# 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].

## See also

imaging.m, fdmat.m, v2fplanck.m, fourdif.m

*Version 1.10, authors: Ahmed Allami, Ilya Kuprov*