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(spin_system,parameters)

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

Outputs

Fx, Fy, Fz - derivative matrices, SI units

Note: the direct product order is Z(x)Y(x)X(x)Spin, this cor-
      responds to a column-wise vectorization of a 3D array
      with dimensions ordered as [X Y Z].

Note: polyadic objects are returned, use inflate() to get the
      corresponding sparse matrix.

ilya.kuprov@weizmann.ac.il
a.j.allami@soton.ac.uk

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

Description

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

Returns

Fx, Fy, Fz - derivative matrices, SI units