Rotating field

Experimental evidence shows that there are correlations between the physiological state of the cell and its CSR spectrum. A comparison of the CSR of normal and cancerous fibroblasts was shown in an earlier paper.  

FIGURE 3. Spin rate spectra of living (triangles) and dead (circles) yeast (Saccharomyces cerevisiae). The live cells were from a 7-day-old culture the dead cells were heat-killed by exposure to 70°C for 3 min. The applied voltage was 10 V p-p, and the resistivities of the suspensions were 250 to 460 kQ cm. 

FIGURE 4. Dependence of the CSR spectrum of yeast (Saccharomyces cerevisiae) upon the colony age. (Circles, triangles, and squares refer to data for colony ages of 2, 6, and 8 days, respectively.) Note the shift of the 2- and the 20-kHz peaks to lower frequency as the colony age increases. 

FIGURE 5. The CSR spectrum of 1-day-old culture of bovine kidney cells. 

FIGURE 6. The CSR spectrum of CRFK (Crandall feline kidney) cells from a 4-day-old culture. 

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In the language of quanPim meehanies, the time-dependent B -field provides a perturbation with a nonvanishing matrix element joining the stationary states a) and P). If the rotating field is written in temis of an amplitude a perturbing temi in tlie Hamiltonian is obtained... 

Mention must also be made of magnetic stirring. A rotating field of magnetic force is employed to induce variable speed stirring action within either closed or open vessels. The stirring is accomplished with... 

Many other devices are available for laboratory use. These include the Davis tube, Frantz isodynamic separator, laboratory dmm-type separators, low intensity rotating field separator, and superconducting high gradient separator (2). 

The current in the copper ring opposes the main flux in that area of the pole and behaves like an artificial second winding, and develops a rotating field. Although the torque so developed is extremely low, it is enough to rotate such small drives, requiring an extremely low starting torque, of the order of 40-50% of the full load torque. 

For field-oriented controls, a mathematical model of the machine is developed in terms of rotating field to represent its operating parameters such as /V 4, 7, and 0 and all parameters that can inlluence the performance of the machine. The actual operating quantities arc then computed in terms of rotating field and corrected to the required level through open- or closed-loop control schemes to achieve very precise speed control. To make the model similar to that lor a d.c. machine, equation (6.2) is further resolved into two components, one direct axis and the other quadrature axis, as di.sciis.sed later. Now it is possible to monitor and vary these components individually, as with a d.c. machine. With this phasor control we can now achieve a high dynamic performance and accuracy of speed control in an a.c. machine, similar to a separately excited d.c. machine. A d.c. machine provides extremely accurate speed control due to the independent controls of its field and armature currents. 

Blascke, F., The principle of the field oriented iransvertor as applied to the new closed loop control. system for rotating field machines, Siemens Review 34. 217-220 (1972). 

The negative sequence voltage sets up a reverse rotating field and the slip of the rotor becomes 2 - 5 , compared to the positive sequence slip S. The motor will thus operate under the cumulative influence of these two slips, where power output P can be expressed by (see also Section 2.3). 

If the motor is switched on, in a single phasing condition, it will not rotate in the absence of a rotating field, similar to a single-phase motor without a start winding. 

Equation (4-53) describes the precession of the magnetization vector about the field vector with angular frequency yHo, in the absence of the rotating field W, (see Fig. 4-4A). 

Dreh-federwage, /, torsion balance, -feld, n. (Elec.) rotating field, -gelenk, n, swivel joint, -geschwindigkeit, /. speed (or velocity) of rotation or of revolution, -impuls,... 

The motor synchronous speed is determined by the frequency of the rotating field in the stator (60 cycles in the U.S.) and the number of poles (coil connections in the stator) such that motor synchronous speed... 

Similar to the PIP, the Hamiltonian [Eq. (52a)] of a periodic pulse shows an infinite number of effective RF fields with both x and y components of the scaling factors X a and the phases 0na. The periodic pulse, however, acquires a different symmetry as that of the PIP. From Eq. (52c) and = ana, it follows that the scaling factor Xm, is symmetric in respect to the sideband number n, while the phase 6na is anti-symmetric according to Eq. (51c). These symmetries seem to be a coincidence arising from the mathematical derivations. As a matter of fact, they are the intrinsic natures of the periodic pulse. Considering the term f x i)Ix for instance, any Iy component created by the rotating field denoted by a> must be compensated at any time t by its counter-component oj n in order to reserve the amplitude modulated RF field. 

In paramagnetic resonance experiments, the sample is usually placed in a large constant magnetic field H0, whose direction is taken as that of the z axis. This field determines the quantum levels of the individual spins and polarizes them according to Curie s law. In a typical nuclear resonance experiment, a radiofrequency field H1( perpendicular to H0 and rotating in the x,y plane is applied to the sample. The response of the system is, under stationary conditions, described by the radiofrequency susceptibility %(co). The rotating field is given by... 

Thus, for a r.h. rotating field, only nuclei which belong to molecules with an electron spin state ms = 1/2 and which have a hf coupling a, > 2/ NgnB0 will contribute to the ENDOR spectrum. 

In a spin system with anisotropic g and A tensors, the transition probability Wba between two nuclear spin states energy levels Eb and Ea may be calculated from the coupling operator given in (3.20). For a circularly polarized rf field, B2(t)R. in (3.20) has to be replaced by Bep(t)ft with the l.h. or r.h. rotating field B t) defined in (2,1). The nuclear transition probability is then given by... 

As mentioned in Sect. 3.3, the electron Zeeman term contributes to Wba if first order base functions. Explicit first order expressions of Wba for l.h. and r.h. rotating fields, I = 1/2 and an isotropic or purely dipolar hfs tensor are given in Table 2. 

The inversion of Bcff for the low-frequency line takes place at a = 2 vn = 2 Ng B0. As a consequence the nuclear spin states belonging to ms = 1/2 change their precession direction from l.h. (ais0 < a J) to r.h. (aiso > aj J). For ms = -1/2, ENDOR transitions are only observed with a l.h. rotating field. 

A different situation is found for a dipolar hfs tensor. The relative nuclear transition probabilities for B0 parallel to Ap or Aj are given in Table 2.2 and 2.3. As in the case of an isotropic hfs tensor, again Beff is oriented parallel or antiparallel to B0. Since the enhancement factor E is isotropic for B0 parallel to Ay, the net circularly polarized field rotates in the same sense as the applied field. In the case of B0 parallel to Ai however, the enhancement factor E is anisotropic. This anisotropy of E is responsible for the generation of counter rotating fields which induce residual lines. 

For an arbitrary orientation of B0, Beff will no longer be parallel or antiparallel to B0. The intensity ratio of transitions induced by l.h. and r.h. rotating fields is then not only determined by the anisotropic enhancement factor but also by the noncoincidence of Beff and B0. For proton hfs with Af1 < 15 MHz the residual lines induced by a r.h. rotating ... 

In the kinetic energy term [the first line of Eq. (11)] q2 is the actual coupling constant associated with the rotated massive field Ax, g2 is the analogous constant associated with the chromomagnetic fields Aa and the rotated field Az. 

D. Application to Maxwell-Ferrier Equations Study of Rotational Fields... 

The preceding set of relations demonstrates that the classification of rotational fields can result from the coupling of unitary vectors s, t, b in Frenet s trihedron, to the concepts of curvature and torsion of a curve. 

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