# Hydrodynamics.m

A basic hydrodynamics infrastructure provider, returns first derivative operators with respect to the three sample coordinates. Periodic boundary conditions are used.

## Syntax

    [Fx,Fy,Fz]=hydrodynamics(parameters)


## Description

The function returns finite difference or Fourier differentiation matrices for first derivatives, correctly normalised to account for physical sample dimensions.

## Arguments

  parameters.dims    - dimensions of the sample (meters),
one, two, or three-element row
vector

parameters.npts    - number of points in each dimension
of the sample, one, two, or three-
element row vector

parameters.deriv   - {'fourier'} requests Fourier diffe-
rentiation matrices; {'period',n}
requests n-point central finite-
difference matrices with periodic
boundary conditions


## Returns

  Fx, Fy, Fz         - derivative matrices, SI units


## Examples

This function is used by imaging.m context in situations when spatial dynamics, such as diffusion and flow, is present in the sample.

## Notes

Empty arrays are returned for inactive dimensions. The direct product order is Z(x)Y(x)X(x)Spin, this corresponds to a column-wise vectorization of a 3D array with dimensions ordered as [X Y Z].