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Surface Growth in Non-Homogeneous Environments and the Elevated Noise

Hejazi, Kasra | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48348 (04)
  4. University: Sharif University of Technology
  5. Department: physics
  6. Advisor(s): Moghimi-Araghi, Saman; Naji, Ali
  7. Abstract:
  8. Surface Growth processes, as critical phenomena, have long attracted physicists’ attention. In many cases, the surfaces exhibit scale-free properties and they become fractals. Based on the large scale dy- namics of each model, one can divide the different models into niversality classes. Two well-known universality classes are Edwards-Wilkinson and KPZ. the kind of noise present in the stochastic differ- ential equation describing the model, can determine the large-scale dynamics to a large extent. In this research, we have perturbed the Edwards-Wilkinson dynamics to make it suitable for describing growth processes in non-homogeneous environments, such that the noise gets stronger in higher points of the surface. We name this model as the “Elevated Noise Model”, because of the stronger fluctuations in the heights. Rough calculations show that such a perturbation might be able to change the large-scale be- havior of Edwards-Wilkinson dynamics, this is also suggested by naive numerical solutions. Detailed numerical solutions and Dynamical Renormalization methods are used to investigate the model, and it is shown that the model loses its criticlaity due to this new kind of noise
  9. Keywords:
  10. Surface Growth ; Roughness ; Edwards-Wilkinson's Model ; Gaussian Noise ; Critical Exponent ; Heterogeneous Media ; Dynamical Renormalization

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