%0 Book Section %1 statphys23_0567 %A Ogawa, H. %A Shibata, T. %A Kawakatsu, T. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K boundary condition incommensurate method simulation statphys23 system topic-4 %T Maximum Entropy Method for the Boundary Condition for Simulating Incommensurate Spatially Periodic Patterns %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=567 %X Computer simulation is widely used as a general method to explore statics and dynamics of spatial patterns. Periodic boundary condition is usually adopted to the real space numerical scheme. However, in quite a few cases, an intrinsic nature of the model equation is suffered from the periodicity of the finite system size. As a result, the obtained spatial morphology does not match the real solution of the model. \\\\To circumvent this problem, alternative schemes for better bondary condition have been extensively studied 1-3. Parinello-Rahman 2 method is propably the most popular one, which adjusts the simulation box size with a dynamic equation, and using the periodic boundary condition. This method relieves the finite size effect as long as the spatial morphology consists either of a single periodicity or of multiple periodicities commensurate with each other. However, incommensurate periodic or totally disordered patterns cannot be properly reproduced with the Parinello-Rahman method. We need another boundary scheme replacing the periodic boundary condition. \\\\Here we propose a new simulation method sloughing off the conventional boundary treatments. Maximum entropy method (MEM) is utilized to determine the values at the boundary sites from the bulk pattern. MEM combines the real space and the wave-number space simulations to minimize the finite size effect. \\\\We perform the static and dynamic simulations with the MEM boundary condition. In the static one, we reproduce the pattern outside the bulk sites from the information of the narrower bulk area, to examine the validity of our boundary method. In the dynamic calculation, we compare the results obtained with the periodic boundary condition and those obtained with our MEM condition, and discuss the domain growth law of these results. \\\\Reference: 1) H. C. Andersen, J. Chem. Phys. 72, 15 (1980).\\ 2) M. Parinello and A. Rahman, J. Appl. Phys. 52, 7182 (1981).\\ 3) H. Ogawa and N. Uchida, Phys. Rev. E, 72, 056707 (2005).

@incollection{statphys23_0567, abstract = {Computer simulation is widely used as a general method to explore statics and dynamics of spatial patterns. Periodic boundary condition is usually adopted to the real space numerical scheme. However, in quite a few cases, an intrinsic nature of the model equation is suffered from the periodicity of the finite system size. As a result, the obtained spatial morphology does not match the real solution of the model. \\\\To circumvent this problem, alternative schemes for better bondary condition have been extensively studied [1-3]. Parinello-Rahman [2] method is propably the most popular one, which adjusts the simulation box size with a dynamic equation, and using the periodic boundary condition. This method relieves the finite size effect as long as the spatial morphology consists either of a single periodicity or of multiple periodicities commensurate with each other. However, incommensurate periodic or totally disordered patterns cannot be properly reproduced with the Parinello-Rahman method. We need another boundary scheme replacing the periodic boundary condition. \\\\Here we propose a new simulation method sloughing off the conventional boundary treatments. Maximum entropy method (MEM) is utilized to determine the values at the boundary sites from the bulk pattern. MEM combines the real space and the wave-number space simulations to minimize the finite size effect. \\\\We perform the static and dynamic simulations with the MEM boundary condition. In the static one, we reproduce the pattern outside the bulk sites from the information of the narrower bulk area, to examine the validity of our boundary method. In the dynamic calculation, we compare the results obtained with the periodic boundary condition and those obtained with our MEM condition, and discuss the domain growth law of these results. \\\\Reference: 1) H. C. Andersen, J. Chem. Phys. {\bf 72}, 15 (1980).\\ 2) M. Parinello and A. Rahman, J. Appl. Phys. {\bf 52}, 7182 (1981).\\ 3) H. Ogawa and N. Uchida, Phys. Rev. E, {\bf 72}, 056707 (2005).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Ogawa, H. and Shibata, T. and Kawakatsu, T.}, biburl = {https://www.bibsonomy.org/bibtex/2fabe03faaa0d199ee30a6f5ff50edcab/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {3b1a12b08e669fb7f8c4b969caab2ba7}, intrahash = {fabe03faaa0d199ee30a6f5ff50edcab}, keywords = {boundary condition incommensurate method simulation statphys23 system topic-4}, month = {9-13 July}, timestamp = {2007-06-20T10:16:23.000+0200}, title = {Maximum Entropy Method for the Boundary Condition for Simulating Incommensurate Spatially Periodic Patterns}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=567}, year = 2007 }