Encoding time

Fig. 1.13 Left schematic plot of the distribu- water flowing under laminar conditions in a tion of flow velocities, vz, for laminar flow of a circular pipe the probability density of dis-Newtonian fluid in a circular pipe the max- placements is constant between 0 and imum value of the velocity, occurring in the Zmax = i>ZimaxA, where A is the encoding time center of the pipe, is shown for comparison. of the experiment.

Fig. 1.14 Propagators for water flowing with an average interstitial velocity of 610 pm s-1 through a sample of sandstone of 15.3% porosity. The curves in both plots refer to encoding times of A = 50, 85, 140, 220, 330, 500, 750, 1100 and 1650 ms. Left propagators in the z direction (along the flow axis) the disappearance of a pronounced peak near zero...

Fig. 1.15 Left propagator for unrestricted self- tained in an experiment, 5(q), plotted semi-diffusion. The propagator P(R, A) is shown for logarithmically over q2. In this representation, increasing encoding times A and becomes the slope of the decaying function is equal to broader with increasing A, while its intensity at (4 jt)2AD, so that the diffusion coefficient D zero displacement is reduced due to the re- can be obtained directly by comparing at least quirement that the area remains normalized to two measurements taken at different values unity. Right signal function as would be ob- of q.

In order to verify the conditions of this averaging process, one has to relate the displacements during the encoding time - the interval A between two gradient pulses, set to typically 250 ms in these experiments - with the characteristic sizes of the system. Even in the bulk state with a diffusion coefficient D0, the root mean square (rms) displacement of n-heptane or, indeed, any liquid does not exceed several 10 5 m (given that = 2D0 A). This is much smaller than the smallest pellet diameter of 1.5 mm, so that intraparticle diffusion determines the measured diffusion coefficient (see Chapter 3.1). This intrapartide diffusion is hindered by the obstades of the pore structure and is thus reduced relative to D0 the ratio between the measured and the bulk diffusion coeffident is called the tortuosity x. More predsely, the tortuosity r is defined as the ratio of the mean-squared displacements in the bulk and inside the pore space over identical times ... 

The one-dimensional propagators P(Z, A) and P(X, A) of displacements parallel and perpendicular to the flow axis, respectively, were determined for a range of encoding times A and volume flow rates. 

SPRITE is termed a pure phase encode technique because spatial encoding occurs through the application of variable amplitude magnetic field gradients (which yield spatially varying frequencies) applied for fixed periods of time. Variable frequency with a fixed evolution or encoding time yields a variable signal phase. 

Fig. 3.4.1 Schematic description of the three-dimensional SPI technique. Gz, Cx and Gy are the phase encode magnetic field gradients and are amplitude cycled to locate each /(-space point. A single data point is acquired at a fixed encoding time tp after the rf excitation pulse from the free induction decay (FID). TR is the time between excitation (rf) pulses. Notice that the phase encode magnetic field gradients are turned on for the duration of the /(-space point acquisition.

Fig. 3.4.8 One-dimensional SPI drying profiles drying are indicated by the symbols ( ) and of concrete moist-cured for 28 days and of a (O), respectively. The measurement para-0.6 water-cement ratio [9]. The specimen was meters were field of view (FOV) 150 mm, sealed except for one face and exposed to a acquisition points 64, tp = (55 - 300 ps, 8 val-drying regime at 38 °C and 40% relative humi- ues), a = 6°, TR = 100 ms, acquisition time dity for 28 days. The spatial moisture content 3.5 min per encoding time, after 28 days of moist curing and 28 days of...

The two timescales in the pulse sequence, te and to, play different roles. The encoding time te determines the local phase winding, < > = yB(r)te, and thus the... 

A second imaging gradient (Gy) is added in order to obtain a spatial map of the displacements. A notable feature of the stimulated echo protocol is that during the flow encoding time, A, the magnetization is stored along the z axis and is subject to the longitudinal... 

The resolution of the wire per wire readout is restricted to one wire distance, which for many applications is not sufficient. However, the high count rate capability is certainly an advantage where no high spatial resolution is necessary. The encoding time can be made as short as 50 nsec with standard circuits (Schottly TTL or ECL). The storage of the large amount of data in a memory systems however, is not trivial, and is certainly accompanied by high expenses. 

The superscript H on the square bracket in (8.3.4) indicates that the Liouville expression inside the bracket needs to be transformed back into Hilbert space before multiplication with the Hilbert-space operator 1 = 1 - ily = I- and formation of the trace. Inverse Fourier transformation over k produces an image of the spin density. Given the form of the density matrix after the initial pulse, the spin density corresponds to 1+ (r). It is weighted by the phase evolution under the internal Hamiltonians Hx(r) during the space-encoding time ti,... 

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