Difference between revisions of "Hydrodynamics.m"
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| + | {{DISPLAYTITLE:hydrodynamics.m}} __NOTOC__ | ||
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A basic hydrodynamics infrastructure provider, returns first derivative operators with respect to the three sample coordinates. Periodic boundary conditions are used. | A basic hydrodynamics infrastructure provider, returns first derivative operators with respect to the three sample coordinates. Periodic boundary conditions are used. | ||
==Syntax== | ==Syntax== | ||
| − | + | [Fx,Fy,Fz]=hydrodynamics(spin_system,parameters) | |
| − | |||
| − | |||
| − | |||
==Arguments== | ==Arguments== | ||
| − | + | parameters.dims - dimensions of the sample (meters), | |
one, two, or three-element row | one, two, or three-element row | ||
vector | vector | ||
| Line 24: | Line 23: | ||
boundary conditions | 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== | ==Examples== | ||
| + | |||
This function is used by [[imaging.m]] context in situations when spatial dynamics, such as diffusion and flow, is present in the sample. | This function is used by [[imaging.m]] context in situations when spatial dynamics, such as diffusion and flow, is present in the sample. | ||
==Notes== | ==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]. | 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== | ==See also== | ||
| + | |||
[[imaging.m]], [[fdmat.m]], [[v2fplanck.m]], [[fourdif.m]] | [[imaging.m]], [[fdmat.m]], [[v2fplanck.m]], [[fourdif.m]] | ||
''Version 1.10, authors: [[Ahmed Allami]], [[Ilya Kuprov]]'' | ''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 | ||
Revision as of 15:03, 5 April 2026
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
