Morphological measurements

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

The set of the reaction-diffusion equations (78) can be solved by different methods, including bifurcation analysis [185,189-191], cellular automata simulations [192,193], or numerical integration [194—197], Recently, two-dimensional Turing structures were also successfully studied by Mecke [198,199] within the framework of integral geometry. In his works he demonstrated that using morphological measures of patterns facilitates their classification and makes possible to describe the pattern transitions quantitatively. 

The events of the estrous cycle can be used as an indicator of reproductive neuroendocrine and ovarian function in the non-pregnant female. Hormonal, histological and morphological measurements can also be interpreted relative to stage of the cycle and can be used to... 

To access the LAA transseptal puncture is necessary. Angiography is performed for further morphologic measurements. The PLAATO system is engaged via a delivery catheter and unfolded in the appendage. Compression of I0% is mandatory and at least two rows of anchors should be engaged into the surrounding tissue. 

Morphology Measure the angles between crystal faces if they are well developed. Drawing a stereographic projection (see Chapter 2) may help. Note any cleavage directions and any tendency to form twins. Sometimes etching of the crystal faces will reveal their symmetry. 

An appropriate combined use of molecular chemical information (NIR) and morphological measurements in macroscopic images (e.g., shape, optical texture, size) can enable the analysis of further complicated systems. This is particularly relevant when objects composed of different color-same compartments are being processed (e.g., meat slices), or when the product is composed of heterogeneous pieces within a bulk, such as animal feed. 

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