A New Method to Study Stochastic Growth Equations: Application to the Edwards-Wilkinson Equation
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| Natura: | Artículo científico |
| Lingua: | en |
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Sociedade Brasileira de Física
2006
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| _version_ | 1876478027256299520 |
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| author | T. G. Mattos |
| author_facet | T. G. Mattos |
| contents | A New Method to Study Stochastic Growth Equations: Application to the Edwards-Wilkinson Equation T. G. Mattos J. G. Moreira A. P. F. Atman Física, Astronomía y Matemáticas Dynamic Scaling Interface Growth Cellular Automata In this work we introduce a method to study stochastic growth equations, which follows a dynamics based on cellular automata modeling. The method defines an interface growth process that depends on height differences between neighbors. The growth rules assign a probability p i(t) for site i to receive a particle at time t, where p i(t) = rho exp[<FONT FACE=Symbol>kG</FONT>i(t)]. Here r and k are two parameters and gammai(t) is a kernel that depends on height h i(t) of site i and on heights of its neighbors, at time t. We specify the functional form of this kernel by the discretization of the deterministic part of the equation that describes some growth process. In particular, we study the Edwards-Wilkinson (EW) equation which describes growth processes where surface relaxation plays a major role. In this case we have a Laplacian term dominating in the growth equation and gammai(t) = h i+1(t)+h i-1(t)-2h i(t), which follows from the discretization of <FONT FACE=Symbol>Ñ</FONT>2h. By means of simulations and statistical analysis of the height distributions of the profiles, we obtain the roughening exponents, beta, alpha and z, whose values confirm that the processes defined by the method are indeed in the universality class of the original growth equation. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46413654030 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.3A Vol.36 |
| format | Artículo científico |
| id | redalyc_46413654030 |
| institution | Redalyc |
| language | en |
| publishDate | 2006 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | A New Method to Study Stochastic Growth Equations: Application to the Edwards-Wilkinson Equation T. G. Mattos Física, Astronomía y Matemáticas Dynamic Scaling Interface Growth Cellular Automata A New Method to Study Stochastic Growth Equations: Application to the Edwards-Wilkinson Equation T. G. Mattos J. G. Moreira A. P. F. Atman Física, Astronomía y Matemáticas Dynamic Scaling Interface Growth Cellular Automata In this work we introduce a method to study stochastic growth equations, which follows a dynamics based on cellular automata modeling. The method defines an interface growth process that depends on height differences between neighbors. The growth rules assign a probability p i(t) for site i to receive a particle at time t, where p i(t) = rho exp[<FONT FACE=Symbol>kG</FONT>i(t)]. Here r and k are two parameters and gammai(t) is a kernel that depends on height h i(t) of site i and on heights of its neighbors, at time t. We specify the functional form of this kernel by the discretization of the deterministic part of the equation that describes some growth process. In particular, we study the Edwards-Wilkinson (EW) equation which describes growth processes where surface relaxation plays a major role. In this case we have a Laplacian term dominating in the growth equation and gammai(t) = h i+1(t)+h i-1(t)-2h i(t), which follows from the discretization of <FONT FACE=Symbol>Ñ</FONT>2h. By means of simulations and statistical analysis of the height distributions of the profiles, we obtain the roughening exponents, beta, alpha and z, whose values confirm that the processes defined by the method are indeed in the universality class of the original growth equation. 2006 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46413654030 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.3A Vol.36 |
| title | A New Method to Study Stochastic Growth Equations: Application to the Edwards-Wilkinson Equation |
| topic | Física, Astronomía y Matemáticas Dynamic Scaling Interface Growth Cellular Automata |
| url | https://www.redalyc.org/articulo.oa?id=46413654030 |