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Longitudinal harmonic

If j = 0 there is only one vector spherical harmonic which is identical with the longitudinal harmonic Y 1 = nVoo- From this observation it follows that there are no transverse spherical harmonics for j = 0. It also means that the state with angular momentum zero represents a spherically symmetrical state, but a spherically symmetrical vector field can only be longitudinal. Thus, a photon cannot exist in a state of angular momemtum zero. [Pg.258]

Figure 3 Contributions e" to the loss factor of water at 27°C (a, c, e) and of ice at —7°C (b, d, f) due to longitudinal harmonic vibration of a nonrigid dipole (a, b) harmonic reorientation of a permanent dipole (c, d) and nonharmonic transverse vibration of a nonrigid dipole (e, f). Symbols T and V refer, respectively, to the T- and V-bands. Figure 3 Contributions e" to the loss factor of water at 27°C (a, c, e) and of ice at —7°C (b, d, f) due to longitudinal harmonic vibration of a nonrigid dipole (a, b) harmonic reorientation of a permanent dipole (c, d) and nonharmonic transverse vibration of a nonrigid dipole (e, f). Symbols T and V refer, respectively, to the T- and V-bands.
Regarding the longitudinal harmonic vibration of H-bonded charged molecules, we determine A from classical theory as a quantity, which concerns breaking of hydrogen bonds ... [Pg.370]

In NMR theory the analogue of the relation (1.57) connects the times of longitudinal (Ti) and transverse (T2) relaxation [39]. In the case of weak non-adiabatic interaction with a medium it turns out that T = Ti/2. This also happens in a harmonic oscillator [40, 41] and in any two-level system. However, if the system is perturbed by strong collisions then Ti = T2 as for y=0 [42], Thus in non-adiabatic theory these times differ by not more than a factor 2 regardless of the type of system, or the type of perturbation, which may be either impact or a continuous process. [Pg.26]

Any dipole has a scalar potential between its ends, as is well known. Extending earlier work by Stoney [23], in 1903 Whittaker [8] showed that the scalar potential decomposes into—and identically is—a harmonic set of bidirectional longitudinal EM wavepairs. Each wavepair is comprised of a longitudinal EM wave (LEMW) and its phase conjugate LEMW replica. Hence the formation of the dipole actually initiates the ongoing production of a harmonic set of such biwaves in 4-space (see Section III.A.l). [Pg.647]

Further, in 1904 Whittaker [28] showed that any EM held or wave pattern can be decomposed into two scalar potential functions. Each of these two potential functions, of course, decomposes into the same kind of harmonic longitudinal EM wavepairs as shown in Whittaker [8], plus superposed dynamics. In other words, the interference of scalar14... [Pg.652]

Each little composite dipole also has a scalar potential between its ends. We may decompose that potential into a harmonic set of bidirectional EM longitudinal wave (LW) pairs [8], where each pair consists of an outgoing LW and an incoming LW. Now, however, the incoming (convergent) LWs are virtual i.e., comprised of organization and dynamics in the virtual flux of the vacuum [9(a)]. [Pg.683]

T. Whittaker, Math. Ann. 57, 333-355 (1903) (an excellent paper which decomposes the scalar potential into a harmonic set of bi-directional phase conjugate longitudinal wavepairs). [Pg.693]

So let us consider the -potential most simply as being replaced with such a Whittaker [1,56] decomposition. Then each of these scalar potentials—from which the A potential function is made—is decomposable into a set of harmonic phase conjugate wavepairs (of longitudinal EM waves). If one takes all the phase conjugate half-set, those phase conjugate waves are converging on... [Pg.724]

Figure 1 graphically shows Whittaker s decomposition [1] of the scalar potential into a harmonic set of phase conjugate longitudinal EM wavepairs. The 3-symmetry of EM energy flow is broken [16,20] by the dipolarity of the potential, and 4-symmetry in energy flow without 3-flow symmetry is implemented [1,16]. [Pg.746]

Figure 1. The scalar potential is a harmonic set of phase conjugate longitudinal EM waves. Figure 1. The scalar potential is a harmonic set of phase conjugate longitudinal EM waves.
Reordering is into form of Whittaker harmonic set of bidirectional EM longitudinal wavepairs. Reordering is totally deterministic. [Pg.748]

Analysis of total ozone monthly means (TOMS data, satellite Nimbus-7) was performed with aim to study a temporal variability of ozone longitudinal inhomogeneities. On Figure 8.a) is plotted the values of first three harmonics of total ozone at latitude 60N for period December 1991 - May 1992. It is seen that the wave number 1 with the maximum value of 40 DU at latitude 60N is still dominated in March. [Pg.380]

On the U(l) level, the transverse components of eM are physical but the longitudinal component corresponding to M = 0 is unphysical. This asserts two states of transverse polarization in the vacuum left and right circular. However, this assertion amounts to Cq = e[i = 0, meaning the incorrect disappearance of some vector spherical harmonics that are nonzero from fundamental group theory because some irreducible representations are incorrectly set to zero. [Pg.130]

Figure 8. Second harmonic intensity as a function of inter-electrode position for a longitudinally poled, crosslinked film of 22. The dotted lines indicate approximate positions of the electrodes. Figure 8. Second harmonic intensity as a function of inter-electrode position for a longitudinally poled, crosslinked film of 22. The dotted lines indicate approximate positions of the electrodes.
The symmetry of the problem can be used to analyze the structure of such a second-order contribution. The spin-rotational symmetry (about the B-field s direction) and the time-translational symmetry imply that (i) the longitudinal and transverse fluctuations, Xj and X, do not interfere and may be considered separately (ii) it is convenient to expand the transverse fluctuating field in circularly polarized harmonic modes, and the latter contribute independently. [Pg.23]

First, the underlying principles upon which bulk acoustic wave (BAW) devices operate are described. When a voltage is applied to a piezoelectric crystal, several fundamental wave modes are obtained, namely, longitudinal, lateral and torsional, as well as various harmonics. Depending on the way in which the crystal is cut, one of these principal modes will predominate. In practice, the high-frequency thickness shear mode is often chosen since it is the most sensitive to mass changes. Figure 3.4 schematically illustrates the structure of a bulk acoustic wave device, i.e. the quartz crystal microbalance. [Pg.65]


See other pages where Longitudinal harmonic is mentioned: [Pg.58]    [Pg.390]    [Pg.343]    [Pg.58]    [Pg.390]    [Pg.343]    [Pg.439]    [Pg.61]    [Pg.143]    [Pg.121]    [Pg.171]    [Pg.648]    [Pg.652]    [Pg.667]    [Pg.682]    [Pg.700]    [Pg.725]    [Pg.734]    [Pg.746]    [Pg.377]    [Pg.380]    [Pg.381]    [Pg.131]    [Pg.106]    [Pg.288]    [Pg.153]    [Pg.154]    [Pg.100]    [Pg.23]    [Pg.210]    [Pg.52]    [Pg.23]    [Pg.255]    [Pg.606]   
See also in sourсe #XX -- [ Pg.258 ]




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