Homogeneous and inhomogeneous

Integral equations provide a satisfactory formalism for the study of homogeneous and inhomogeneous fluids. If the usual OZ equation is used, the best results are obtained from semiempirical closures such as the MV and DHH closures. However, this empirical element can be avoided by using integral equations that involve higher-order distribution functions, but at the cost of some computational complexity. 

N. Steigerwald, M. L. and Brus, L. E. (1988) Electronic states of semiconductor clusters - homogeneous and inhomogeneous broadening ofthe optical-spectrum./. Chem. Phys., 89, 4001 1011. 

Dahnke S, Keil F (1998) Modeling of three dimension linear pressure field in sonochemical reactores with homogenous and inhomogenous density distribution of cavity bubbles. Ind Eng Chem Res 37 848-864... 

The technical terms homogeneity and inhomogeneity defined in analytical chemistry must be distinguished from the physicochemical concept of homogeneity and heterogeneity (Danzer and Ehrlich [1984]). Whereas the thermodynamical definition refers to morphology and takes one-phase-or multi-phase states of matter as the criterion, the analytical-chemical definition is based on the concentration function... 

Besseling, N. A. M. and Scheutjens, J. M. H. M. (1994). Statistical thermodynamics of fluids with orientation-dependent interactions in homogeneous and inhomogeneous systems, J. Phys. Chem., 98, 11 597-11 609. 

In (5.297), the interpolation parameter is defined separately for each component. Note, however, that unlike the earlier examples, there is no guarantee that the interpolation parameters will be bounded between zero and one. For example, the equilibrium concentration of intermediate species may be negligible despite the fact that these species can be abundant in flows dominated by finite-rate chemistry. Thus, although (5.297) provides a convenient closure for the chemical source term, it is by no means guaranteed to produce accurate predictions A more reliable method for determining the conditional moments is the formulation of a transport equation that depends explicitly on turbulent transport and chemical reactions. We will look at this method for both homogeneous and inhomogeneous flows below. 

Despite the ability of the GLM to reproduce any realizable Reynolds-stress model, Pope (2002b) has shown that it is not consistent with DNS data for homogeneous turbulent shear flow. In order to overcome this problem, and to incorporate the Reynolds-number effects observed in DNS, a stochastic model for the acceleration can be formulated (Pope 2002a Pope 2003). However, it remains to be seen how well such models will perform for more complex inhomogeneous flows. In particular, further research is needed to determine the functional forms of the coefficient matrices in both homogeneous and inhomogeneous turbulent flows. 

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... 

Homogeneous and inhomogeneous band broadening. Red-edge effects... 

Lierse W, Horstmann E (1965) Quantitative anatomy of the cerebral vascular bed with especial emphasis on homogeneity and inhomogeneity in small parts of the grey and white matter. Acta Neurol Scand 14 15-19... 

Here f(c) is the free energy density of a hypothetical completely homogeneous system with volume fraction c. It is understood that c=c(r). For small fluctuations, one can expand f(c) about c, the bulk composition of the mixture. Keeping only terms to second order and invoking conservation of mass, one may obtain an expression for AF, the difference between the free energy of homogeneous and inhomogeneous mixtures ... 

A. N. Garroway, Homogeneous and inhomogeneous nuclear spin echoes in organic solids adamantane. J. Magn. Reson., 1977, 28, 365-371. 

The second question concerns the amplitude ratios between the reflected and incident waves. For both homogeneous and inhomogeneous incident waves these ratios must have a modulus equal to unity, because no energy loss through the instantaneous reflection process at x = 0 is expected. 

A. H. Zewail I thought that on the femtosecond time scale the separation of homogeneous and inhomogeneous relaxations is fuzzy. But now you are making a separation in definition. Could you elaborate on their meaning ... 

Are the weak homogeneous fields present in most experiments sufficient to cause the observed lifetime lengthening, and if not, what is the relative importance of homogenous and inhomogeneous field effects ... 

Fig. 1.27. Self-organization in spatially homogeneous and inhomogeneous media.

We can distinguish first between homogeneous and inhomogeneous networks (Chapter 7). In homogeneous networks a distinction between ideal and nonideal structures may be performed. This concept is presented in Chapters 10 and 11. 

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