Difference between revisions of "Grad sandw.m"

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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 gradients are linear, and that they are antisymmetric about the middle of the sample. Syntax:
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{{DISPLAYTITLE:grad_sandw.m}}
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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.
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==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:
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==Arguments==
 
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               rho  - spin system state vector
 
               rho  - spin system state vector
 
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                 L  - system Liouvillian
 
                 L  - system Liouvillian
 
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                 P  - total propagator for all events happening
 
                 P  - total propagator for all events happening
 
                       between the two gradients
 
                       between the two gradients
 
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           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
 
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             s_len  - sample length, cm
 
             s_len  - sample length, cm
 
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           g_durs  - row vector containing the durations of
 
           g_durs  - row vector containing the durations of
 
                       the two gradients, seconds
 
                       the two gradients, seconds
 
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           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
  
Note: the function integrates over sample coordinates - subsequent gradient pulses would not refocus the magnetization that it has left defocused. More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011).
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==Outputs==
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      rho - spin system state vector, integrated over
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            the spatial coordinate
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==Examples==
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See examples/fundamentals/gradient_test_2.m file for an example of using this function.
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==Notes==
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# '''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.  
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# More information on the subject is available in Luke's paper (http://dx.doi.org/10.1016/j.jmr.2014.01.011).
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==See also==
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[[grad_pulse.m]], [[imaging.m]]
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''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.

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

  1. 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.
  2. 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