# Kernel contexts

A context is an intermediate layer between the kernel (which runs the mathematics) and the experiment (which is programmed as it would be on a spectrometer). Context functions are responsible for creating operators (evolution, kinetics, relaxation, diffusion, *etc.*) and for running miscellaneous housekeeping operations (rotating frame transformations, transmitter offsets, powder averages, magic angle spinning, *etc.*).

Most built-in pulse sequences in Spinach should be called via a context, for example:

fid=liquid(spin_system,@noesy,parameters,'nmr');

This calls liquid.m context and tells it that noesy.m must be called. The parameters and the spin system are specified with the assumptions set to liquid state NMR. The context function will build the Hamiltonian, the relaxation superoperator, the kinetics superoperator, apply the offsets and the rotating frame transformations, and pass the resulting operators to noesy.m, which runs the simulation.

In this way, a lot of work is saved to whoever has to program the pulse sequence, particularly in situations when the operators and settings involved are complicated, *e.g.* gradients, diffusion and flow. *Spinach* contexts generate all of those in correct units and correct normalisation; the pulse sequence should simply treat them as a given. Because parameter lists of different pulse sequences are broadly similar, this allows rapid switching of the simulation context (for example, from liquid to powder) by simply calling the same experiment from a different context.

## Available contexts

- crystal.m - single static orientation simulations.
- doublerot.m - double rotation simulations using Fokker-Planck formalism for the rotation part and a spherical grid for the powder average operation.
- floquet.m - single rotation simulations using Floquet formalism for the rotation part and a spherical grid for the powder average operation.
- gridfree.m - single rotation simulations using Fokker-Planck formalism for both the rotation part and the powder average operation. This module also supports stochastic Liouville equation formalism for spin relaxation theory.
- imaging.m - imaging and spatial encoding simulations.
- liquid.m - liquid state simulations.
- powder.m - static powder simulations using a spherical grid for the powder average operation.
- roadmap.m - static powder simulations using a spherical grid. Simulation results are returned as an array with an answer reported at each orientation found in the spherical grid.
- singlerot.m - single rotation simulations using Fokker-Planck formalism for the rotation part and a spherical grid for the powder average operation.

## Call syntax for spectroscopy contexts

The following is a syntax example for a spectroscopy context (in this case DOR NMR):

answer=doublerot(spin_system,pulse_sequence,parameters,assumptions);

The first argument is the spin system object, the second is a function handle for the pulse sequence, the third is the parameter set expected by the sequence, and the last argument is the assumption set.

All pulse sequences using a context must have the same call syntax:

answer=pulse_sequence(spin_system,parameters,H,R,K);

where H is the Hamiltonian commutation superoperator, R is the relaxation superoperator, and K is the kinetics superoperator.

## Call syntax for imaging contexts

The imaging context has a similar call:

answer=imaging(spin_system,pulse_sequence,parameters)

but the assumptions are set internally to 'nmr' and the pulse sequence must have the following syntax:

answer=pulse_sequence(spin_system,parameters,H,R,K,G,F);

where H is the Hamiltonian commutation superoperator, R is the relaxation superoperator, K is the kinetics superoperator, G is a cell array of three gradient operators normalized to 1 Tesla/m, and F is the diffusion and flow superoperator.

*Version 2.1, authors: Ilya Kuprov*