Frequency coupled

Fig. 9.10 Transfer scheme between states l ) - 0) —> T ). The first (dump) laser pulse, with Rabi frequencies flo.t W, couples all k ) final (empty) states to state 0), while the second (pump) pulse, with Rabi frequency couples state 0) to the initial (populated),...

For a perturbing electric field in the v-direction we have V = W = Dv and W — Y = 0, while for a magnetic field in the v-direction we have for the imaginary magnetic moment operator W = —V = +MV and V + W = 0. A nonzero frequency couples the symmetric and the antisymmetric part of the perturbed density matrix, whereas in the static case the two equations in (16) are not coupled. For comments on the apparent lack of symmetry for the perturbation equations for static electric and magnetic fields see [46]. 

Experimentally, these effects can be distinguished by using isotope mixtures. As shown theoretically by Hammaker et al. [73], only vibrations with identical frequencies couple strongly. Therefore, an isotopic CO/ CO mixture is appropriate to differentiate experimentally between dipole-dipole coupling and other effects. The experimental method has been reviewed by Hoffmann and the effects upon CO adsorbed on Pd(lOO) have been analyzed in detail [21]. 

The description of imaging experiments in reciprocal space is not restricted to k space, the Fourier conjugate space of physical space. The modification of the spin density by other parameters like resonance frequencies, coupling constants, relaxation times, etc., can be treated in a similar fashion [Miil4]. For the frequency-dependent spin density, the Fourier transformation with respect to 2 is already explicitly included in (5.4.7). Introduction of a Ti-dependent density would require the inclusion of another integration over T2 in (5.4.7) and lead to a Laplace transformation (cf. Section 4.4.1). 

Coherent anti-Stokes Raman spectroscopy (CARS) is a potentially powerful method which is now emerging for high-pressure studies, both in large-volume cells and in DACs. Due to frequency coupling in the sample, CARS allows transitions with energies higher than the absorption edge of the win-... 

Synchronization is a fundamental phenomenon found in nonlinear oscillatory systems [12]. The most prominent example, known since long time ago (Huygens, 1665), is the adjustment to a common frequency of two pendulum clocks with slightly different frequencies, coupled via a common support. This type of synchronization between two coupled systems is called mutual synchronization. In the following we are interested in the synchronization of a system to a periodic driving, called forced synchronization. In a synchronized state the systems dynamics is entrained to the signal, i.e. the system inherits the very same frequency of the signal (1 1 synchronization) or the frequencies are locked with some rational n m relation. This... 

If we consider the picture of the London-Van Der Waals forces as given above, viz., as an attraction between the temporary dipole of one atom and the dipole induced by it of the second atom, the finite velocity of propagation of electromagnetic actions causes the induced dipole to be retarded against the inducing one by a time equal to rn/c (if r is the distance between the two atoms and n the refractive index of the medium for the frequency coupled with the temporary dipole). The reaction of the induced dipole on the first one again is retarded by the same time, and if in this total time-lag of 2rn/c the direction of the first dipole is altered by 90 ", the force exerted is exactly nullified, and by a change of 180 " even reverted from an attraction into a repulsion. 

The first three natural frequencies and vibration modes were determined using modal analysis. The first natural axial frequency was found to be /, = 3.98 Hz. The seeond natural, and transverse (vertical) frequency (coupled with bending of the pipe) was /2 = 12.35 Hz. The third natural frequency was /j = 30.16 Hz this mode of vibration was the roeking mode of the assembly. The equivalent determinations based on EJMA (1993) are 3.93,15.7, and 27.2 Hz respectively. The axial mode agrees well, but the inclusion of the offset pipe appears to reduce the transverse and increase the rocking modes. 

The C-N frequency couples with vibrations of the rest of the molecule, generally resulting in a band about 1100 and at 860-750 cm" Nitrosophenols are in tautomeric equilibrium with the quinone oximes. Nitrosoanilines are resonance hybrids. 

Designing in a system a corrosion allowance based on the possible loss of a material thickness is one of the simplest methods for dealing with uniform attack. Ultrasonic inspection has been used for decades to measure the thickness of solid objects. A piezoelectric crystal serves as a transducer to oscillate at high frequencies, coupled directly or indirectly to one surface of the object whose thickness is to be measured. The time the wave of known velocity takes to travel through the material is used to determine its thickness. Since the late 1970s,... 

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