By Mauro Ferrario, Giovanni Ciccotti, Kurt Binder
This large and accomplished choice of lectures via world-leading specialists within the box introduces and experiences all correct machine simulation equipment and their functions in condensed topic platforms. quantity 1 is an in-depth advent to an enormous spectrum of computational options for statistical mechanical structures of condensed subject. it is going to allow the graduate scholar and either the professional and nonspecialist researcher to get familiar with the instruments essential to perform numerical simulations at a sophisticated point. quantity 2 released as LNP 704 (ISBN 3-540-35283-X) is a suite of cutting-edge surveys on numerical experiments conducted for a number of platforms, starting from fabrics sciences to chemical biology.
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Additional resources for Computer simulations in condensed matter systems: from materials to chemical biology
Because of the hard-core repulsion, a Monte Carlo algorithm involving local moves is relatively ineﬃcient, since any move that generates a particle overlap is rejected. Instead, the geometric cluster algorithm (GCA)  is designed to avoid such overlaps while generating a new conﬁguration, by proceeding as follows (cf. Fig. 1). 1. In a given conﬁguration C of particles, a “pivot” is chosen at random. 2. 4 3. The conﬁguration C and its transformed counterpart C˜ are superimposed, which leads to groups of overlapping particles.
41 2 Basic Equipment . . . . . . . . . . . . . . . . . . . . . 2 Statistical Mechanics . . . . . . . . . . . . . . . . . . . . 41 Tools: Elements of Monte Carlo . . . . . . . . . . . . . . . 43 3 Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Meaning and Speciﬁcation . . . . . . . . . . . . . . . . . . 46 Generic Routes . . . . . .
4 Implementation Issues The actual implementation of the generalized GCA involves a variety of issues. The point reﬂection with respect to the pivot requires careful consideration of the periodic boundary conditions. Furthermore, as mentioned above, particles that have been translated via a point reﬂection must not be translated again within the same cluster move, and particles that interact with a given cluster particle both before and after the translation of that cluster particle must be considered only once, on the basis of the diﬀerence in pair potential.