Macroscopic features

In the analysis of crystal growth, one is mainly interested in macroscopic features like crystal morphology and growth rate. Therefore, the time scale in question is rather slower than the time scale of phonon frequencies, and the deviation of atomic positions from the average crystalline lattice position can be neglected. A lattice model gives a sufiicient description for the crystal shapes and growth [3,34,35]. 

This section will consider first the structure of pure metals and this will be followed by a description of the structure of alloys. In general, structural features will be discussed in order of increasing size, i.e. starting with atomic features and continuing through microscopic features to macroscopic features. 

Ad. 1. Theoretical considerations including calculations based on the knowledge of anatomical features. While considering whether or not it is reasonable to believe that the non-mono-exponential transverse relaxation reflects an intra- and extra-cellular compartmentalisation, it should be questioned if the slow-exchange assumption is reasonable taking into account the macroscopic features of a muscle cell from a theoretical point of view. The NMR-timescale criterion for exchange limit is comparison of the quantity (rr1 + t"1), where r, and t0 are the average lifetime of a water molecule inside and outside the cell, respectively, with Rt — R , which is the absolute difference in the intrinsic relaxation rates. If R —Rfl > (h 1 + ), the... 

Ad. 4. Alteration of anatomical features. Finally, several studies have attempted to manipulate the macroscopic features of muscle/meat tissue in order to verify or disprove the intra-/extra-cellular model. Efforts have been made to disrupt cell membranes by glycerination and DMSO treatment in order to make assessment of the potential role of membranes possible.30,40,41 All these studies showed unaltered relaxation behaviour upon membrane disintegration, which suggests that intact cell membranes in themselves are not necessary for a non-mono-exponential relaxation. Irrelevance of membranes... 

Another macroscopic feature that arises from surface tension is the rate, u, at which a liquid will spread on a solid surface (again, ignoring any viscoelastic... 

On the other hand, the macroscopic features are determined by all particles together. Thus one expects the importance of fluctuations to be relatively small when the system is large. In fact, this has been amply illustrated by the examples of linear systems treated so far. They led to the rule of thumb that in a collection of N particles the fluctuations are of order N1/2. Their effect on the macroscopic properties will therefore be of order iV-1/2. Thus it is clear that the size of the system is a parameter that measures the relative importance of the fluctuations. We shall therefore introduce a size parameter Q. The precise definition of Q depends on the system, but we here formulate its general properties. 

As pointed out in Chapter 1, supramolecular chemistry comprises two broad, partially overlapping areas covering on the one hand the oligomolecular supermolecules and, on the other, the supramolecular assemblies, extended polymolecular arrays presenting a more or less well-defined microscopic organisation and macroscopic features depending on their nature (layers, films, membranes, vesicles, micelles, microemulsions, gels, mesomorphic phases, solid state species, etc.). 

Following a variational solution of the ground (Is) and first excited state (2p) of the electron in this potential well, various other polarization terms are added and a variety of characteristics for the solvated electron (optical transition energy, heat of solution, etc.) can be calculated (101,105). For illustrative purposes, we shall utilize this simple model because of its obvious transparency in relating certain (macroscopic) features of solvent properties to the energy levels and wave functions for the solvated electron in polar solvents. 

Several experimentally available macroscopic features have been used to validate the results of MD simulations. Among them are ... 

Until today the mechanism of Nd-catalyzed BD polymerization is not understood in full detail. This state of understanding is reflected by contradictory results between numerous studies. In spite of these differences there are reaction models which allow for a qualitative explanation of most of the macroscopic features observed. In this section the common points of understanding between the various studies as well as the contradictions are addressed. In the first step results on the polymerization kinetics are summarized. 

Here, we shall consider several macroscopic features of the plastic deformation of glassy epoxy-aromatic amine networks. Mostly, the tensile or compression deformation has an inhomogeneous character. Usually, diffuse shear zones (or coarse shear bands) are clearly seen at room temperature deformation. Shear zones start from the defects on the sample boundaries or voids (dust) in the bulk. At higher temperatures, the samples are homogeneously deformed with neck formation (DGER-DADPhS, P = 1) 34>. 

In order to appreciate the application of pulsed n.m.r. spectroscopy, it is instructive to consider the macroscopic features of an assembly of magnetic moments of the nuclei. 

These observations, coupled with the effects of bubble texture (1,13-15) and various history dependent phenomena, clearly demonstrate the inadequacy of conventional fractional flow approaches to describe foam flow in porous media. Also, early approaches which treated the foam simply as a fluid of modified viscosity are also inadequate in explaining the above characteristics. To achieve a fuller understanding of such phenomena, a detailed description of the pore level events is required. In what follows, a simple pore level model is utilized to explain some of the above macroscopic features and to identify some of the key pore level mechanisms. 

Macroscopic features such as the shapes of membrane elements, modules and systems and general application characteristics will be covered in Chapter 5. Good understanding of the basic membrane characteristics should provide the much needed background and guidelines for design and operation of the membrane systems. 

Unless there is a macroscopic feature, such as an external electric field, defining the global axis system, the coordinate system is just an abstract frame of reference, and U(R, Q.) cannot depend on the relative orientation of the two... 

Part of the experiments described in this chapter have been performed using a SAS transparent precipitator that has two quarts windows placed along the entire height of the vessel. This apparatus allows the visual observation of the macroscopic features of the precipitation process. 

Lundberg, N. and Casey Moore, J. 1986. Macroscopic features in Deep Sea Drilling Project cores from forearc regions. Geol. Soc. Am. Mem., 166 13-44... 

Figure 2.9 Characteristics of groundwater calcretes. (A) Generalised macroscopic features based on various sources. Some workers, such as Carlisle (1980), identify two zones in the massive phreatic unit an upper earthy zone with remnant soil and alluvium, and a lower, dense porcellaneous zone with abundant cracks and cavities. Phreatophytic plants may also produce features such as rhizocretions and laminar rhi-zolite crusts (Seminiukand Meagher, 1981). (B) Generalised model for the evolution of groundwaters and their precipitates in semi-arid to arid alluvial systems based on Arakel (1986).

Clearly, w,(f) will depend on the averaging interval x. We need to choose x large enough so that an adequate number of fluctuations are included, but yet not so large that important macroscopic features of the flow would be masked. For example, if Xi and %2 are timescales associated with fluctuations and macroscopic changes in the flow, respectively, we would want X2 x xi. 

The problem of thermal initiation can be seen to be that of confining the heat produced in a sufficiently small volume so that the temperature rises enough to generate a fast reaction. In this section some mechanisms are considered in which hot spots are produced mechanically. But first, it will be instructive to establish a framework for the discussion by considering further the macroscopic features of thermal decomposition and the comparative reactivity of the azides. 

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