Field variations

Fig. 4.3 Left A-scan of the field variation above the test sample. Right Test sample with different sawcuts. Right below line scan at positions indicated by white arrows.

Two-dimensional models can be used to provide effective approximations in the modelling of polymer processes if the flow field variations in the remaining (third) direction are small. In particular, in axisymraetric domains it may be possible to ignore the circumferential variations of the field unlaiowns and analytically integrate the flow equations in that direction to reduce the numerical model to a two-dimensional form. 

A Self-Consistent Field Variational Calculation of IP for the Helium Atom... 

Consider a one-dimensional optical structure that consists of nonlinear layers. The structure is illustrated in Fig. 1. Assuming no field variation in the X and z directions and the convention exp(icot) for the time dependence of the fields, Maxwell s equations take the form... 

The FDTD approach is based on direct numerical solution of the time dependent Maxwell s curl equations. In the 2D TM case the nonzero field components are E Hy and E, the propagation is along the z direction and the transverse field variations are along x. In lossless media. Maxwell s equations... 

Since, during an actual measurement, the shuttling process is repeated many times in a cyclic manner, the technique has been named field-cycling (FC) NMR relaxometry, a term which underlines the fact that it is the magnetic field variation that matters and not the manner in which it is achieved. 

We have mentioned earlier that, as shown in Fig. 15a, small but perceptible magnetic field variations occur when the magnet temperature changes. 

Fig. 4.41 (a) Cross-sectional view showing field variation across a plane. (b) In the absence of an applied field, the surface potential of an adatom, except at the plane edges, is symmetric. Atomic jumps are symmetric, (c) In an applied field, the surface potential of an adatom becomes inclined owing to the additional polarization binding. Atomic jumps are now asymmetric. 

One Effect of the Oriented Water Molecules in the Electrode Field Variation of the Interfacial Dielectric Constant... 

Fig. 14. R.f. field dependence of the C-13 T, times. The T, values havfe been normalized by Tch (at 1 kHz spinning). The broken line estimates the field variation expected if the observed rotating frame relaxation were exclusively determined by spin-spin coupling. The dashed line represents the same field dependence and has been drawn through the 32 kHz data as an even more restrictive estimate there is no evidence whether or not the low field data are determined exclusively by spin-spin effects. As the relaxation times at 43 and 66 kHz are shorter than those predicted for purely spin-spin effects, the high field results (and perhaps even at 32 kHz) indicate molecular motion 62>.

Fig. 10.10 Multiphoton resonant transition at an avoided crossing from the photon and field points of view. The solid curves are the avoiding levels and the dashed lines are the levels which cross when the coupling is ignored. The static field Es gives rise to a six photon resonant transition, indicated by the stacked arrows. The range of the electric field variation is shown for the case in which the peak field + mw exactly reaches the crossing...

The effect of field variations on measured mobility are considerable and discussion of this in terms of double layer relaxations provides the major thrust of Stotz paper. When the field is applied to a particle and its double layer, the particle moves in one direction relative to the double layer and there is, therefore, an induced asymmetry. The relaxation time required to restore the original symmetry can be defined as... 

The choice of magnetic field variation as the process that distinguishes the two curves in Figs, la and lb is of practical, but not of theoretical, significance. If we could find any reversible isothermal process whose entropy change remained finite as 0 K was approached, it would be described by a diagram similar to Fig. la and theoretically permit the attainment of 0 K in a finite number of steps. The third law therefore requires the following ... 

Functional derivatives are indicated here because aq may be a parametric field, as for example a Lagrange multiplier field. Variations of aq determine J11 = Jq daq, where... 

Field variations driven by the infinitesimal local gauge transformation... 

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