Field plane

For plane waves propigating in an isotropic homogeneous medium, three acoustic properties are important the speed of sound, the attenuation coefficient (to be discussed), and the characteristic impedance of the media. This impedance z is defined as the ratio of the acoustic pressure to the particle velocity associated with the wave motion in the material. For simple free-field plane waves, tliis is simply the product of the sound speed and density p. 

Radicals of similar structures also studied. ) Maximum value. Plane of film parallel to the magnetic field. Plane of film perpendicular to the magnetic field. ... 

Spectral representations of the fields (plane, cylindrical, spherical wave expansions Hermite-Gaussian and Laguerre-Gaussian beams prolate spheroidal harmonics)... 

Concerning the same transition, an induced SmA-SmC transition was observed when an electric field was applied in a chiral compound at a temperature near the transition [136, 137], the SmA-SmC transition temperature increasing under an electric field (Fig. 18). This field-induced transition was attributed to the large spontaneous polarization and to the first order behavior of the transition. Further studies have shown that the first order transition between the polarized smectic A phase and the ferroelectric smectic C phase terminates at a critical point in the temperature-electric field plane [138, 139]. 

Figure 1.12 Electromagnetic field (plane xz) generated by a unit dipole in the z direction and/c = 1 electric (z and x non-zero component and the field norm E = y/ Ex + zP] and magnetic (y non-zero component] field. For visualization purpose, the intensity of the field is multiplied by r. Colors pink (positive], white (null], cyan (negative].

It is often found that, in practice, the measured value of Gic or K c varies with the width of the specimen over a certain range of widths, and this usually arises because the state of stress near the crack tip varies from plane stress in a very thin specimen to plane strain near the centre of a wide plate. The general form of the relationship between Kic (or Gic) and specimen width, b, is shown schematically in Fig. 7.6. The value for fracture in plane strain conditions is usually less than under plane stress. This arises because the tensile stress at which a material yields is greater in a triaxial stress field (plane strain) than in a biaxial one (plane stress) and thus, in the former, a more limited degree of plasticity develops at the crack tip cf. Equations 7.26 and 7.27. The lower, conservative, plane strain value is usually the one required for engineering design and life prediction studies. The width, fe, necessary to achieve this condition is usually taken to be ... 

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