Single-bond effective medium

The simplesf mefhod of solution of fhe Kirchhoff equations that correspond to the random network of conducfance elemenfs in three dimensions is in the single-bond effective medium approximation (SB-EMA), wherein a single effective bond between two pores is considered in an effective medium of surrounding bonds. The conductivify (7b, of fhe effective bond is obtained from the self-consistent solution of fhe equation ... 

This model, when applied to Nation as a function of water content, indicated a so-called quasi-percolation effect, which was verified by electrical impedance measurements. Quasi-percolation refers to the fact that the percolation threshold calculated using the single bond effective medium approximation (namely, x = 0.58, or 58% blue pore content) is quite larger than that issuing from a more accurate computer simulation. This number does not compare well with the threshold volume fraction calculated by Barkely and Meakin using their percolation approach, namely 0.10, which is less than the value for... 

The simplest approach to solve the Kirchhoff equations that correspond to the random network of conductance elements is obtained in single-bond effective medium approximation (SB-EMA), wherein a single effective bond... 

Let us consider the lattice of bonds illustrated in Fig. 4.16. The real bond introduces the interaction wL (with values w or 0), but no diagonal term. In contrast, the effective bond introduces an interaction weff(z) and a bond potential s(z) at the two ends. In the case of a lattice with all bonds equivalent, the effective medium is represented by a single type of bond the Green s function of this medium takes the form... 

A stress that is describable by a single scalar can be identified with a hydrostatic pressure, and this can perhaps be envisioned as the isotropic effect of the (frozen) medium on the globular-like contour of an entrapped protein. Of course, transduction of the strain at the protein surface via the complex network of chemical bonds of the protein 3-D structure will result in a local strain at the metal site that is not isotropic at all. In terms of the spin Hamiltonian the local strain is just another field (or operator) to be added to our small collection of main players, B, S, and I (section 5.1). We assign it the symbol T, and we note that in three-dimensional space, contrast to B, S, and I, which are each three-component vectors. T is a symmetrical tensor with six independent elements ... 

Recent ab initio calculations of a wide series of Si-substituted 2,8,9-tricarbasilatranes (X = H, Me, H2N, HO, F, 113 S i, H2P, HS and Cl) found a single minimum corresponding to the endo form on the potential energy coordinate of the Si<—N bond deformation194. The transannular bond was shown to be very soft and sensitive to the medium. The substituent effect on this bond length and mutual weakness of the axial bonds of the TBP silicon are well described by the 3c4e bonding model. 

---