Field intensity

The sensibility to defects and other testing parameters of pieces can be modified by the geometry of the piece to be controlled and the conception of the probe. It is sufficient to set the direction of circulation of eddy currents, regulate the magnetic field intensity and choose the coil of the appropriate size. 

Since the absorption spectrum is a ratio it is amenable to other interpretations. One such interpretation is that the absorption spectrum is the ratio of energy absorbed to energy incident. From this perspective, the quantity /)co(d/d0< li 0l f 0) is interpreted as the rate of energy absorption (per unit volume), since d E/d t = /)co(d AVd t) while tire quantity E dha is interpreted as the incident energy flux, which depends only on the field intensity and is independent of frequency. 

Equation (Cl.4.35) yields two remarkable predictions first, tliat tire sub-Doppler friction coefficient can be a big number compared to since at far detuning Aj /T is a big number and second, tliat a p is independent of tire applied field intensity. This last result contrasts sharjDly witli tire Doppler friction coefficient which is proportional to field intensity up to saturation (see equation (C1.4.24). However, even tliough a p looks impressive, tire range of atomic velocities over which is can operate are restricted by tire condition tliat T lcv. The ratio of tire capture velocities for Doppler versus sub-Doppler cooling is tlierefore only uipi/uj 2 Figure Cl. 4.6 illustrates... 

Tsao C-C, Napolitano R, Wang Y and Weiner J 1995 Ultraoold photoassooiative ionization oollisions in an atomio beam optioal field intensity and polarization dependenoe of the rate oonstant Phys.Rev. A 51 R18-21... 

In a non-Abelian theory (where the Hamiltonian contains noncommuting matrices and the solutions are vector or spinor functions, with N in Eq. (90) >1) we also start with a vector potential Af, [In the manner of Eq. (94), this can be decomposed into components A, in which the superscript labels the matrices in the theory). Next, we define the field intensity tensor through a covaiiant curl by... 

If the vector potential components have the property that the derived field intensity, the YM field in Eq. (99) is nonzero, then the vector potential cannot be... 

The consistency condition for this set of equations to possess a (unique) solution is that the field intensity tensor defined in Eq. (99) is zero [72], which is also known as the curl condition and is written in an abbreviated form as... 

Then, two things (that are actually interdependent) happen (1) The field intensity F = 0, (2) There exists a unique gauge g(R) and, since F = 0, any apparent field in the Hamiltonian can be transformed away by introducing a new gauge. If, however, condition (1) does not hold, that is, the electronic Hilbert space is truncated, then F is in general not zero within the tmncated set. In this event, the fields A and F cannot be nullified by a new gauge and the resulting YM field is true and irremovable. 

The vanishing of the YM field intensity tensor can be shown to follow from the gauge transformation properties of the potential and the field. It is well known (e.g., Section II in [67]) that under a unitary transfoiination described by the matrix... 

We define the field intensity tensor Fi,c as a function of a so far undetermined vector operator X = Xj, and of the partial derivatives dt... 

In conclusion, we have shown that the non-Abelian gauge-field intensity tensor fi sc(X) shown in Eq. (113) vanishes when... 

In Chapter IV, Englman and Yahalom summarize studies of the last 15 years related to the Yang-Mills (YM) field that represents the interaction between a set of nuclear states in a molecular system as have been discussed in a series of articles and reviews by theoretical chemists and particle physicists. They then take as their starting point the theorem that when the electronic set is complete so that the Yang-Mills field intensity tensor vanishes and the field is a pure gauge, and extend it to obtain some new results. These studies throw light on the nature of the Yang-Mills fields in the molecular and other contexts, and on the interplay between diabatic and adiabatic representations. 

The intensity of the magnetic field H is measured in amperes per meter. For a single-laver solenoid, at anv point along its axis the magnetic field intensity is... 

Flux density is calculated as the permeability of free space times the sum of the magnetic-field intensity and the induced magnetization... 

The magnetic susceptibility of a material (%, volume susceptibility) is dimensionless and is defined as the ratio of induced magnetization to magnetic field intensity. It is expressed as... 

H = magnetic-field intensity dB/dz = magnetic-field gradient T = fluid viscosity b = particle diameter... 

Separations similar to those obtained with dry induced-roll devices can be obtained with cross-belt separators (Fig. 19-42). These units are built with up to eight poles, each of which can operate at different magnetic-field intensities to allow simultaneous production of different concentrates. However, capacity is low, and installed costs per ton capacity are high compared with induced-roll units. 

Heuristic Fxplanation As we can see from Fig. 22-31, the DEP response of real (as opposed to perfect insulator) particles with frequency can be rather complicated. We use a simple illustration to account for such a response. The force is proportional to the difference between the dielectric permittivities of the particle and the surrounding medium. Since a part of the polarization in real systems is thermally activated, there is a delayed response which shows as a phase lag between D, the dielectric displacement, and E, the electric-field intensity. To take this into account we may replace the simple (absolute) dielectric constant by the complex (absolute) dielectric... 

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