Stationary magnetic fields

Another method of introducing heat to fluids in rotating devices involves the generation of eddy currents by rotation through a stationary magnetic field. This approach was successfully used in a polymer devolatilization process (47). 

The changes of the X-band spectrum over the temperature range 4-120 K at the stationary magnetic field HII (1 0 0) (C4) axes are shown in Fig. 1. The parameters of the spin Hamiltonian describing the spectrum are provided in Table 1. 

FIGURE 3.4 Assemblage of precessing nuclei with net macroscopic magnetization Mn in the direction of the stationary magnetic field B0. 

An assemblage of equivalent protons precessing in random phase around the z axis (i.e., in the direction of the stationary magnetic field B0) has a net macroscopic magnetization M0 along the z axis, but none in the xy plane (Figure 3.4). 

Delocalization of electrons, especially in the outer layer, i. e. valence electrons, must also occur in a magnetic field. Evidence does exist that a stationary magnetic field actually affects some chemical reactions. Turro... 

Fig. 8.7 Relative intensities ofthe time-dependent magnetization of CH3 of c/s-Ala-Tyr in H20 D20 9 1 pH 5.9 in a 7, experiment ( ) and the magnetization-transfer experiments with the cis signal parallel (A) and antiparallel to the stationary magnetic field (V) at 316 K. Solid lines represent the correspondingly fitted biexponential decays with 7, = 0.984 s, k= 3.7 s-1 and a cis content of 0.61% [53].

V.A. Goldade, L.S. Pinchnk and V.V. Snezhkov. Strnctnral orientation and electric polarization of polymers in stationary magnetic fields. Proc. 7th Intern. Symp. on Electrets, 1991, pp. 316-321. 

Be = thermodynamic critical field Bc2 = upper critical field Bdc = stationary magnetic field crit = rf critical magnetic field Ep = peak electric field at the cavity surface / = frequency Fp = volume pinning force jc = critical current density k = Boltzmann constant / = mean free path R(T) = measured surface resistance Bcs = surface resistance, as described by the BCS theory Rres = residual surface resistance Tc = transition temperature... 

Within the past decade, an exciting new form of matter, the Bose-Einstein (BE) condensate, has been produced (7). In a typical experiment, a gaseous sample of pure sodium containing several million atoms is cooled to about a microkelvin and trapped in the F = 1, mp = -1 hyperfine state by a combination of stationary magnetic fields and laser fields. Under these conditions, the sodium atoms are bosons and essentially all of them enter the lowest energy state of the trapping potential, which is similar to the familiar three-dimensional particle-in-a-box system. When two such boxes of sodium atoms are prepared, and the atoms are subsequently released fi"om these traps, the... 

The value of hyperfine interaction is assumed to be small enough as compared with the Zeeman interaction energy of an unpaired electron with a stationary magnetic field. 

The variation dJ = 0 yields the so-called time-dependent coupled Hartree-Fock equations. When the field does not break the periodic symmetry of the polymer, these equations are already formulated for a polymer. Since, however, the different cases of the effects of stationary magnetic fields on the band structure of a polymer have not yet been programmed, and therefore no calculations are available for this problem, we shall not give here the rather complicated equations obtained for the case of nonstationary magnetic fields. 

All static magnetic traps for atoms use nonuniform stationary magnetic fields. In a nonuniform magnetic field B = B(r), an atom with a permanent magnetic moment /LX has a magnetic dipole interaction energy... 

In order to transform the interaction vector in the laboratory coordinate frame defined by the stationary magnetic field to the final coordinate frame F, defined by the jump axis, which is diagonal with the DD vector or aligned with the principal axis system of the CSA tensor, it may be useful to express the overall transformation as a series of transformations through intermediate coordinate frames N. This will enable the amplitude and frequency of each motion to be explicitly included in the correlation function. In the case of overall isotropic motion with diffusion constant D, the dipolar correlation function can be expressed as (Keepers and James, 1982)... 

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