Crankshaft moves

A variety of rules can be introduced to generate stochastic changes. Local changes (or bead-jump moves) in a chain should include end moves, usually bents of terminal bond, and inner moves [103]. Figure 6 contains illustrations of these moves on a simple cubic lattice. Inner bents (in which a unit between two perpendicular bonds moves to the empty opposite corner) should alternate with crankshafts (moves involving two units and three bonds that take place when the... 

On a lattice, so-called crankshaft moves are trivial implementations of concerted rotations [77]. They have been generalized to the off-lattice case [78] for a simplified protein model. For concerted rotation algorithms that allow conformational changes in the entire stretch, a discrete space of solutions arises when the number of constraints is exactly matched to the available degrees of freedom. The much-cited work by Go and Scheraga [79] formulates the loop-closure problem as a set of algebraic equations for six unknowns reducible... 

Carlo simulation (1) end flip, (2) corner move, (3) kink jump, and (4) crankshaft move. The solid lines are bonds in one of many possible configurations and the dotted lines are potential new bond positions. 

FIGURE 5.5. The idea of the pivot aigorithm (A), and the iocai moves aigorithm (B). The biack contours indicate the initiai structures, the iighter bonds show the accepted modifications. The iocai moves inciude (from top to the bottom of B) random chain end modification, a crankshaft move and a corner move. 

The move set used for both thermodynamic sampling and dynamics (the use of the word dynamics here should be taken cautiously) of the AB model is similar to that employed for the HP model. The move set includes corner, end, and crankshaft moves as indicated in Figure 5c. To advance from one conformation to the next, a monomer is chosen at random, and, depending on its location on the lattice, either a corner, an end, or a crankshaft move is attempted. If the attempted move puts the monomer on an already occupied site, that move is rejected to preserve excluded volume, and a new monomer is chosen. Once a monomer has been selected and the move deemed possible, the energy of that new conformation is calculated. If the new conformer s energy is lower than that of the previous conformation, the move is accepted. If the energy is higher, it is accepted with the usual Boltzmann probability ... 

Figure 9.15 Kinks and kink inversion, (a) The conformational sequence. .. TTTGTG TTT. .. has parallel offset planar zigzag stems (indicated by arrows) on either side of the GTG portion. The transition TGTG TG TGT (called here kink inversion) creats a mirror image of the kink about the displaced stems, (b) A three-bond crankshaft move is shown at a kink site (as dashed line). This move advances the kink along the chain by 2CH2 units. (Reproduced with permission from Boyd, Polymer, 26, 1123 (1985))...

A comparison between RCBl, RCB2, and simple crankshaft moves was also considered (Fig. 17). One can see that the improvement over the simple crankshaft move is significant for both the RCBl and RCB2 moves. The optimum number of sites to be regrown depends on the system conditions, but in general the improvements tend to be large for the first sites that are excised, and they taper off gradually. 

In Fig. 2.2 we show all the possible internal two-bead moves. Move D is a 180° crankshaft . Move E is a 90° crankshaft of course it is possible only in dimension d> 3. Move F is a two-bead L-flip . Move G permutes three successive mutually perpendicular steps (which lie along the edges of a cube) again this is possible only in dimension d> 3. 

Fig. 7.5 In dynamic Monte Carlo simuiations of the original Fiory-Huggins modei ehain configurations are relaxed by end-bond rotations, kink jump motions, and 90° crankshaft moves (A). Only such moves are allowed that do not violate the excluded voltmie constraint. In a semi-grand-canonical simulation, where the chemical potential difference A/x between A-and B-monomers is fixed, A-chains are taken out of the system and B-chains are inserted in exactly the same configuration, or vice versa (B). (From Binder. )...

Figure 2 Illustration of the principle of operation of various elementary Monte Carlo moves a simple reptation move (top), a Continuum configurational bias move (center) and a crankshaft move (bottom)...

Example for a simple Monte Carlo move set consisting of end and corner flips, crankshaft moves, and pivot updates on a square lattice. 

This arrangement of valves defines a push-rod engine. In the alternative approach of Figure 2, the camshaft is moved to a position above the cylinder head, eliminating the push rod. This configuration defines an overhead-cam engine. The overhead camshaft is driven from the crankshaft by either a belt or a chain. 

Few machines involve linear reciprocating motion exclusively. Most incorporate a combination of rotating and reciprocating linear motions to produce work. One example of such a machine is a reciprocating compressor. This unit contains a rotating crankshaft that transmits power to one or more reciprocating pistons, which move linearly in performing the work required to compress the media. 

Fig. 6a-d. Scheme of bead-jump moves for a linear chain on a simple cubic lattice a bent (end move) b bent (inner move) c crankshaft (end move) d crankshaft (inner move). Solid lines Initial bonds broken lines final bonds (alternative possibilities included)... 

The crankshaft model treats the molecule as a collection of mobile segments that have some degree of free movement. This is a very simplistic approach, yet very useful for explaining behavior (Fig. 2). As the free volume of the chain segment increases, its ability to move in various directions also increases. This increased mobility in either side chains or small groups of adjacent backbone atoms results in a greater compliance (lower modulus) of the molecule. These movements have been studied, and Heijboer classified p and y transitions by their type of motions. The specific temperature and frequency of this softening help drive the end use of the material. 

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