Displacement propagator

From Euler s equation applied to ay, and assuming a quasi-constant density, the displacement propagation can be expressed as ... 

Robinson s theory was one of electron displacements propagated by electrostatic induction along the length of a carbon chain. As a hydrogen atom at one end of a carbon chain becomes a weakly held proton, electron charge drifts... 

Fig. 8. Displacement propagators recorded for flow of water through a packed bed of l-mm-diarnctcr glass beads packed within a 10-inin-diameter column. The average flow velocity was 0.77mms corresponding to Pe and Re of 350 and 0.77, respectively. Propagators are shown for observation times, A = 0.3s (----), Is (-----), and 2s ( ).

Further extensions of chemical mapping within a fixed bed lie in quantifying mass transfer between the intra-pellet and inter-pellet pore space. One approach to measuring mass transfer processes is to use displacement propagator measurements (see Section II.C). The data acquired for the esterification reaction described previously are shown in Fig. 31. In this propagator measurement, the total propagator measured for the system has been separated into two... 

This is the equation for the displacement propagation wave. It should be noted that a similar equation could be obtained for the stress propagation wave. 

Ifthe conditional probability density W(r, R A) is independentofpositionr, the inner integral is different from zero only for r = 0. This defines the displacement propagator... 

If the ions at one end of a crystal lattice are somehow suddenly uniformly displaced from their equilibrium positions, as a consequence of interionic forces, information on the sudden displacement propagates through the lattice in the form of a displacement wave. Such a displacement wave can always be described in terms of linear combinations of plane wave Fourier components of the form... 

L = FID liquid signal intensity Mg = initial magnetization Ps,y R, A) = average displacement propagator P = permeability q = diffusion wavevector defined as 2k) yG5 R = distance diffused by a spin S= amplitude of solid component in FID S = chemical shift 5 = FID solid signal intensity S q, A) = stimulated echo amplitude q = pulse separation time T2 = transverse relaxation time VI/= width of lamellar regions A = diffusion time Y= gyromagnetic ratio. 

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