Structural inhomogeneity fluctuations

A major source of real-structure inhomogenities are wire-thickness fluctuations and polycrystallinity, and geometrical features at wire ends [54, 55, 114, 158]. As expected from 2.3.4, the localization of the modes is accompanied by a coercivity reduction [54, 55, 114]. 

Fig. 5. Fluctuating band edges of amorphous semiconductors arising from compositional or structural inhomogeneities. A typical eigenstate near the conduction band edge is shown transport of conduction electrons involves tunneling between neighboring minima or thermal activation.

Here, x and are material parameters x is proposed to be proportional to the degree of interpenetration of chains and junctions, and it defines the strength of restrictions on junction fluctuations. The value x = 0 corresponds to the free-fluctuation limit and for X - 00 the affine network is obtained. The parameter (< 1) characterizes departures of the shapes of domains from the affine transformation assumption and reflects the effect of structural inhomogeneities on the network structure Although its presence is not as critical as that of x, comparison of experiment with the theory of restricted junction fluctuations shows that it is necessary... 

All the wavelengths which are amplified for b > b do not correspond to physically realisable patterns. The curve D.. (q, e ) = 0 and Dj (q.> e ) = 0 delineate the region where the structure (rolls) is stable against inhomogeneous fluctuations. From Eq. (111.6,7)> the system becomes unstable with respect to compression and dilatation of the rolls for > e / 3 (Eckhaus instability) whereas for Q < 0, it is unstable against wavy distor-... 

Gas-particle flows in fluidized beds and riser reactors are inherently unstable and they manifest inhomogeneous structures over a wide range of length and time scales. There is a substantial body of literature where researchers have sought to capture these fluctuations through numerical simulation of microscopic TFM equations, and it is now clear that TFMs for such flows do reveal unstable modes whose length scale is as small as ten particle diameters (e.g., see Agrawal et al., 2001 Andrews et al., 2005). 

The width of a band in the absorption spectrum of a chromophore located in a particular microenvironment is a result of two effects homogeneous and inhomogeneous broadening. Homogeneous broadening is due to the existence of a continuous set of vibrational sublevels in each electronic state. Inhomogeneous broadening results from the fluctuations of the structure of the solvation shell... 

The second cause of broadening of electronic spectra is the fluctuations in the structure of the solvation shell surrounding the fluorophore. The distribution of solute-solvent configurations and the consequent variation in the local electric field leads to a statistical distribution of the energies of the electronic transitions. This phenomenon is called inhomogeneous broadening (for a review see Nemkovich et al., 1991). 

It is not an easy task to define inhomogeneities in the structure of a polymer network. Every system will exhibit the presence of defects and fluctuations of composition in space when the scale of observation becomes smaller and smaller. A hierarchy of structures exists, from atomic dimensions to the macroscopic material. A scheme of different scale levels used to describe linear and crosslinked polymer structures is shown in Fig. 7.2. Inhomogeneities described in the literature for polymer networks are ascribed to permanent fluctuations of crosslink density and composition, with sizes varying from 10 nm up to 200 nm. This means that their size lies in the range of the macromolecular scale. 

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