Ebook: Burgers-KPZ Turbulence: Göttingen Lectures

These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.

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These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.

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These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.
Content:
Front Matter....Pages -
Shock waves and the large scale structure (LSS) of the universe....Pages 1-11
Hydrodynamic limits, nonlinear diffusions, and propagation of chaos....Pages 13-24
Hopf-Cole formula and its asymptotic analysis....Pages 25-42
Statistical description, parabolic approximation....Pages 43-95
Hyperbolic approximation and inviscid limit....Pages 97-133
Forced Burgers turbulence....Pages 135-201
Passive tracer transport in Burgers' and related flows....Pages 203-270
Fractal Burgers-KPZ models....Pages 271-298
Back Matter....Pages -

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These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.
Content:
Front Matter....Pages -
Shock waves and the large scale structure (LSS) of the universe....Pages 1-11
Hydrodynamic limits, nonlinear diffusions, and propagation of chaos....Pages 13-24
Hopf-Cole formula and its asymptotic analysis....Pages 25-42
Statistical description, parabolic approximation....Pages 43-95
Hyperbolic approximation and inviscid limit....Pages 97-133
Forced Burgers turbulence....Pages 135-201
Passive tracer transport in Burgers' and related flows....Pages 203-270
Fractal Burgers-KPZ models....Pages 271-298
Back Matter....Pages -
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