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