Difference between revisions of "Grad sandw.m"
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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_2.m file for an example of using this function. | ||
+ | |||
+ | ==Notes== | ||
+ | # '''WARNING''' This function integrates over the spatial coordinate after the gradient pulses are completed - subsequent gradient pulses would not refocus the magnetisation that this function removed because it is removed mathematically. If your experiment has multiple gradient pulses, you must model the spatially distributed spin dynamics explicitly using [[imaging.m]] context. | ||
+ | # More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011). | ||
+ | |||
+ | ==See also== | ||
+ | [[grad_pulse.m]], [[imaging.m]] | ||
+ | |||
+ | |||
+ | ''Version 2.2, authors: [[Luke Edwards]], [[Ilya Kuprov]]'' |
Latest revision as of 08:56, 25 August 2019
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_2.m file for an example of using this function.
Notes
- WARNING This function integrates over the spatial coordinate after the gradient pulses are completed - subsequent gradient pulses would not refocus the magnetisation that this function removed because it is removed mathematically. If your experiment has multiple gradient pulses, you must model the spatially distributed spin dynamics explicitly using imaging.m context.
- More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011).
See also
Version 2.2, authors: Luke Edwards, Ilya Kuprov