Critical displacement amplitude

In the case of a normal absorber as shown in Fig. 8.63, one could evaluate the efEciency by considering the mass ratio ma/mi. Clearly, in most applications the efHciency of the absorber is a critical parameter and should therefore be maximized. In the case of an absorber installed in a building, efEciency is proportional to the mass ratio and square of the displacement amplitude of the building. Therefore, the absorber must be located on a high floor. In the case of the gondola, the efficiency is given by... 

If, however, the transition is of a pure displacive nature, the fluctuation amplitude of the order parameter is critical and is by no means temperature-independent. Since the soft mode is an under-damped lattice vibration (at least outside the close vicinity of Tc), defined by its frequency a>s and damping constant Tj, the spectral density is a Lorentzian centred at s and the... 

Capillary forces in mixed fluid phase conditions are inversely proportional to the curvature of the interface. Therefore, menisci introduce elasticity to the mixed fluid, and mixtures of two Newtonian fluids exhibit global Maxwellian response. For more details see Alvarellos [1], his behavior is experimentally demonstrated with a capillary tube partially filled with a water droplet. The tube is tilted at an angle (3 smaller than the critical angle that causes unstable displacement. Then, a harmonic excitation is applied to the tube in the axial direction. For each frequency, the amplitude of the vibration is increased until the water droplet becomes unstable and flows in the capillary. Data in Figure 3 show a minimum required tube velocity between 40 and 50 Hz. This behavior indicates resonance of the visco-elastic system. The ratio of the relaxation time and characteristic time for pure viscous effect is larger than 11.64. 

This process may be repeated as many times as needed until all atoms in the unit cell are located and the following Fourier map(s) do not improve the model. Equations 2.132 to 2.134 may be combined with a least squares refinement using the observed data, which results in a more accurate model of the crystal structure, including positional and displacement parameters of the individual atoms already included in the model. The success in the solution of the crystal structure is critically dependent on both the accuracy of the initial model (initial set of phase angles) and the accuracy of the experimental structure amplitudes. Needless to say, when the precision of the latter is low, then the initial model should be more detailed and precise. 

Nevertheless, things are even more complicated. It has been shown [50,51] that the analytic critical point (ACP - maximum, minimum or saddle point of dispersion, in case of MgB2 it is maximum) of the o band at F point crosses Fermi level (FL) at vibration displacement 0.016A°/B-atom, i.e. with amplitude 0.032A°, which is smaller than root-mean square (rms) displacement ( 0.036A°) for zero-point vibration energy in Egg mode. Thus, in vibrations when ACP approaches FL for... 

---