- Title Pages
- Dedication
- Preface
- Acknowledgements
- Part I Kinetic Theory of Fluids
- 1 Why a Kinetic Theory of Fluids?
- 2 Boltzmann’s Kinetic Theory
- 3 Approach to Equilibrium, the <i>H</i>-Theorem and Irreversibility
- 4 Transport Phenomena
- 5 From Kinetic Theory to Navier–Stokes Hydrodynamics
- 6 Generalized Hydrodynamics Beyond Navier–Stokes
- 7 Kinetic Theory of Dense Fluids
- 8 Model Boltzmann Equations
- 9 Stochastic Particle Dynamics
- 10 Numerical Methods for the Kinetic Theory of Fluids
- Part II Lattice Kinetic Theory
- 11 Lattice Gas-Cellular Automata
- 12 Lattice Boltzmann Models with Underlying Boolean Microdynamics
- 13 Lattice Boltzmann Models without Underlying Boolean Microdynamics
- 14 Lattice Relaxation Schemes
- 15 The Hermite–Gauss Route to LBE
- 16 LBE in the Framework of Computational-Fluid Dynamics
- Part III Fluid Dynamics Applications
- 17 Boundary Conditions
- 18 Flows at Moderate Reynolds Numbers
- 19 LBE Flows in Disordered Media
- 20 Lattice Boltzmann for Turbulent Flows
- Part IV Lattice Kinetic Theory: Advanced Topics
- 21 Entropic Lattice Boltzmann
- 22 Thermohydrodynamic LBE Schemes
- 23 Out of Legoland: Geoflexible Lattice Boltzmann Equations
- 24 Lattice Boltzmann for Turbulence Modeling
- Part V Beyond Fluid Dynamics: Complex States of Flowing Matter
- 25 LBE for Generalized Hydrodynamics
- 26 Lattice Boltzmann for reactive flows
- 27 Lattice Boltzmann for Non-Ideal Fluids
- 28 Extensions of the Pseudo-Potential Method
- 29 Lattice Boltzmann Models for Microflows
- 30 The Fluctuating Lattice Boltzmann
- 31 LB for Flows with Suspended Objects: Fluid–Solid Interactions
- Part VI Beyond Newtonian Mechanics: Quantum and Relativistic Fluids
- 32 Quantum Lattice Boltzmann (QLB)
- 33 QLB for Quantum Many-Body and Quantum Field Theory
- 34 Relativistic Lattice Boltzmann (RLB)
- 35 Advanced RLB models
- 36 Coda
- 37 Notation
- Appendices
- Part VII Hands-On
- Index

# Stochastic Particle Dynamics

# Stochastic Particle Dynamics

- Chapter:
- (p.136) 9 Stochastic Particle Dynamics
- Source:
- The Lattice Boltzmann Equation
- Author(s):
### Sauro Succi

- Publisher:
- Oxford University Press

Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical development of kinetic theory. Among others, it provided conclusive evidence in favor of the atomistic theory of matter. This chapter introduces the basic notions of stochastic dynamics and its connection with other important kinetic equations, primarily the Fokker–Planck equation, which bear a complementary role to the Boltzmann equation in the kinetic theory of dense fluids.

*Keywords:*
dense fluids, Brownian motion, Einstein diffusion, stochastic dynamics, fluctuations, Fokker–Planck equation

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- Title Pages
- Dedication
- Preface
- Acknowledgements
- Part I Kinetic Theory of Fluids
- 1 Why a Kinetic Theory of Fluids?
- 2 Boltzmann’s Kinetic Theory
- 3 Approach to Equilibrium, the <i>H</i>-Theorem and Irreversibility
- 4 Transport Phenomena
- 5 From Kinetic Theory to Navier–Stokes Hydrodynamics
- 6 Generalized Hydrodynamics Beyond Navier–Stokes
- 7 Kinetic Theory of Dense Fluids
- 8 Model Boltzmann Equations
- 9 Stochastic Particle Dynamics
- 10 Numerical Methods for the Kinetic Theory of Fluids
- Part II Lattice Kinetic Theory
- 11 Lattice Gas-Cellular Automata
- 12 Lattice Boltzmann Models with Underlying Boolean Microdynamics
- 13 Lattice Boltzmann Models without Underlying Boolean Microdynamics
- 14 Lattice Relaxation Schemes
- 15 The Hermite–Gauss Route to LBE
- 16 LBE in the Framework of Computational-Fluid Dynamics
- Part III Fluid Dynamics Applications
- 17 Boundary Conditions
- 18 Flows at Moderate Reynolds Numbers
- 19 LBE Flows in Disordered Media
- 20 Lattice Boltzmann for Turbulent Flows
- Part IV Lattice Kinetic Theory: Advanced Topics
- 21 Entropic Lattice Boltzmann
- 22 Thermohydrodynamic LBE Schemes
- 23 Out of Legoland: Geoflexible Lattice Boltzmann Equations
- 24 Lattice Boltzmann for Turbulence Modeling
- Part V Beyond Fluid Dynamics: Complex States of Flowing Matter
- 25 LBE for Generalized Hydrodynamics
- 26 Lattice Boltzmann for reactive flows
- 27 Lattice Boltzmann for Non-Ideal Fluids
- 28 Extensions of the Pseudo-Potential Method
- 29 Lattice Boltzmann Models for Microflows
- 30 The Fluctuating Lattice Boltzmann
- 31 LB for Flows with Suspended Objects: Fluid–Solid Interactions
- Part VI Beyond Newtonian Mechanics: Quantum and Relativistic Fluids
- 32 Quantum Lattice Boltzmann (QLB)
- 33 QLB for Quantum Many-Body and Quantum Field Theory
- 34 Relativistic Lattice Boltzmann (RLB)
- 35 Advanced RLB models
- 36 Coda
- 37 Notation
- Appendices
- Part VII Hands-On
- Index