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Mullins-Herring Equation with Lateral Growth

Ghamari, Danial | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53203 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Moghimi Araghi, Saman
  7. Abstract:
  8. Surface growth have been one of the most interesting topics of research in non-equilibrium Statistical physics, due to their relevance in studying industrial growth processes. Many models such as Edwards-Wilkinson and KPZ have been proposed to study these systems where by incorporating renormalization group, numerical integration and computer simulations we can derive their critical exponents. In general, a thermal noise is implemented in these models, however, other types can be used as well. In particular for the case of Edwards-Wilkinson, it has been shown that a multiplicative noise changes the universality class of the model. In this thesis we want to investigate the effects of multiplicative noise in Mullins-Herring model. By using a multiplicative noise, we will observe that lateral growth becomes present in Mullins-Herring systems, and by incorporating numerical experiments and renormalization group approach, we studied the crossover from Mullins-Herring to Edwards-Wilkinson and eventually to KPZ universality classes. To achieve this we have first implemented a lateral growth term in Mullins-Herring equation and next a new type of nonlinearity has been introduced to Mullins-Herring and Edwards-Wilkinson models. In particular in case of lateral growth in Mullins-Herring, we have seen that only through numerical integrations one can derive the scaling exponents of the model and perturbative renormalization fails to identify them. However, for Edwards-Wilkinson in presence of new nonlinear term, perturbative approach has been constructive to evaluate the repulsive fixed point of the model where numerical calculations verify them. In general, our new models have been successful in determining the origins of the crossovers and furthermore pave the way for future studies
  9. Keywords:
  10. Numerical Integration ; Multiplicative Noise ; Surface Growth ; Critical Exponent ; Universality Class ; Mullins-Herring Equation

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