Transverse field

The last attribute of tire electromagnetic field we need to discuss is wave polarization. The nature of tire transverse field is such tliat tire oscillating field disturbance (which is perjDendicular to tire propagation direction) has a particular orientation in space. The polarization of light is detennined by tire time evolution of tire direction of tire electric field... 

In continuous-flow zone electrophoresis the solute mixture to be separated is injec ted continuously as a narrow source within a body of carrier fluid flowing between two electrodes. As the solute mixture passes through the transverse field, individual components migrate sideways to produce zones which can then be taken off separately downstream as purified fractions. 

Quer-ebene, /. lateral plane, -effekt, m, transverse effect. -faser,/. transverse fiber cross grain, -feld, n. transverse field, cross field. 

Stigter, D, Electrophoresis of Highly Charged Colloidal Cylinders in Univalent Salt Solutions. 1. Mobility in Transverse Field, Journal of Physical Chemistry 82, 1417, 1978. 

In this section, we will analyze the effects of a nano-sized HRI overlay on the distribution of the cladding modes (transversal fields, effective indices, coupling coefficients) to changes of its thickness and refractive index and to changes of the SRI. 

To attain a transverse field profile that is confined within the defect, the profile must exponentially increase for p < pdef, and exponentially decrease for p > pdef. This requirement determines which index-interfaces (lowhigh or highlow) should be positioned at zeros of the field and which at the extrema of the field. The constraints on the index profile are similar to the Cartesian case and differ for the TE and TM polarizations. For the TE polarization, the interfaces for decreasing (increasing) field should be at the zeros (extrema) of If, if nip ) > n(p 1) at the interface and at the extrema (zeros) of Hz if nip ) < nip 1) at the interface. For the TM polarization, the interfaces for decreasing (increasing) field should be at the extrema (zeros) of E, if n(p ) > n(p+) at the interface and at the zeros (extrema) of E, if n(p ) < nip 1) at the interface. The interfaces of the defect must be located at zeros of II, for TE and of E, for TM. 

From the present stand point, the physical processes are described as quantum transitions among stationary states obtained from the adequate Ho. The coupling with the electromagnetic transversal field is the necessary cause producing changes among the states. Thus, seen from the viewpoint of the global system, the molecular system is not made of stationary states. 

As has already been mentioned, at the interface between two neighboring seetions, two transversal field components are continuous. Their distributions ean be expressed by two expansions corresponding to modes of each section. From Eq. (11) we get for the interface between sections s and t... 

The transversal field distribution of Bloch modes at the longitudinal position Cb of the interface between two period is defined (see Fig. 3) can be explicitly written as... 

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... 

For a complete suppression of the local magnetic field effects, however, one should also compensate its transversal component perpendicular to the magnet axis. This requires a pair of auxiliary coils, oriented in a correct direction in the magnet s azimuth plane, and capable of generating a transversal field component of the correct magnitude and sign (for more details, see Ref. 70)). 

There is no general expression for the relaxation rate in the presence of a nonzero transversal field valid for all values of the relevant parameters [53], but Garanin et al. have derived a low-temperature formula valid for weak transversal fields [38], which can be used to determine the coefficient cx ... 

Here a = X and y(a, z) = Jo dt e is the incomplete gamma function. It can be noted that for the axially symmetric potential with a longitudinal field, the only dependence on X is the trivial one in Xp, while in the nonaxially symmetric potential obtained with a transversal field the relaxation rate will strongly depend on X through F(oc), which is plotted in Figure 3.6. 

In FFF, separation is determined by the combined action of the nonuniform flow profile and transverse field effects. The classical configuration assumes the FFF channel as two infinite parallel plates (see Figure 12.4), of which the accumulation wall lies at x=0, where x is the cross-channel axis (directed upward from the accumulation wall). Inside the channel, the carrier fluid, assumed to have a constant viscosity, has a velocity profile u(x) that takes the form... 

If e = = 0, the electric field is divergence free this is the general condition for a transverse field. Except possibly at frequencies where e = 0, therefore, the medium cannot support longitudinal fields. 

Transverse Field Overlapping Energy Flux Preservation... 

The case of transverse field overlapping is far more complicated than that of longitudinal overlapping. According to the previous analysis, the field energy is limited mainly within a well-defined radius r. As long as the ratio 0 exceeds the critical value 0 c, the photon wavepackets of the beam will not overlap and will have hardly any mutual interaction. The beam then behaves as a stream of individual photon particles, that is, when representing each photon as an axisymmetric wavepacket. 

Any vectorial field can be split into a sum of two different kinds of vectorial fields known respectively as the longitudinal field and the transverse field j. These fields satisfy, anywhere in space, the following conditions ... 

Helicoidal motions mix ordinary fields with Beltrami fields. Indeed, the U field can always be split into a longitudinal field Uy along a given direction (in the present case, direction z), and a transverse field Uj along a direction normal to the previous one (in the present case, a direction normal to z), thus ensuring the following set of identities ... 

As a consequence of the definitions given above the U field, both the longitudinal and transverse fields satisfy the following set of conditions... 

In this measurement, the hysteresis problem was solved by applying a constant transverse field. In eq. (18), this transverse field does not occur due to cancelling of terms. The same holds for the (in-plane) anisotropy and the shape anisotropy. Baril et al. (loc. cit.) claim that this is a reliable method, giving results consistent with the cantilever method and with a sensitivity better than I x 10-7. It is perhaps worthwhile, however, to consider all... 

For the purely transverse field, the spacial components of the propagator are... 

Thus the role of the high-frequency oscillators is to suppress the transverse field component (in other words, the transverse g-factor). If we are interested only in the contribution to the level spacing (the Lamb shift), one should consider only the longitudinal ( B) part of the renormalization, i.e. multiply the result by sin0, to obtain Eq. (13). 

With this identification of the transverse field variables, the second term in (33) can be written as... 

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