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Investigation of Isotropic Laplacian Operators by Computer Simulation for A-B Diblock Copolymers


Sohail Ahmed Memon, Imtiaz Ali Halepoto, Nazar Hussain Phulpoto, Ayaz Hussain, Muhammad Sulleman Memon


Vol. 18  No. 5  pp. 100-108


The cell dynamics simulation (CDS) technique is elaborated for the lamellar system of A-B diblock copolymer. In which, the averaging operator (Laplacian) plays a key role for ensuring the isotropy. To achieve this objective, the original Laplacian used in CDS has been replaced by various other Laplacian schemes to observe more isotropic results. Generally, the CDS is used to evaluate the Time?Dependent Ginzburg?Landau (TDGL) equations where analysis remains inconclusive for optimal isotropy. In this paper, the stencil size with focus on its behavior for two dimensional Laplacian operators are considered. In simulations, the short stencil 5-point 5P was found anisotropic produced anisotropic results while the 9-point PK, BV1, BV2 and BV3 were found isotropic.


Laplacian Operators, CDS, Isotropy, Diblock copolymers