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The Stochastic Properties Of Burgers And Kardar-Parisi-Zhang EquationsS In The Strong Coupling Limit

Dehghan Niry, Mohammad | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 39905 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rahimi Tabar, Mohammad Reza
  7. Abstract:
  8. In this thesis, some aspects of the Burges and Kardar-Parisi-Zhang (KPZ) equations will be studied. At first we introduce Turbulence and describe historical view of Burgers and KPZ equations. Then in second section we study analytically the time issue of Burgers equation in 1+1-dimenssion. Then by using recently developed precise numerical methods by J. Bec and U. Frisch, we check result of previous section numerically. Our numerical simulation of the Burgers equation stirred by a kicking force support our analytical results. In small time scale our result show dynamical exponent of structure function z is one. This is the essence of the assumption first made by Sir G. I. Taylor in his 1938 paper from which he could infer the spatial structure function of the velocity from temporal fluctuations at a single point. The Taylor’s hypothesis is significantly clear when there’s a large scale average flow; nevertheless it’s also believed to be valid in homogeneous isotropic flows. The later always is meant to reflect the picture that larger eddies randomly sweep the smaller eddies with their root mean square velocities. From a general analytical point of view there is no derivation of the hypothesis in isotropic case. In this perspective our calculations suggest an analytical ground for the Taylor’s frozen hypothesis for homogeneous system of Burgers flow. After that we introduce a method to simulate KPZ surface in long time in 1+2-dimension. We preciously describe some difficulty in numeric work such as instability. The statistics of isoheight lines in the 2+1-dimensional KPZ model is shown to be conformally invariant and equivalent to those of self-avoiding random walks.
  9. Keywords:
  10. Kardar-Parisi-Zhang (KPZ)Equation ; Burger Turbulence ; Intermittency ; Structure Function ; Restricted Solid-on-Solid

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