Homogeneous fields

An important factor controlling the absorption linewidth is the applied magnetic field Bg. It is very important that this field be constant over all parts of the sample, which may be 1-2 in. long. If the field is not homogeneous, Bg is different for different parts of the sample, and therefore the 

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In contrast to a direct injection of dc or ac currents in the sample to be tested, the induction of eddy currents by an external excitation coil generates a locally limited current distribution. Since no electrical connection to the sample is required, eddy current NDE is easier to use from a practical point of view, however, the choice of the optimum measurement parameters, like e.g. the excitation frequency, is more critical. Furthermore, the calculation of the current flow in the sample from the measured field distribution tends to be more difficult than in case of a direct current injection. A homogenous field distribution produced by e.g. direct current injection or a sheet inducer [1] allows one to estimate more easily the defect geometry. However, for the detection of technically relevant cracks, these methods do not seem to be easily applicable and sensitive enough, especially in the case of deep lying and small cracks. 

It was found that that in the case of soft beta and X-ray radiation the IPs behave as an ideal gas counter with the 100% absorption efficiency if they are exposed in the middle of exposure range ( 10 to 10 photons/ pixel area) and that the relative uncertainty in measured intensity is determined primarily by the quantum fluctuations of the incident radiation (1). The thermal neutron absorption efficiency of the present available Gd doped IP-Neutron Detectors (IP-NDs) was found to be 53% and 69%, depending on the thicknes of the doped phosphor layer ( 85pm and 135 pm respectively). No substantial deviation in the IP response with the spatial variation over the surface of the IP was found, when irradiated by the homogeneous field of X-rays or neutrons and deviations were dominated by the incident radiation statistics (1). 

Mass transfer Irreversible and spontaneous transport of mass of a chemical component in a space with a non-homogeneous field of the chemical potential of the component. The driving force causing the transport can be the difference in concentration (in liquids) or partial pressures ( in gases) of the component. In biological systems. 

For a homogeneous field (i.e. the field gradient and higher derivatives are zero), the total energy of a neutral moleeule may be written as a Taylor expansion. 

NMR spectrometers have improved significantly, particularly in the present decade, with the development of very stable superconducting magnets and of minicomputers that allow measurements over long time periods under homogeneous field conditions. Repetitive scanning and signal accumulation allow H-NMR spectra to be obtained with very small sample quantities. 

A change in dB/dt can be produced either by a demagnetization process or by a vibration in a non-perfectly homogeneous field. To reduce the effect of eddy currents, low-resistivity (plastic) MCs have been built (in which the sample under study is immersed in the mixture, see Fig. 6.15 showing the electrical feedthrough) and even complete plastic DR [34],... 

The reader familiar with the various forms of averaging (Pope 2000) will recognize this as a spatial average over a locally statistically homogeneous field. 

Typically, binary Laves compounds AM2 are formed in several systems of A metals such as alkaline earths, rare earths, actinides, Ti, Zr, Hf, etc., with M = Al, Mg, VIII group metals, etc. Laves phases are formed also in several ternary systems either as solid solution fields extending from one binary phase (or possibly connecting the binary phases of two boundary systems) or as true ternary phases, that is forming homogeneity fields not connected with the boundary systems. 

The homogeneous field equation of 0(3) electrodynamics is inferred from the Jacobi identity of variant derivatives... 

The development just given illustrates the fact that the topology of the vacuum determines the nature of the gauge transformation, field tensor, and field equations, as inferred in Section (I). The covariant derivative plays a central role in each case for example, the homogeneous field equation of 0(3) electrodynamics is a Jacobi identity made up of covariant derivatives in an internal 0(3) symmetry gauge group. The equivalent of the Jacobi identity in general relativity is the Bianchi identity. 

It was seen above that a polar molecule in a homogeneous field is not displaced, but that a couple is exerted by the field of strength Fy the moment of which is eF. d, which will tend to turn the molecule in a direction against the field. The significance of the word moment now becomes clear the dipole moment is the couple corresponding to unit field strength. 

Are the weak homogeneous fields present in most experiments sufficient to cause the observed lifetime lengthening, and if not, what is the relative importance of homogenous and inhomogeneous field effects ... 

Fig. 1.4. The force lines of a magnetic field Bn. (A) A weak, homogeneous field. (B) A strong, homogeneous field. (C) An inhomogeneous field with weak and strong field regions.

As a result of this Jacobi identity, the homogeneous field equation... 

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