Second-order structure

Second-order structural transitions are less frequently represented in applied thermodynamic calculations. Still, the Landau approach for determination of... 

The position of the intensity minimum depends sensitively on the ratio of the first- and second-order electron structure factors. It is commonly assumed that the second-order structure factor can be described in the independent-atom... 

A second-order structural transformation in La uC at 233 5°C was reported (118) in a thermal expansion study. The LajCu04 product was prepared at high temperature (1100°C) by the solid-state reaction of the corresponding binary oxides. The material was found to decompose above 1200°C with the loss of oxygen. Samples of La uC, prepared at 1200°C, then maintained at 750°C in vacuum, yielded products having the general composition La2Cu04.x, or... 

Pauling and Corey also proposed a second ordered structure, the p-pleated sheet for polypeptide. This structure is a resiilt of intermolecular hydrogen bonding between the polypeptide chains to form a sheet like arrangement (Fig. 5.3). 

To estimate the average turbulent fluid particle velocity, the second-order structure function (9.14) is interpreted as an absolute particle velocity squared and defined for two points in the fluid separated by a distance equal to the bubble diameter d. The structure function is then given as 5v [d) = uz z + d) — Vz(z)]. If the magnitude of the diameter d lies within the inertial subrange of turbulence, the structure function can be calculated as 5v d) = C(ed) / . The discrete absolute mean velocity of bubbles with diameter di is thus approximated as ... 

Since the glass transition is characterized by discontinuous changes in second- (and higher) order thermodynamic properties, it would seem relevant to give some attention to what might be termed second-order structural properties. Just as n r), from which g(r) is derived, is the average number of particles within a sphere of radius r around a reference particle, so we can define moments about this mean distribution. Here we focus on the second moment, termed the radial fluctuation function W(r), and defined as follows ... 

Proteins are the most abundant species in cells and tissues and hence their absorptions dominate the spectra of cells and tissues (see the section above on proteins). The spectra of proteins vary with the second order structures of proteins, that is, spiral form (a-helix), an extended chain O-form) and a random coil arrangement, the protein s state of hydration and the ionic strength of the solvent. The spectra of metabolic and structural proteins found in cells have similar features. The only proteins to exhibit distinctly different features are found in connective tissue, such as collagen. 

Structure tensors have been shown to work well in segmenting and locating structures of specific shape. Several books published in the recent years present extensive literature reviews on structure tensors and their applications [13, 15, 19, 48]. In this chapter, we present in Section 2 a brief review of their application in image processing, focusing on their application to the analysis of seismic data. Section 3, describes the 2D first and second order structure tensors and their properties in more detail. Also, two well known corner detectors, based on the structure tensors, namely the Harris and the... 

Hessian-based (otherwise known as DET) corner detector are reviewed. In Section 4, we present the 3D first and second order structure tensors and their properties. Section 5 demonstrates the use of these tensors in the analysis of 2D and 3D seismic data, and in Section 6 we draw our conclusions. 

The UV-vis, CD, photoluminescence, and CPL spectra of cyclic trimers (/ p)-44 and (5p)-44 are shown in Fig. 16. The absolute [6] values were reached at approximately 2.0 X10 deg cm dmoL (Fig. 16a), which were greater than the values for the polymers (0.8 x 10 deg cm dmoL ) because of the completely fixed chiral triangular structure. As shown in Fig. 16b, CPL was clearly observed for (/ p)-44 and (5p)-44 in the observed photoluminescence range however, the absolute CPL g-factor values were smaller than those of the polymers. Although the reason for that remains unclear, the following may be considered. The polymer adopts a second-ordered structure such as an optically active zigzag or one-handed helix in the... 

These events such as those shown in Figure 33 which displays an alleged change in skin structure can be attributed to plasticisation and a consequent change in the second-order structure of the skin. A variety of skins has been used to examine penetrants varying from human cadaver skin to porcine skin. It is well understood that the passage of drugs is modified by the hydration status of the skin. 

Dielectric interaction destabilizes the homogeneous director configuration no(r) and at Ec = rj/ToeoSg) the fluctuations along Ox axis freeze and correspondingly a second order structural transition takes place. Contrary to this, the relaxation rate of fluctuations 6n parallel to the Oy axis is not influenced by E = EoOx and remains the same as in the absence of the field (4.21). 

Ferroelectricity is an electrical phenomenon and also an important property in solids. It arises in certain crystals in terms of spontaneous dipole moment below Curie temperature [1], The direction of this moment can be switched between the equivalent states by the application of an external electric field [2-4], It is observed in some crystal systems that undergo second-order structural changes below the Curie temperature, which results in the development of spontaneous polarization. This can be explained by Landau-Ginzburg free energy functional [3, 4, 9]. The ferroelectric behavior is commonly explained by the presence of domains with uniform polarization. This behavior is nonlinear in terms of hysteresis of polarization (P) and electric field (E) vectors. Phenomenological models of ferroelectrics have been developed for engineering computation and for various applications. 

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