Wave profiles phase transformations

Fig. 2.12. If solids undergo a shock-induced polymorphic transformation, the volume change at the transformation causes significant changes in the wave profile produced by shock loading. In the figure, is the applied pressure, Pj is the pressure of the phase transition, and HEL is the Hugoniot elastic limit.

Eq. (15.25) is well defined since the components of q" do not change sign. Anderson localization theory [45] predicts exponentially decaying localized states for one and two dimensional lattices with some localization length I, which after applying the reverse Cole-Hopf transformation yields the observed tent-shape phase profile with wavelength A 7/. Concentric waves emerge when A becomes smaller than the system size. 

A polarizer is a device that transforms a linear polarized wave into a circular polarized wave, or vice versa. The common principle is simply to decompose the incident field into two components where the phase of one is advanced and the other is delayed such that their difference is 90° while their amplitudes are the same. It appears that Pakan [128] was the first to utilize this principle. Later improvements were introduced by Lemer [129]. These devices were not of the meander-line type, as will be discussed here. These seem to appear first in a paper by Young et al. [130] and were subsequently unproved by Epis [131]. Later, a paper by Terret et al. [132] discussed how to calculate the susceptance of a meander line. All of these contributions were primarily focused on normal angle of incidence while Chu and Lee [133] extended the calculation to include oblique angle of incidence. A recent contribution was supplied by Marino [134], It was apparent that meander-line polarizers gradually deteriorate for higher angles of incidence. The present appendix will demonstrate that introduction of a dielectric profile can greatly improve this calamity. 

In an experimental study of the combustion of a polymer material it is especially important to investigate all the stages in which phase and chemical transformations of the substance are taking place. The complete scheme of the combustion process could be deduced from the study of such characteristics as the morphological structure of the burning surface, the temperature distribution inside the combustion wave, the structure and concentration profiles of each individual-stage product, the heat liberation ant heat losses, the structural properties of the flame and the limitations on combustion stability [16]. 

Fig. 1.32 The axial reflections of the SmA phase. In this phase the layers are disordered, thus causing the peaks to be difluse. The projection of the electron density pattern perpendicular to the layers has the profile of a more or less sinusoidal wave, in contrast to the more detailed pattern that a perfect layer structure would give. The Fourier transform of this profile has a single dominant term and this explains why the characteristic diffraction pattern of the SmA phase has only a single strong axial reflection corresponding to the layer spacing and the higher orders, i.e., 0 0 2, 0 0 3 etc., are generally very weak...

---