HIGH-DIMENSIONAL AND VERY LARGE CELLULAR AUTOMATA FOR IMMUNOLOGICAL SHAPE SPACE

Dietrich Stauffer and Muhammad Sahimi
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Dietrich Stauffer: Institute for Theoretical Physics, Cologne University, D-W-5000 Köln 41, Germany
Muhammad Sahimi: HLRZ, KFA, D-W-5170 Jülich 1, Germany, and Department of Chemical Engineering, University of Southern California, Los Angeles, CA 90089-1211, USA

International Journal of Modern Physics C (IJMPC), 1993, vol. 04, issue 02, 401-408

Abstract: Simulations with109cells are made on an iPSC Hypercube with 32 parallel i860 processors, updating more than a million sites per second and per processor. This size reaches into the size range of natural immune systems. Smaller sizes are simulated in higher dimensions up to ten. These cellular automata due to de Boer. van der Laan, and Hogeweg model the idiotypic shape space and differ from usual Ising models through interactions with the mirror sites of the lattice. For majority rules (voter rules) we find Ising-like behavior with a spontaneous magnetization vanishing at some critical temperature which approaches its mean field value for high dimensions. The previously observed self-organization in the form of domain formation is thus explained as spinodal decomposition.

Keywords: Immunology; cellular automata; parallel computing; large-scale simulations (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1142/S0129183193000434

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