Anisotropy longitudinal

Substance Energy gap equivalentvalleys and direction Anisotropy Longitudinals TransvemeK=mjm. ... 

Substance equivalent valleys Enei gap and direction Anisotropy Longitudinal m Transverse m. K = mjm. ... 

PR = perpendicular recording LR = longitudinal recording HFRH = high frequency recording heads RH/HDTV = recording heads for high definition television and Pa = perpendicular perpendicular anisotropy. 

In the following development we consider a plane wave of infinite lateral extent traveling in the positive Xj direction (the wave front itself lies in the Xj, Xj plane). When discussing anisotropic materials we restrict discussion to those propagation directions which produce longitudinal particle motion only i.e., if u is the particle velocity, then Uj = Uj = 0. The <100>, <110>, and <111 > direction in cubic crystals have this property, for example. The derivations presented here are heuristic with emphasis on the essential qualitative features of plastic flow. References are provided for those interested in proper quantitative features of crystal anisotropy and nonlinear thermoelasticity. 

Anisotropy increases as the density decreases. The transverse strength is usually between 1 0% and 20% of the longitudinal. 

Although CNTs showed similar EELS pattern in plasmon-loss and core-loss regions to graphite, SWCNT and fine MWCNT with a diameter less than 5 nm had different features. Furthermore, it has been found out that the angular-dependent EELS along the direction normal to the longitudinal axis of CNT shows stronger contribution from Jt electrons than [Pg.38]

Here p and pj are the transverse and longitudinal resistivities with respect to the magnetization direction, respectively. The off-diagonal element pn represents the spontaneous or anomalous Hall resistivity (AHR) [3]. Conventionally, the anisotropy of the resistivity is expressed by the SMA ratio... 

There is no reason to believe that the off-diagonal Q integrals which yield this increase in U over I should be equal for longitudinal and transverse polarization but neither is there at present any basis for selecting different values. Hence we assume U1 = U2 and by use of the a values given above for the chlorine atom, the value of —El is calculated to be about 30 per cent smaller than was obtained in Table VI. Since the effect of anisotropy would be expected to be about the same for all of the halogens, the qualitative conclusions drawn from the results in Table VI are not affected. It is clear that anisotropy may be important, however, and must be considered in quantitative work. 

Apart from the conditions of load transmission from fiber to matrix, the anisotropy of mechanical characteristics is also due to the considerable anisotropy of the fibers themselves in the longitudinal and transverse directions, especially in the case of fibrous reinforcements of polymeric nature [154]. 

As we shall see, all relaxation rates are expressed as linear combinations of spectral densities. We shall retain the two relaxation mechanisms which are involved in the present study the dipolar interaction and the so-called chemical shift anisotropy (csa) which can be important for carbon-13 relaxation. We shall disregard all other mechanisms because it is very likely that they will not affect carbon-13 relaxation. Let us denote by 1 the inverse of Tt. Rt governs the recovery of the longitudinal component of polarization, Iz, and, of course, the usual nuclear magnetization which is simply the nuclear polarization times the gyromagnetic constant A. The relevant evolution equation is one of the famous Bloch equations,1 valid, in principle, for a single spin but which, in many cases, can be used as a first approximation. 

When l l, the above gives the so-called cross-correlation functions and the associated cross-correlation rates (longitudinal and transverse). Crosscorrelation functions arise from the interference between two relaxation mechanisms (e.g., between the dipole-dipole and the chemical shielding anisotropy interactions, or between the anisotropies of chemical shieldings of two nuclei, etc.).40 When l = 1=2, one has the autocorrelation functions G2m(r) or simply... 

A new NMR method for the determination of the anomeric configuration in mono- and disaccharides has been described.18 The protocol is based on the different cross-correlated relaxation between proton chemical shift anisotropy (CSA) and dipolar relaxation for the a and (3 anomers of sugars. Only the ot-anomers show the presence of CSA (HI or Hl )-proton dipole (H1-H2 or Hl -H2 ) in the longitudinal relaxation of the anomeric protons. The method is of special interest for cases in which vicinal coupling constants between HI and H2 in both anomers a and (3 are similar and small, such as D-mannose, and the non-ambiguous description of the anomeric configuration needs additional measurements. 

Ki = a y/a is the stress intensity factor, and F, the material constant, both of which depend on the degree of anisotropy of the composite controlled by the composite elastic moduli in the longitudinal and transverse directions, El and Ej, in-plane Poisson ratio, vlt, and Glj. For a perfectly isotropic material, jr/8(l + Vlt) 0.3. Also, the material parameters, i and < 2 are given by ... 

Assuming an axially symmetric potential, the anisotropy energy of n) will be an even function of the longitudinal component of the magnetic moment s n. The averages we need to calculate are aU products of the form = (n =i (cn ))a> where the c are arbitrary constant vectors. Introducing the polar and azimuthal angles of the spin d, tp), we can write as... 

Fig. 11.4. Velocities of bulk and surface waves in an (001) plane the angle of propagation in the plane is relative to a [100] direction, (a) Zirconia, anisotropy factor Aan = 0.36 (b) gallium arsenide, anisotropy factor Aan = 1.83 material constants taken from Table 11.3. Bulk polarizations L, longitudinal SV, shear vertical, polarized normal to the (001) plane SH, shear horizontal, polarized in the (001) plane. Surface modes R, Rayleigh, slower than any bulk wave in that propagation direction PS, pseudo-surface wave, faster than one polarization of bulk shear wave propagating in...

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