# grad_sandw.m

From Spinach Documentation Wiki

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

**grad_sandw.m**, imaging.m

*Version 2.2, authors: Luke Edwards, Ilya Kuprov*