Lennard-Jones systems algorithm

It is also possible to perform simultaneous random or biased moves on many degrees of freedom. This was shown not to be advantageous for the simulation of liquid phases of simple molecules [27,33]. However, polymeric systems are expected to behave differently. For example, in simple Lennard-Jones systems it was found that the maximum efficiency of a Metropolis MC algorithm (fastest sampling of configuration space) corresponded to an overall acceptance rate of roughly 50%. This was found not to be the case in MC simulations of a model protein, where maximum efficiency corresponded to an arx ptance rate of only 15% [41, 51]. 

Figure 8 shows the r-dependent thermal conductivity for a Lennard-Jones fluid (p = 0.8, 7o = 2) [6]. The nonequilibrium Monte Carlo algorithm was used with a sufficiently small imposed temperature gradient to ensure that the simulations were in the linear regime, so that the steady-state averages were equivalent to fluctuation averages of an isolated system. 

The first MC (16) and MD (17) studies were used to simulate the properties of single particle fluids. Although the basic MC (11,12) and MD (12,13) methods have changed little since the earliest simulations, the systems simulated have continually increased in complexity. The ability to simulate complex interfacial systems has resulted partly from improvements in simulation algorithms (15,18) or in the interaction potentials used to model solid surfaces (19). The major reason, however, for this ability has resulted from the increasing sophistication of the interaction potentials used to model liquid-liquid interactions. These advances have involved the use of the following potentials Lennard-Jones 12-6 (20), Rowlinson (21), BNS... 

This algorithm has been applied to calculate the thermal conductivity of a variant of the Gay-Beme fluid where the Lennard-Jones core has been replaced by a purely repulsive 1/r core [20]. Two systems were studied, one consisting of prolate ellipsoids with a length to width ratio of 3 1 and another one consisting of oblate ellipsoids with a length to width ratio of 1 3. The potential parameters are given in Appendix II. They both form nematic phases at high densities. 

The first molecular simulations were performed almost five decades ago by Metropolis et al. (1953) on a system of hard disks by the Monte Carlo (MC) method. Soon after, hard spheres (Rosenbluth and Rosenbluth, 1954) and Lennard-Jones (Wood and Parker, 1957) particles were also studied by both MC and molecular dynamics (MD). Over the years, the simulation techniques have evolved to deal with more complex systems by introducing different sampling or computational algorithms. Molecular simulation studies have been made of molecules ranging from simple systems (e.g., noble gases, small organic molecules) to complex molecules (e.g., polymers, biomolecules). 

It is also important that the method used to simulate multi-protein systems be fast. Most of the models used in simulating multi-protein systems are based on continuous intermolecular potentials like the Lennard-Jones potential. Simulations based on continuous potentials proceed by solving Newton equations at a uniformly spaced time intervals. They have an algorithm complexity of C>(Mog N), where IVis the number of particles in the system. The big-(9 notation describes how the performance or complexity (referring to the number of operations) required to mn an algorithm depends on the number of particles in the system. Therefore, the required computational time for continuous MD simulations increases dramatically with the number of beads in the system, limiting their application to relatively small systems. 

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