Anisotropy, state-dependent

The dielectric constants of an aligned nematic phase are dependent upon both the temperature and the frequency of the applied field at temperatures below the clearing point. The dielectric permitivity, j, measured parallel to all three axes above the clearing point in the isotropic liquid is the same. Therefore, the dielectric anisotropy of the same compound in the liquid state is zero, see Figure 2.10. The sign and magnitude of the dielectric constants and, therefore, the dielectric anisotropy are dependent upon the anisotropy of the induced molecular polarisability, Aa, as well as the anisotropy and direction of the resultant permanent molecular polarisation determined by permanent dipole moments. 

Dy2Ti207 and H02Ti2O7 are widely regarded as examples of spin ice ground-state materials and a very nice summary of this phenomenon is available. The spin ice state depends on two conditions one, that the magnetic moments be constrained by anisotropy to lie parallel to the (111) directions and two. 

The analogy with the interfacial energy is more appropriate since dislocations, like free surfaces, have an anisotropy which leads to the conclusion that the energy cost for a small excursion from some flat reference state depends upon the orientation of that reference state. However, the analogy between dislocations and interfaces is imperfect since models of this type have an inherent locality assumption which is exceedingly fragile. To explore this further, we note that in... 

In the preceding ch t we described the measurement and interpretation of steady state fluorescence anisotropies. These values are measured using continuous illumination and r resent an average of the anisotropy decay ov - the intensity decay. Measurement of steady-state anisotropies is simple, but interpretation of the steady-state anisotropies usually d nds on an assumed form for the anisotropy decay, which is not directly observed in the experiment. Additional information is available if one measures the time-dependent anisotropy> that is, the values of r(t) following pulsed excitation. The form of the anisotropy decay depends on the size, shape, and flexibility of the labeled molecule, and the data can be compared with the decays calculated from various molecular models. Anisotropy decays can be obtained using the TD or the FD method. 

It is well known that matter exists in three different states depending upon the temperature sohd, hquid, and gas. Between the crystalline solid and the isotropic liquid (normal, isotropic hquid) there actually exists a series of transitions as temperature increases, giving rise to several new phases. These new phases have mechanical, optical, and stractural properties and are referred to as hquid-crystalline phases. Materials isolated from these phases are liquid crytals. A hquid crystal may, therefore, be as an intermediate phase or mesomorphic (meaning in between) phase which has hquidhke order in at least one direction and possesses a degree of anisotropy (also a kind of order). 

Generally, anisotropy cannot be eliminated by stretching. Suppose, for instance, that diffusion of both the activator and of the inhibitor is anisotropic and the directions of fast diffusion for these two species do not coincide. When such more complicated anisotropy takes place, functions Vb( ) and Go 9) differ from (69) and (70) and may even have several maxima at different propagation directions. Complex anisotropy can also be found in the media with only one diffusion component, provided that diffusion is state-dependent and the direction of fast diffusion varies for different values of the variables n and v. 

While all two-dimensional patterns in the CO oxidation on Pt(l 10) presented above reflect the anisotropy of the surface in that they are elliptically deformed, they are not really qualitatively different from effects to be expected for isotropic media. However, there is evidence that the 1 x 2-reconstructed surface exhibits stronger anisotropy than the 1 x 1-phase. In the model this gives rise to state-dependent anisotropy, which cannot be removed by rescal-... 

Crystallography is a very broad science, stretching from crystal-structure determination to crystal physics (especially the systematic study and mathematical analysis of anisotropy), crystal chemistry and the geometrical study of phase transitions in the solid state, and stretching to the prediction of crystal structures from first principles this last is very active nowadays and is entirely dependent on recent advances in the electron theory of solids. There is also a flourishing field of applied crystallography, encompassing such skills as the determination of preferred orientations, alias textures, in polycrystalline assemblies. It would be fair to say that... 

Einstein coefficient b, in (5) for viscosity 2.5 by a value dependent on the ratio between the lengths of the axes of ellipsoids. However, for the flows of different geometry (for example, uniaxial extension) the situation is rather complicated. Due to different orientation of ellipsoids upon shear and other geometrical schemes of flow, the correspondence between the viscosity changed at shear and behavior of dispersions at stressed states of other types is completely lost. Indeed, due to anisotropy of dispersion properties of anisodiametrical particles, the viscosity ceases to be a scalar property of the material and must be treated as a tensor quantity. 

The broad behavior of the anisotropy parameter versus speed curves is similar for all photolysis wavelengths. Unfortunately the 266 nm photolysis data at high 0(3P2) speeds was of insufficient quality to fit anisotropy parameters satisfactorily, so we cannot state with confidence whether the speed dependence of (3 changes at higher photolysis wavelengths. The overriding feature in Fig. 15 is the steady increase in [3 as the 0(3P2) fragments travel faster. Some structure is also apparent in the curves, with a plateau between approximately 1200 and 3700 m/s. 

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