Difference between revisions of "Grad sandw.m"
(Created page with "Computes the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gra...") |
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| − | + | {{DISPLAYTITLE:grad_sandw.m}} | |
| + | Emulates the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradients are linear, and that they are antisymmetric about the middle of the sample. | ||
| + | |||
| + | ==Syntax== | ||
rho=grad_sandw(spin_system,L,rho,P,g_amps,s_len,g_durs,s_facs) | rho=grad_sandw(spin_system,L,rho,P,g_amps,s_len,g_durs,s_facs) | ||
| − | Arguments | + | ==Arguments== |
| − | + | ||
rho - spin system state vector | rho - spin system state vector | ||
| − | + | ||
L - system Liouvillian | L - system Liouvillian | ||
| − | + | ||
P - total propagator for all events happening | P - total propagator for all events happening | ||
between the two gradients | between the two gradients | ||
| − | + | ||
g_amps - row vector containing the amplitudes of | g_amps - row vector containing the amplitudes of | ||
the two gradients, Gauss/cm | the two gradients, Gauss/cm | ||
| − | + | ||
s_len - sample length, cm | s_len - sample length, cm | ||
| − | + | ||
g_durs - row vector containing the durations of | g_durs - row vector containing the durations of | ||
the two gradients, seconds | the two gradients, seconds | ||
| − | + | ||
s_facs - shape factors of the two gradients, use | s_facs - shape factors of the two gradients, use | ||
[1 1] for square gradient pulses | [1 1] for square gradient pulses | ||
| − | + | ==Outputs== | |
| + | |||
| + | rho - spin system state vector, integrated over | ||
| + | the spatial coordinate | ||
| + | |||
| + | ==Examples== | ||
| + | See examples/fundamentals/gradient_test_1.m file for an example of using this function. | ||
| + | |||
| + | ==Notes== | ||
| + | # The function integrates over sample coordinates - subsequent gradient pulses would not refocus the magnetization that it has defocused. To simulate a gradient sandwich, use grad_sandw.m function. More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011). | ||
| + | #This function is OK for standalone gradient pairs; for more sophisticated gradient work, use the imaging context. | ||
| + | |||
| + | ==See also== | ||
| + | [[grad_sandw.m]], [[imaging.m]] | ||
| + | |||
| + | |||
| + | ''Version 2.2, authors: [[Luke Edwards]], [[Ilya Kuprov]]'' | ||
Revision as of 14:26, 15 August 2018
Emulates the effect of a gradient sandwich on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradients are linear, and that they are antisymmetric about the middle of the sample.
Contents
Syntax
rho=grad_sandw(spin_system,L,rho,P,g_amps,s_len,g_durs,s_facs)
Arguments
rho - spin system state vector
L - system Liouvillian
P - total propagator for all events happening
between the two gradients
g_amps - row vector containing the amplitudes of
the two gradients, Gauss/cm
s_len - sample length, cm
g_durs - row vector containing the durations of
the two gradients, seconds
s_facs - shape factors of the two gradients, use
[1 1] for square gradient pulses
Outputs
rho - spin system state vector, integrated over
the spatial coordinate
Examples
See examples/fundamentals/gradient_test_1.m file for an example of using this function.
Notes
- The function integrates over sample coordinates - subsequent gradient pulses would not refocus the magnetization that it has defocused. To simulate a gradient sandwich, use grad_sandw.m function. More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011).
- This function is OK for standalone gradient pairs; for more sophisticated gradient work, use the imaging context.
See also
Version 2.2, authors: Luke Edwards, Ilya Kuprov
