Slithering snake algorithm

Clearly, both the pivot and the slithering snake algorithms are incapable of reproducing true chain dynamics at molecular basis, covering the time range of typical chain relaxation times. Therefore, in the following we focus on two alternative methods, broadly used at present to this end. 

Fig. 5.13. Relaxation time r3 plotted vs. temperature for the coarse-grained model of PE with N = 20, using the random hopping algorithm (upper set of data) or the slithering snake algorithm (lower set of data), respectively. The time r3 is of the same order as the Rouse relaxation time of the chains, and is defined in terms of a crossing criterion for the mean-square displacements [41], g3(t = r3) = g2(t = r3) [See Eqs. (5.2) and 5.3)]. From [32]...

On the other hand, one strength of the approach is the availability of algorithms (such as the slithering snake algorithm) by which undercooled polymer melts can be equilibrated at relatively low temperatures. This allows the static properties of the model to be established over a particularly wide parameter range. Furthermore, the lattice structure allows many questions to be answered in a well-defined, unique way, and conceptional problems of the approach can be identified and eliminated. Last but not least, the lattice structure allows the formulation of very efficient algorithms for many properties. 

By virtue of the slithering-snake algorithm it is (hitherto) possible to remove all non-equilibrium effects up to T 0.16 so that one can study the equilibrium dynamic properties of the model in the supercooled state. During supercooling the structural relaxation time increases over several orders of magnitude, and dynamic... 

FIG. 6 (a) Example of a SAW on the square lattice that cannot move if the slithering snake algorithm is used, (b) Example of a SAW on the square lattice that cannot move if a combination of the slithering snake algorithm and the... 

Fig. 1.4 Various examples of dynamic Monte Carlo algorithms for SAWs sites taken by beads are shown by dots, and bonds connecting the bead are shown by lines. Bonds that are moved are shown as a wavy line (before the move) or broken line (after the move), while bonds that are not moved are shown as full lines, (a) Generalized Verdier-Stockmayer algorithm on the simple cubic lattice showing three type of motions end-bond motion, kink-jump motion, 90° crankshaft rotation (b) slithering snake algorithm (c) pivot algorithm. (From Kremer and Binder )...

The physical picture, giving gz t > tn) = 6D N)t comes from the diffusion of the chain along the tube. This motion is the same as used in the standard slithering snake algorithm. If we follow Semenov and Rubinstein and Obukhov, this diffusion is retarded due to the long life-... 

Similar restrictive comments need to be made about the existing simulations of spinodal decomposition in polymer blends. First studies addressed the two-dimensional case. In this case, there is no chain interpenetration, and since polymer mixtures in d =2 dimensions are not predicted to become mean-field-like for AT —> oo, one expects the same behavior as in small molecule mixtures, and this is what has been found. Using the slithering snake algorithm, the dynamics of the model is neither realistic at short times (where the chain dynamics should be described by Rouse-model type motions ) nor at late times (where hydrodynamic effects play a role, as discussed above, at least in d=3 dimensions). 

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