Segmentation fuzzy

Before proceeding to a review of both scaled particle theory and fuzzy cylinder model theory, it would be useful to mention briefly the unperturbed wormlike (sphero)cylinder model which is the basis of these theories. Usually the intramolecular excluded volume effect can be ignored in stiff-chain polymers even in good solvents, because the distant segments of such polymers have little chance of collision. Therefore, in the subsequent reference to wormlike chains, we always mean that they are unperturbed . 

Fig. 14. The Kuhn segment number N dependence of the axial ratio Le/d for fuzzy cylinders with different d [104]...

We may have to consider that the segment distribution fluctuates in the cylindrical domain in order to formulate the effects of entanglement and jamming in a solution as illustrated in Fig. 13b. In other words, we may no longer be permitted to consider the fuzzy cylinder a hard-core cylinder of the geometry specified by Eq. (43), but have to make its periphery fluctuate. 

Before inserting t, pBX, and bx obtained above into Eq. (44), we have to mention the fluctuation effect of the fuzzy cylinder. When a hindering fuzzy cylinder is entering the periphery of the laminar region, the hindrance that it exerts may be released by fluctuation of the segment distributions in the... 

If we neglect the distortion of the segment distribution in the fuzzy cylinder by the shear flow, we can apply Doi s stress expression, Eq. (61), to fuzzy cylinder systems as it stands. The neglect of the distortion may be justified when the shear-rate is low. Equation (61) expresses the contribution of the end-over-end rotation of the chain to asegment distribution is not distorted, the orientational entropy term Sor in the static free energy expression contains only the orientational entropy loss of the entire chain, but not the conformational entropy loss cf. Sect. 2.3. 

Values of B calculated from the ordinate intercepts are shown in Fig. 23 as a plot of B/(2q)3 against the number of the Kuhn segments N. For N<4, the data points for the indicated systems almost fall on the solid curve which is calculated by Eq. (78) along with Eqs. (43), (51), (52), and Cr = 0. A few points around N 1 slightly deviate downward from the curve. Marked deviations of data points from the dotted lines for the thin rod limit, obtained from Eq. (78) with Le = L and de = 0, are due to chain flexibility the effect is appreciable even at N as small as 0.5. The good lit of the solid curve to the data points (at N 4) proves that the effect of chain flexibility on r 0 has been properly taken into account by the fuzzy cylinder model. 

Topological Analysis of Complex Molecular Surfaces. W. Heiden and J. Brickmann, J. Mol. Graphics, 12, 106 (1994). Segmentation of Protein Surfaces Using Fuzzy Logic. 

In reality, most micellar systems made up from polymers are not as perfect as depicted in Fig. 9. Instead, the micelles are expected to be more fuzzy and may more resemble the situation depicted in Fig. 10. In this case, the segmental distribution must be considered [44, 45, 48, 74, 79, 84-86] by calculating the scattering amplitude from a realistic density profile. In addition, the intrinsic polymer scattering must be incorporated by explicitly taking into account long-range excluded volume interactions. 

Moments provide useful information about the layout or shape of an image subset that contrasts with its complement they can be computed without the need to segment the subset explicitly from the rest of the image. (Many of the geometric properties defined in Section XII can also be defined for fuzzy image subsets that have not been explicitly segmented.)... 

Lim YW, Lee SU (1990) On the color image segmentation algorithm based tm the thresholding and the fuzzy c-means technique. Pattern Recogn 23(9) 935-952... 

Although the main focus is on gas-phase reactions, the discussion would be incomplete without including processes that are at the interface between the different phases of matter (the boundaries of chemical processes in the gas, liquid or solid phase are indeed rather fuzzy). This area is addressed in the segment on cluster and surface reactions, evolving from van der Waals and cluster entities (Chapter 24), via elementary reactions in a solvent cage (Chapter 25), to laser-induced processes in adsorbates on surfaces (Chapters 26 and 27). 

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