Equations
5 Boundary Conditions for Navier–Stokes Equations
References
Discrete- and Continuous-Time Random Walks in 1D Lévy Random Medium
1 Introduction
1.1 General Notation
2 Discrete-Time Random Walk
2.1 Finite Mean Distance Between Targets, Quenched Theorems
2.2 Finite Mean Distance Between Targets, Annealed Theorems
2.3 Infinite Mean Distance Between Targets, Annealed Theorems
3 Continuous-Time Random Walk
3.1 Finite Mean Distance Between Targets, Quenched Theorems
3.2 Finite Mean Distance Between Targets, Annealed Theorems
3.3 Infinite Mean Distance Between Targets, Annealed Theorems
4 A Brief Discussion on Perspectives
References
Mesoscale Modelling of the Tolman Length in Multi-componentSystems
List of Symbols
1 Introduction
2 Lattice Boltzmann Model
3 Method
4 Results
5 Conclusions
References
Kinetic and Macroscopic Epidemic Models in Presence of Multiple Heterogeneous Populations
1 Introduction
2 Interplay Between Contact Distribution and Epidemic Dynamics
2.1 Formation of the Contact Distribution
2.2 The Kinetic Model
2.3 Saturated Incidence Rate
3 Numerical Results
4 Conclusion and Perspectives
References
Electron Transport in Graphene Nanoribbons
1 Introduction
2 Semiclassical Charge Transport in Graphene
3 Numerical Scheme
4 Numerical Results and Mobility Models
5 Conclusions
References
A Review on a General Multi-Species BGK Model: Modelling, Theory and Numerics
1 Introduction
2 The General BGK Model for Gas Mixtures
3 Theoretical Results of This Model
4 Possible Choices and Meaning of the Free Parameters
5 On Existing Numerical Schemes
6 Conclusions and Outlook
References
Gas-Kinetic Methods for Turbulent Flow
1 Introduction
2 Gas-Kinetic Scheme
2.1 Gas Model at the Interface Between Two Computational Cells
2.2 Numerical Fluxes
2.3 Artificial Dissipation
2.4 Boundary Conditions
3 Extension of the Gas-Kinetic Scheme to Turbulent Flow
3.1 Relaxation Time Based on Eddy Viscosity
3.2 Modification of the Timescales Ratio
3.3 Second-Order Turbulent Stress Tensor Obtained from the Second-Order Chapman–Enskog Expansion
3.4 Boundary Conditions for Turbulent Flow
4 Gas-Kinetic Schemes for RANS
4.1 Flow Around a Supercritical Aerofoil in Transonic Regime
4.2 Supersonic Compression Corner at Mach 5
5 Discussion
6 Conclusions
References
Density Functional Kinetic Theory for Soft Matter
1 Introduction
2 Density Functional Theory
3 Density Functional Kinetic Theory
4 Families of Lattice DFKT
4.1 Free-Energy Lattice Models
4.2 Lattice Many-Body Models
4.3 Lattice Chromodynamic DFKT
4.3.1 Near-Contact Interactions
5 Applications: Simulating Dropland
5.1 Dense Emulsions and Soft Granular Materials
6 Summary and Future Outlook
References
A Multi-Agent Description of Social Phenomena with Lognormal Equilibria
1 Introduction
2 Gibrat's Law and Distribution of Firms
3 Distribution of Winnings in a Multi-Agent Jackpot Game
4 Social Phenomena with Lognormal Equilibria
5 Conclusions
References
Oscillatory Rarefied Gas Flows in Long Capillaries
1 Introduction
2 Linear Oscillatory Fully Developed Binary Gas Mixture Flow
3 Nonlinear Oscillatory Fully Developed Single Gas Flow
4 Concluding Remarks
References