Match condition

Using now the phase matching condition, it can be seen that besides the quasi shear wave (qSV) which is obtained as usual, a second quasi shear wave (qSV(2)) results from the upper quasi shear wave part. Since the direction of the group velocity vector points downwards this wave is able to propagate and can be seen in the snapshot (see Fig. 10) if a is properly adjusted, i.e. is pointing upwards as in Fig. 2. 

A gas turbine plant with an overall efficiency t]cq = 0.25 matching a heat load Acc, = 2.25 is again considered as the basic CHP plant also implied is a non-useful heat rejection ratio (Cnu)cg( cg = [1 ( cg)( g + 1)1 =. 3/16. For FESR calculations, we again take the conventional plant efficiency as 0.4 and the conventional boiler efficiency as 0.9. At the fully matched condition the.se assumptions previously led to EUF = 0.8125 and FESR = 0.2. 

As a consequence of the time-averaging of the quasienergy Lagrangian, the derivative in the last equation gives only a nonvanishing result if the frequencies of the external fields fulfill the matching condition Wj = 0. In fourth order Eq. (29) gives the cubic response function ... 

In the normal dispersion region below the first pole, response functions can be expanded in power series in their frequency arguments. The four frequencies, associated with the operator arguments of the cubic response function are related by the matching condition a -fwfl +wc -t-U ) — 0. Thus second hyperpoiarizabiiities or in general cubic response properties are functions of only three independent frequency variables, which may be chosen as u>b, ljc and U > ... 

Hirose et al. [26] proposed a homodyne scheme to achieve the background-free detection of the fourth-order field. With pump irradiation in a transient grating configuration, the fourth-order field propagates in a direction different from that of the second-order field because of different phase match conditions. The fourth-order field is homodyned to make ffourth(td. 2 D) and spatially filtered from the second-order response hecond td, 2 D). 

In order to study the resonant behavior of spectral density, let us plot the SNR as function of driving frequency go. From Fig. 22 one can see, that SNR as function of co has strongly pronounced maximum. The location of this maximum at co = mlnax approximately corresponds to the timescale matching condition mlnax 7i/Tmm, where Tmm is the minimal transition time from one state to another one. 

The spin-locking and CP behavior of the most commonly used SQ coherence (CT) in quadrupolar nuclei under static and MAS conditions has been described in detail by Vega using the fictitious spin-1/2 approximation [223]. In a static sample, the Hartmann-Hahn matching condition requires that co = nut where co ut is one of the nutation frequencies associated with the SQ coherence of the quadrupolar S spin (see Sect. 2.3.4). In the simple case of on-resonance SQ-CP this translates to [224]... 

Using these relations we can construct the bond wave functions (2) and express the matching conditions (1) in terms of the vectors (f)1,11 only. The resulting quantization conditions can be expressed in terms of the matrix,... 

From the coupled mode theory, it is possible to retrieve a modified phase matching condition, which is more accurate than (3.1)26 ... 

The resonance wavelength (2rcs) of a LPFG can be roughly estimated by the following phase matching condition ... 

Non Perturbative Exact Results Anomaly Matching Conditions... 

While the anomaly matching conditions are still in force at nonzero quark chemical potential [32] the persistent mass condition [50] ceases to be valid. Indeed a phase transition, as function of the strange quark mass, between the CEL and the 2SC phases occurs. 

The integration must go until the fluid-vacuum interface at rs, where an exterior vacuum solution continues the interior one. The details of matching conditions can be found in Ref. [14]. Applying them on the present problem we get the continuity of certain derivatives of the metric tensor, and those for the energy-momentum tensor result in the single equation,... 

Although might be anything at rs from the matching conditions, it will be zero for all general (not very exotic) systems. Namely, P = 0 is expected at some low particle number density ns on the surface, which is generally much below Po = h/Rc. So motions in the hth dimension cease already somewhere in the interior of the star. 

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