Cluster trial move

Keywords Charged coUoids Monte Carlo simulation - Mean force Ewald summation Cluster trial move... 

Figure 18 displays the acceptance ratio and for cluster trial moves... 

Fig. 17 Schematic illustration of a cluster trial move showing the location of a macroion (large filled circles) and counterions (small circles) a before and b after the cluster trial move. Counterions moved together with the macroion are denoted hy filled circles, those within Pci before the move but not moved by open circles, and new ions within Pd after the move by shaded circles. In this example, Mnew = 7, ttoid = 7, and new - Mold = 0...

Fig. 18 a Macroion acceptance ratio and b macroion root-mean-square displacement per MC pass as a function of the cluster displacement parameter for System 11 from simulations with cluster trial moves using pd = 1.0 and indicated cluster radii R i in Ru units. At = Rm fhe single-particle move is recovered. In a, the acceptance ratio equal to 0.5, and in b, the relation = A /i/2 are given (dotted lines). Nm = 20 and Npass = 10 ... 

Features of the cluster displacement approach are further illustrated in Fig. 19, displaying acceptance ratio, macroion rms displacement, and mun-ber of cluster members as a function of the electrostatic coupUng parameter Tii at Zr = 80 using the cluster displacement parameter d = Ru at different cluster radii Rc. At an electrostatic coupling below Tn 0.03, cluster trial moves are sHghtly iirferior to single-macroion trial moves (smaller acceptance ratio and smaller see Fig. 19a and b, respectively). As the... 

Finally, the present comparison has been made for salt-free systems. It should be mentioned that the performance of single-macroion trial moves is essentially salt independent, whereas the performance of cluster trial moves deteriorates upon addition of salt, making the difference in their performances smaller. Nevertheless, the cluster displacement procedure is advantageous up to considerable salt concentrations. A promising method to improve... 

We have seen that at high electrostatic coupling macroions with nearby counterions (referred to as dressed macroions) form aggregates (Fig. 6a), eventually leading to a phase separation (Fig. 2). The mobility of dressed macroions in such aggregates is very low, even with optimized cluster trial moves. Besides hard-core overlap with nearby dressed macroions, it is energetically unfavorable to displace a macroion M away from another macroion M with which macroion M shares dressed counterions. 

Fig. 20 Schematic illustration of a cluster move of the second level involving a joint displacement of an aggregate composed of macroions and the small ions near these macroions a before and b after the cluster trial move. Here, three macroions large filled circles) and the small ions small filled circles) within the distance from the macroions form an aggregate subjected to the trial move...

This approach is very general. For example, it is not restricted to monodis-perse systems, and Krauth and co-workers have applied it successfully to binary [17] and polydisperse [18] mixtures. Indeed, conventional simulations of size-asymmetric mixtures typically suffer from jamming problems, in which a very large fraction of all trial moves is rejected because of particle overlaps. In the geometric cluster algorithm particles are moved in a nonlocal fashion, yet overlaps are avoided. 

Sect. 6, different aspects on the simulation of bulk solutions of asymmetric electrolytes using periodic boundary conditions are given. First a comparison of different boundary conditions is presented in Sect. 6.1. Then, in Sect. 6.2, the Ewald summation is examined, and issues such as system size convergence, energy summation convergence, and optimization of the CPU time are discussed. Section 6.3 contains an analysis of the selection of trial moves, and in particular the usefulness of a cluster move technique is illustrated. Furthermore, a second-level cluster move technique, facilitating simulation of phase-separating systems, will also be treated briefly. 

In the present context, a cluster is composed of a central macroion and neighboring small ions. Small ions located within the distance Rc from the macroion center will belong to the cluster with a probability pci < 1 [109]. The trial move of the whole cluster as one entity is accepted with the probability... 

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