Woyczynski Wojbor A. Burgers-KPZ Turbulence

Gottingen Lectures. - Springer-Verlag Berlin Heidelberg, 1998. 325 p. OCR. 300 dpi. ISBN: 3-540-65237-XLectures
Shock Waves and Large Scale Structure (LSS) of the Universe
Nonlinear waves, shock formation, conservation laws
Large scale structure of the Universe and the adhesion approximation
KPZ equation of interface growth and other physical models leading to Burgers equation
Hydrodynamic Limits, Nonlinear Diffusions, Propagation of Chaos
Random walks and linear diffusions
Hydrodynamic limit for asymmetric exclusion particle systems
nteracting and nonlinear diffusions, propagation of chaos
Hopf-Cole Formula and Its Asymptotic Analysis
Elementary, traveling wave and self-similar solutions
The Hopf-Cole formula and exact solutions
Asymptotic analysis of the Hopf-Cole formula in the inviscid limit
KdV equation and solitons
Statisticcil Description, Parabolic Approximation
Statistical description in Burgers turbulence
Polynomial chaos and Wiener-Hermite expansions of nonlinear functionals Parabolic scaling limits for regular initial data
The maximum energy principle for unimodal data
Parabolic scaling limits for singular initial data
Spectral properties of scaling limits for singular initial data
Hyperbolic Approximation and the Inviscid Limit
Hyperbolic scaling limit
Densities and correlations of the limit velocity field
Statistics of shocks
Sinai's theorem—Hausdorff dimension of shock points
Voronoi tessellation of shock fronts in R
Forced Burgers Turbulence
Stationary regimes
Least-action principle
Inviscid limit and multistream regimes
Statistical characteristics
Stream number statistics for a 1-D gas of noninteracting particles
Mechanism of energy dissipation in the inviscid 1-D Burgers turbulence
Variational methods
Quasi-Voronoi tessellation of shock fronts
White noise forcing: existence and Feynman-Kac formula issues
Passive Tracer Transport in Burgers' and Related Flows
Burgers' turbulent diffusion; stochastic interpretation
D cellular structures
Evolution of 1-D model density
KdV-Burgers' transport in 1-D compressible gas
Exact formulas for 1-D Burgers' turbulent diffusion
Fourier-Lagrangian representation for non-smooth Lagrangian-Eulerian maps
Concentration field in reacting Burgers' flows
Concentration field in potential and rotational flows
Burgers' density field revisited Generalized variational principles for systems of conservation laws
Fractal Burgers-KPZ Models
Existence and uniqueness problems
Time decay of solutions
Traveling wave and self-similar solutions
Fractal nonlinear Markov processes and propagation of chaos