the orientations or the density after unit time in n Euler steps under the rotation velocity field spin; MATLAB’s doEulerStep

Syntax

ori = doEulerStep(spin, ori0, 10)

Orientations in 10 steps.

odf = doEulerStep(spin, odf0, 40)

A density in 40 steps.

odf = doEulerStep(spin, odf0, 40, bandwidth=16)

The density in harmonics up to 16.

Description

Orientations move along the exponential of the field, one step of a n-th of the time at a time. A density follows the continuity equation, d f / dt = -div(f spin), integrated by the explicit Euler method in its harmonic space. MATLAB’s implicit variants (‘implicit’, ‘implicit_fixPoint’) are not offered.

Input

`spin`	SO3VectorField or a callable of orientations, the rotation velocity
`x`	orientation or SO3Fun, the start

Keywords

keyword	default	description
`n`	`1`	the number of steps
`bandwidth`	`None`	the bandwidth of the density, by default that of SO3FunHarmonic(x)

Output

`x`	orientation or SO3FunHarmonic after unit time

Used on

SingleSlipModel

MATLAB’s doEulerStep

source

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/doEulerStep_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

doEulerStep