Cellular Automaton Simulation of Polymers
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CELLULAR AUTOMATON SIIMULATRION OF IPOLYMERS M. A. SMrIH,a Y. BAR-YAMb Y. RABIN,c N. MARGOLUS,a T. TOFFOLI,a ANDC. H. BENNETFrd a MIT Laboratory for Computer Science, Cambridge, MA 02139 b ECS, 44 Cummington St., Boston University, Boston MA 02215 c Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel d IBM T. J. Watson Res. Ctr., Yorktown Heights, NY 11973 ABSTRACT In order to improve our ability to simulate the complex behavior of polymers, we introduce dynamical models in the class of Cellular Automata (CA). Space partitioning methods enable us to overcome fundamental obstacles to large scale simulation of connected chains with excluded volume by parallel processing computers. A highly efficient, two-space algorithm is devised and tested on both Cellular Automata Machines (CAMs) and serial computers. Preliminary results on the static and dynamic properties of polymers in two dimensions are reported. INTRODUCTION
Polymers vary from "simple", usually synthetic, linear chains of identical monomers to highly complex chains consisting of sequences of amino-acids that form the building blocks of living organisms. Realistic dynamical simulations of polymers for study of such problems as protein folding are expected to be one of the major scientific undertakings in upcoming years. An ability to take advantage of massively parallel computer architectures with up to 10' processors would dramaticaly improve the effectiveness of simulations. In order to illustrate the difficulties in simulating polymer dynamics and their resolution, it proves quite fruitful and enlightening to consider abstract polymer models. One of the basic paradigms of polymer science is that many of the dynamical and structural properties of sufficiently2long macromolecules can be understood within the framework of an abstract polymer model. f, In this model the polymer consists of elements which are connected in sequence and avoid intruding on each other's space. There are only two essential parameters, the length and the excluded volume. Even for this simple model where analytical tools such as meanfield, scaling and renormalization group methods provide a basic understanding of physical properties, computer simulations are needed to check analytical results in simple systems and study complex systems of dense, grafted, branching, matrix-embeded polymers, etc. For more realistic models, computer simulations provide the only hope of obtaining detailed information. The central difficulty in simulating the behavior of polymers is the large number of individual components necessary to effect the conformation of a long macromolecule. What methods should one use to simulate complex high molecular weight polymers? Conventional simulations are of two types: molecular dynamics, 3 and Monte-Carlo. 4 Molecular dynamics simulations are suggestive of realistic Newtonian dynamics of polymers and are implemented by moving all atoms with small steps according to forces calculated from modeled interatomic forces. Monte Carlo dynamics represent the dyn
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