Difference between revisions of "Grad pulse.m"

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Computes the effect of a gradient pulse on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradient is linear, and that it is antisymmetric about the middle of the sample. Syntax:
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{{DISPLAYTITLE:function.m}}
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Emulates the effect of a gradient pulse on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradient is linear, and that it is antisymmetric about the middle of the sample.
  
      rho=grad_pulse(spin_system,rho,g_amp,s_len,g_dur,s_fac)
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==Syntax==
  
Arguments:
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    rho=grad_pulse(spin_system,rho,g_amp,s_len,g_dur,s_fac)
 
 
              rho   - spin system state vector
 
  
                L  - system Liouvillian
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==Arguments==
  
            g_amp   - gradient amplitude, Gauss/cm
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        rho   - spin system state vector
  
            s_len   - sample length, cm
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          L   - system Liouvillian
  
            g_dur   - gradient pulse duration, seconds
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      g_amp   - gradient amplitude, Gauss/cm
  
            s_fac   - gradient shape factor, use 1 for
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      s_len   - sample length, cm
                      square gradient pulses
 
  
Note: 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).
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      g_dur  - gradient pulse duration, seconds
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      s_fac  - gradient shape factor, use 1 for
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                square gradient pulses
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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_1.m file for an example of using this function.
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==Notes==
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# 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).
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#This function is OK for standalone crusher gradients; for more sophisticated gradient work, use the imaging context.
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==See also==
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[[grad_sandw.m]], [[imaging.m]]
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''Version 2.2, authors: [[Ilya Kuprov]]''

Revision as of 11:31, 14 August 2018

Emulates the effect of a gradient pulse on the sample average density matrix using Edwards formalism. It is assumed that the effect of diffusion is negligible, that the gradient is linear, and that it is antisymmetric about the middle of the sample.

Syntax

    rho=grad_pulse(spin_system,rho,g_amp,s_len,g_dur,s_fac)

Arguments

        rho   - spin system state vector
          L   - system Liouvillian
      g_amp   - gradient amplitude, Gauss/cm
      s_len   - sample length, cm
      g_dur   - gradient pulse duration, seconds
      s_fac   - gradient shape factor, use 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

  1. 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).
  2. This function is OK for standalone crusher gradients; for more sophisticated gradient work, use the imaging context.

See also

grad_sandw.m, imaging.m


Version 2.2, authors: Ilya Kuprov