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Numerical Study of Surface Growth in Presence of Height Dependent Noise using Higher order Approximation Algorithms

Mohammadzade-Hashtroud, Aida | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51163 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Moghimi-Araghi, Saman
  7. Abstract:
  8. Surface growth is one of subjects that has many applications in industry, and its deep recognition in physics remarkably helps us in understanding of critical systems. There are various approaches for analyzing this phenomenon, one of the most important of which is differential equations.In this approach, with respect to surface properties, a partial differential equation is introduced, and the critical exponents are obtained by solving it. In this thesis, after studying several continuum equations such as: Edwards-Wilkinson, KPZ, and Wolf-Villain equation,we provide numerical solutions of these equations in presence of height dependent noise. The role of noise in stochastic differential equations of surface growth is adding fluctuations, but when the intensity of these fluctuations are related to the hight of each point, we obtain some interesting results. In some cases, models leave their critical states and some of them change their universality class to a new one. perusing this issue, we can see some extreme fluctuations in surface of some models, too. So we take a close look at the approximation of numerical solutions of stochastic partial differential equations, particularly for KPZ model.Then generalized model with height dependent noise are introduced and their properties are checked
  9. Keywords:
  10. Surface Growth ; Critical Exponent ; Numerical Solution ; White Noise ; Wolf-Villain Surface Growth Model ; Edwards-Wilkinson's Model ; Kardar-Parisi-Zhang (KPZ)Equation

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