Ordering local

The Bragg peaks indicated an ordered local structure within the sample film, and the interlayer spacings were reproduced compared with the bulk samples, with only... 

An important hierarchy of parameterization schemes based on successive refinements to a mean-field theoretic description, called local structure theory, has been developed by Gutowitz, et. al. ([guto87a], [guto87b], and [guto88]), and is discussed in detail in chapter five. Below we summarize results of what is essentially a zeroth order local structure theory developed by Langton [lang90]. 

Conditions (5) of Section 1 relating to the second-order local approximation for the conservative scheme (17) acquire the form... 

Short-range order (local environment around absorber)... 

Figure 7.17 AFM image of polyethylene grown at 160 °C and subsequently crystalli/.ed during cooling on the surface of a planar CrOVSiOj catalyst. The left hand inset indicates schematically how polyethylene molecules fold into lamellar structures. The AFM image shows how these lamellae have a tendency to order locally. The right hand inset is a measurement at higher magnification in phase contrast, and shows that lamellae contain substructure, attributed to ordered and amorphous domains (courtesy of J. Loos and P. Thiine [48]).

In addition to the effects of motional narrowing, vibrational line shapes for the OH stretch region of water are complicated by intramolecular and intermolecular vibrational coupling. This is because (in a zeroth-order local-mode picture) all OH stretch transition frequencies in the liquid are degenerate, and so the effects of any... 

A similar treatment can be done for bent molecules in the scheme of van Roosmalen. The lowest-order, local-mode limit is given by... 

Putting one cross in the second order diagram the two third order localization diagrams, can be obtained (Figure 2.)... 

This oscillation may have no relation at all to the behavior of the "true" function. Therefore, we cannot recommend global interpolation except for small samples. In large samples interpolation is rarely needed. For medium size samples low order local interpolation considering 3-6 nearest neighbors of the point x of interest does the job in most cases. The most popular method is local cubic interpolation in the Aitken form programmed in the following module. 

Perhaps the most pertinent observation to make at this point is that the process by which the molecule with energy spectrum hypothesized decays is simply a form of predissociation. There is one difference between the process we consider and the usual case of predissociation from a single zero-order molecular energy level. Because the exact resonant level is represented as a linear combination of the zero-order localized level, the... 

As it was already written above, we would like to study structural changes in the charge distribution between macroscopic objects, that is caused by the image forces, and depends on the wall-to-wall distance. To obtain direct structural information about the system, we will introduce a configurational analogue of the phase-space distribution function. At equilibrium, the definition of an fth order distribution function given by Eq. (12) can be applied to the equilibrium probability density [Eq. (13)], and the integration with respect to impulses can easily be carried out. We write for the rth order local density... 

Visual inspection of the wavefunctions reveals another feature of the nonadiabatically delocalized states, which is crucial for rationalizing the effect and building up a model. Namely, the perpendicular quantum numbers v and V3 of the weak component of these states systematically coincide with the perpendicular quanmm numbers of an adjacent adiabatically delocalized state. This suggests that weak delocalization is induced by coupling between a certain zero-order localized state and a neighboring adiabatically delocalized state... 

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