Pivots, moving

Let us leave, for a moment, the domain of discrete torsion angles and consider torsion-angle moves in a torsion continuum. Much effort has been directed to the development of efficient phase-space sampling methods for MC [17,23,37,128-138]. The simplest off-lattice move - being a pivotal move [128,131] of a single torsion angle at a time - hardly samples configuration... 

Only two broad types of useful non-local moves are known at present pivot moves, and cut-and-paste moves. 

In a pivot move, we choose some site w along the walk as a pivot point, and apply some symmetry operation of the lattice (e.g., rotation or reflection) to the part of the walk subsequent to the pivot point, using the pivot point as the origin (Fig. 2.7). That is, the proposed new walk is... 

Fig. 2.7 The pivot move (here a -1-90° rotation). The pivot site is indicated with a cross. Dashed lines indicate the proposed new segment.

The pivot move trail is the more efficient move for the sampling of the polymer chain. 

The bending move is very similar to the pivot move. In this case the rotation is carried out on a segment of the chain between the monomers j and k (see Fig. 4). The rotation axis is determined by the direction that connect the two monomers ... 

The traction thickener includes a traction mechanism where the movement of the rake is suppHed by a single long arm pivoted around the center column and driven by a troUey that moves on a peripheral rail around the basin. Such units have diameters of 60—130 m. 

The elevation angle, and through appropriate data processing a, can be measured with a bivane (a vane pivoted so as to move in the vertical as well as the horizontal). Bivanes require frequent maintenance and caUbra-tion and are affected by precipitation and formation of dew. A bivane is therefore more a research instrument than an operational one. Vertical fluctuations may be measured by sensing vertical velocity w and calculating o- , from the output of a propeller anemometer mounted on a vertical shaft. 

ACTION OF PIVOTED SHOES, 5UPPORTMG A LOAOEO,MOVING PLATE IN AN OIL BATH. 

Kumar, S. and Ramkrishna, D., 1996b. On the solution of population balance by discretization IE A moving pivot technique. Chemical Engineering Science, 51, 1333-1342. 

The universal-coupling configuration used by jackshafts (Figure 44.57) generate an elevated vibration frequency at the fourth (4x) harmonic of its tme rotational speed. This failure mode is caused by the binding that occurs as the double pivot points move through a complete rotation. 

The compound Lajln has Tc = 10.4 K. Because La is hypoelectronic and In is hyperelectronic, I expect electron transfer to take place to the extent allowed by the approximate electroneutrality principle.13 The unit cube would then consist of 2 La, La, and In+, with In+ having no need for a metallic orbital and thus having valence 6 with the bonds showing mainly pivoting resonance among the twelve positions. The increase in valence of In and also of La (to 3 f ) and the assumption of the densely packed A15 structure account for the decrease in volume by 14.3%. Because the holes are fixed on the In + atoms, only the electrons move with the phonon, explaining the increase in Tc. 

It is this integrative attitude that today characterizes most of the work in the area of intelligent systems for process engineering, as the editors of this volume have indicated in a recent review article. (4) It is this need for integrative approaches that has moved the applications of artificial intelligence into the mainstream of engineering activities. This is certainly the pivotal feature that characterizes the ten paradigms discussed in the subsequent chapters. 

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