Higher-order propagators

The first higher-order propagator (TILB) was put forward by Takahashi and Imada [68] and independently by Li and Broughton [69]. TILB is very special in that, although being only second order, 0(P ), it produces a partition function accurate up to fourth order, that is, This is a fortunate consequence of the... 

A full discussion of the reasons for the success of the pair action approach, some estimates of the order of accuracy, and the measures to enhance its performance can be found in Ceperley s review [28], However, the exact density matrix contains not only pair terms but also triplet terms, quadruplet terms, and so on. These terms are needed in the study of situations at very high densities. In relation to this, although some clever tricks can be used to deal with the pair case, the next extension to deal with triplet terms is far from straightforward, because of the increase in the number of variables needed (e.g., for a homogeneous and isotropic fluid from four variables in the pair case to 13 in the triplet case) [28]. Furthermore, it is difficult to anticipate what the order of accuracy ) of a triplet action will be. This situation contrasts sharply with that of the higher-order propagators, for which the order of accuracy is always known. Another problem in this context is that the usefulness of pair actions cannot be extended to deal with non-symmetri-cally spherical potentials (e.g., molecular fluids). 

Within the elastic regime, the conservation relations for shock profiles can be directly applied to the loading pulse, and for most solids, positive curvature to the stress volume will lead to the increase in shock speed required to propagate a shock. The resulting stress-volume relations determined for elastic solids can be used to determine higher-order elastic constants. The division between the elastic and elastic-plastic regimes is ideally marked by the Hugoniot elastic limit of the solid. 

Jacobson-Stockmayer theory (L2.). Usually transfer and termination reactions in polymerization have energies of activation higher than propagation. Thus, we attempted coupling reactions at temperatures lower than usually applied. In order to assure the access of dichlorosilane to the surface of the sodium, the dispersion was continuously regenerated by ultrasonication. 

In deriving Eq. (451), we have systematically neglected the contributions to the propagator coming from the B-particles, which give a higher-order contribution in yv, and we have written, in accordance with Eq. (227) ... 

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