Order parameter local

P is the critical exponent and t denotes the reduced distance from the critical temperature. In the vicinity of the critical point, the free energy can be expanded in tenns of powers and gradients of the local order parameter m (r) = AW - I bW ... 

In principle, the Knn could be deduced from electronic structure calculations, but the smallest ones amount only to fractions of meV, whereas the calculations deal with binding energies, i.e. some eV it can be understood why the calculation techniques are not yet sufficiently accurate to compute detailed interactions, and why we find it better, until now, to extract them from local order parameters ... 

The thermodynamical properties of the APB will be investigated through the behavior of some local order parameter definec for each fee cube having co-ordinates x,y,z = R in a given MonteCarlo (MC) configuration C as ... 

The stability of the chains can also be observed in the time plots of the local order parameter (Fig. 17). For the chain of L = 100, the local order pa-... 

Fig. 17 Comparison of local order parameter for L = 100 and L = 125 chains from Figs.15 and 16. The stability differences between chains of integer multiple lengths versus mismatched chains is evident...

The reorientation of the local chain axis gives rise to the partial narrowing of the amorphous REV-8 spectra and is of a random nature. In a short period of time, a particular segment of the macromolecular chain assumes a distribution of directions which deviate from its orientation at rest. In analogy to the description of molecular ordering in liquid crystals—, we use the concept of a local order parameter for the quantitative characterization of the extent of these fluctuations. 

Figure 12. Temperature dependence of the local-order parameter, So, of the fluctuating chain directions in the amorphous regions of PTFE (O) and a TFE/...

Figure 14. Temperature dependence of p = (1 — Spj/Sp, Sp being the local-order parameter in the amorphous regions of PTFE. This quantity is related to the population of kinks (sec text). AE = 3.3 kcal/mol.

When we now consider a thin film of thickness D, Eq. (41) must be supplemented by boundary conditions of the same type as in the polymer blend case, Eqs. (7) and (10), i.e. we add a (bare) surface free energy contribution to the free energy that accounts for preferential attraction of one kind of monomers to the walls, missing neighbors in the pairwise interactions, and possible changes in the pairwise interactions near the surface. As in the blend case, this surface contribution is taken locally at the walls only and expanded to second order in the local order parameter /(z). Per unit area of the wall, this free energy is written as... 

Other order parameters can be used to characterize ice/water interfaces via change in average density [17, 19] and diffusivity [17] across the interface. Local order parameters can also be defined which depend only on the position of a reference molecule. It was shown in [40] that the local tetrahedral order parameter, which reflects the change in tetrahedral environment, leads to a 10-90 width of 11 A for the basal ice-water interface which is in good agreement with the estimated value from the translational order parameter. 

The origin of the difficulty is the assumption of an equilibrium orientation distribution. In reality, the large spatial gradients at the defect would distort the molecular orientation distribution and severely reduce the local order parameter. 

For He below the lambda point, v(r) represents the velocity of the superfluid. The wavefunction [Eq. (11)] corresponds to a complex local order parameter [130-135] associated with the macroscopic occupation of the Bose-Einstein condensate. 

The free energy density/(r) of the inhomogeneous hnite system with a local order parameter /(r) was expressed by adding to Eq. (24), an even expansion of the gradient term, so that... 

Disregarding any long range forces due to the walls (Dietrich, 1988), we may assume that Fv(bare) depends on the local order parameter = [Pg.229]

Here we have omitted constant terms in the free energy and anticipated that a molecular field treatment of an Ising Hamiltonian that describes exactly the situation considered here, namely eq. (1), is consistent with eq. (220). The coefficient of the linear term in eq. (220) thus describes the action of a local field (i.e., the variable conjugate to the local order parameter) right at the hard walls (or free surfaces, respectively). If

order parameter of gas-liquid condensation, the field H can be interpreted as the binding potential of particles at the hard wall. 

Apart from this local order parameter 0i and its derivatives there is also interest in the surface excess order parameter 0S defined from the shaded area underneath the profile in fig. 46a as... 

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