Oscillatory Term

Droplet suspensions (gas-liquid, two-component system) Since the inertia of a liquid suspended in the gas phase is higher than the inertia of the gas, the time for the displacement of liquid under the pressure waves should be considered. Temkin (1966) proposed a model to account for the response of suspension with pressure and temperature changes by considering the suspensions to move with the pressure waves according to the Stokes s law. The oscillatory state equation is thereby approximated by a steady-state equation with the oscillatory terms neglected, which is valid if the ratio of the relaxation time to the wave period is small, or... 

Here the oscillatory terms like e2,ta> and e 2lt<0 have been ignored, which is called the rotating wave approximation (RWA). Linear susceptibility yl et) is defined by... 

The coupling to the soft mode introduces here oscillatory terms that can become important close to Tc. The fact that the amplitude, as well as the coherence length of the order parameter fluctuations, increase on approaching Tc from either side also probably brings higher order coupling terms into... 

Interference bands in slab transmission may be observed because of the oscillatory term cos in (2.75). Transmission maxima occur when f = 2irp( pX = 2nxh), where p = 1,2,3,. ... If a maximum occurs at a wavelength X, neighboring maxima occur at X + AX, where... 

Since all non-oscillatory terms in the solution are now omitted, we shall determine the non-zero components of the stress tensor according to equation (9.3)... 

In order to describe the signal observed, it is necessary to average over the canonic ensemble of N identical particles j, or, in other words, to pass over to the density matrix Jmm [73]. The oscillatory term does not disappear after such a procedure, because at pulsed excitation all excitation moments are synchronized. 

Suppose we have a solution at z = 0, and want to propagate it over a distance corresponding to an integration step Az. Although we wrote the equation in terms of field, it is more natural to solve numerically for the modal expansion coefficients to eliminate fast oscillatory terms. We therefore express the field through the expansion coefficients A which are actually the native solver variables ... 

To utilize the adiabatic condition, we transform H to a form that does not contain oscillatory terms that might cause rapid variations of dU/dt and hence invalidate tti S... 

The hard sphere oscillatory term, (R), is not sufficient to account for the... 

We also know that if the eigenvalues are complex, the solution to Equation 6.43 contains oscillatory terms due to the relation... 

After neglecting the highly oscillatory terms in Eq. (41), we further obtain... 

Using Eqs. (34,52,54, and 56) and neglecting as before the highly oscillatory terms containing the e 2-o factors, we obtain that... 

These controversial results prompted Schenck et al. (1999) to perform a new ZF- xSR study on a high-quaUty single crystal in the range between 0.1 and 4K. These authors observe helow 3.8 K a spin precession signal in addition to an exponentially relaxing non-oscillatory term. The spectra are well described by... 

Another frequently studied liquid is CCii and is representative of a large class of molecules with Tj symmetry. A simpler homonuclear molecule with tetrahedral geometry is yel low phosphorus, and gives rise to a single oscillatory term in the form-factor which may be expressed as... 

Since Re(/ 23) oscillates and decays with time, Eq. (10.79) indicates that the amplitude of fluorescence from state 2 will execute similar damped oscillations, converging on a level that depends on the population difference pn — P22- The oscillatory term in Eq. (10.79) also applies to fluorescence from state 3, because Re(p23) = Re(p32). 

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