#########################################################################
#                                                                       #
# Copyright (C) 2016-2018 Jan Jaeken <[email protected]>             #
#                                                                       #
# This file is part of Christoffel.                                     #
# "Solving the Christoffel equation: Phase and group velocities"        #
# Computer Physics Communications, 10.1016/j.cpc.2016.06.014            #
#                                                                       #
# Christoffel is free software: you can redistribute it and/or modify   #
# it under the terms of the GNU General Public License as published by  #
# the Free Software Foundation, either version 3 of the License, or     #
# (at your option) any later version.                                   #
#                                                                       #
# Christoffel is distributed in the hope that it will be useful,        #
# but WITHOUT ANY WARRANTY; without even the implied warranty of        #
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         #
# GNU General Public License for more details.                          #
#                                                                       #
# You should have received a copy of the GNU General Public License     #
# along with Christoffel.  If not, see <http://www.gnu.org/licenses/>.  #
#                                                                       #
#########################################################################


This package contains Christoffel, a Python module for calculating wave
velocities from elastic properties. This README is structured as follows:

1) General description
2) Package content
3) How to use Christoffel
    3.1) Input
    3.2) Execution
    3.3) Output
    3.4) Visualization
4) Example


1) General description

This software is designed to determine direction-dependent acoustic phase and
group velocities by solving the Christoffel equation. For detailed information
on the inner workings of the software, we refer to the accompanying paper in 
Computer Physics Communications.


2) Package content

README         -- This file. You are reading it right now.
christoffel.py -- Python module containing all the objects, functions and
                  mathematical machinery required. Toolbox.
__init__.py    -- Empty file, makes the christoffel module importable.
scansurface.py -- Script for sampling wave directions in a material, it outputs
                  phase velocities, group velocities and enhancement factors.
sound.in       -- Example input file for the scansurface script.
*.gnu files    -- Gnuplot scripts to automatically plot the output of the
                  scansurface script.


3) How to use Christoffel

Users are highly encouraged to take a peek into the christoffel.py module and
write their own implementations by using the module as a toolbox.

For those who do not wish to tinker much, the scansurface script and sound.in
should provide adequate functionality at the press of a button.

3.1) Input

All that is required to determine the elastic wave velocities is a material's
stiffness tensor and density. These can be entered in the sound.in file.

The sound.in file should minimally contain three things:

a) A '[SCAN]' tag in the first non-commented line to identify the file.
[SCAN]

b) The density of the material in kg/m^3.
Density = xxxx.x

c) The stiffness tensor of the material in GPa, don't forget the indentation.
Stiffness =
  C11 C12 C13 C14 C15 C16
  C12 C22 C23 C24 C25 C26
  C13 C23 C33 C34 C35 C36
  C14 C24 C34 C44 C45 C46
  C15 C25 C35 C45 C55 C56
  C16 C26 C36 C46 C56 C66

It can further contain these optional tags:

d) Definition of the grid to loop over.
Numtheta = int
Numphi = int  -- These define a rectangular grid in spherical coordinates on
                 the z>0 hemisphere of all possible wave directions. Numtheta
                 is the number of different values taken for the polar angle
                 (0<=theta<pi/2) while Numphi is the number of different
                 values for the azimutal angle (0<=phi<2pi). We suggest setting
                 Numphi equal to 4*Numtheta, though you are of course free to
                 choose these values as you please.

e) Definition of a new z-direction.
zdir = x y z  -- This will rotate the stiffness tensor so the new z-direction
                 will be the one specified. This does not need to be explicitly
                 normalized.

f) Definition of a new x-direction.
xdir = x y z  -- This will rotate the stiffness tensor so the new x-direction
                 will be the one specified. This does not need to be explicity
                 normalized, nor be orthogonal to the defined zdir. However,
                 the zdir tag takes precedence over xdir if it is specified,
                 and the resulting basis will be orthonormalized accordingly.

g) Directions to output data on. Don't forget the indentation.
Directions =
  x1 y1 z1
  x2 y2 z2
  x3 y3 z3
  ...         -- These directions will be looped over and data will be written
                 to directions.dat. Useful for studying only specific special
                 directions, or to manually define a sampling mesh.


3.2) Execution

If the sound.in file is prepared appropriately, all that is necessary is to run

> python scansurface.py

in the appropriate directory. The directory should contain the sound.in file
and the three .py files contained within this package.


3.3) Output

The scansurface script produces 6 output files.

a) slow_secondary.dat, fast_secondary.dat, primary.dat
    Acoustic information on the directions that have been looped over according
    to the grid defined by the 'Numtheta' and 'Numphi' tags. Contains the data
    on the slowest, intermediate and fastest acoustic mode respectively. All
    three files have the same structure of 17 columns:

    1 -------- Theta (rad)
    2 -------- Phi (rad)
    3,4,5 ---- Projection on the unit cube (cartesian)
    6 -------- Phase velocity (km/s)
    7 -------- Phase velocity relative to isotropic velocity (%)
    8,9,10 --- Phase polarization (unit vector, dimensionless)
    11 ------- Group velocity (km/s)
    12 ------- Group velocity relative to isotropic velocity (%)
    13,14,15 - Ray surface in cartesian coordinates (km/s)
    16 ------- Power flow angle (angle between phase and group direction) (deg)
    17 ------- Enhancement factor (dimensionless)

b) anisotropy.dat
    If a grid was defined, this file contains information about the maximal and
    minimal velocities of the three acoustic modes, and in what directions they
    occur. It also provides a measure of the total anisotropy of the material.

c) directions.dat
    This file contains sound velocity information about the directions
    defined under the 'Directions' tag in the sound.in file. Can be empty.

d) sound.out
    This file contains general information about the material of the last run,
    including density, rotated and non-rotated stiffness tensor, bulk and shear
    modulus and isotropic sound velocities.

3.4) Visualization

Gnuplot scripts are provided in the gnuplot subfolder to automatically plot
the data in the slow_secondary.dat, fast_secondary.dat and primary.dat files
generated by the scansurface script. A description of the naming scheme
follows, though if you are impatient you can simply run them all with:

> gnuplot ./gnuplot/*.gnu

Be advised that this may take a few minutes to complete.

The naming scheme of the scripts is as follows:

phase ----- Phase velocity
group ----- Group velocity (only absolute value)
ray ------- Ray surface (group velocity with direction)
pfangle --- Power flow angle
enh ------- Enhancement factor
pol ------- Polarization of phase velocities

relative -- For phase and group: relative to the isotropic sound velocities

sphere ---- Projection onto the unit sphere
cube ------ Projection onto the unit cube
eqar ------ Equal area projection onto the plane
stereo ---- Stereographic projection onto the plane, locally preserves shape
radius ---- Only for phase velocity, plots the data on a sphere with radius
            scaled according to the absolute velocity


4) Example

The sound.in file included in this package contains the density and stiffness
tensor of GaAs and can be used for a testrun.