1. ABOUT THE DATASET
--------------------

Title:	Andrew J. Archer, Tomonari Dotera and Alastair M. Rucklidge (2022): Dataset for ``Rectangle--triangle soft-matter quasicrystals with hexagonal symmetry''. 
https://doi.org/10.5518/1188 

Creator(s): Andrew J. Archer [1], Tomonari Dotera [2] and Alastair M. Rucklidge [3]

Organisation(s):
[1] Department of Mathematical Sciences and Interdisciplinary Centre for Mathematical Modelling, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
[2] Department of Physics, Kindai University, 3-4-1 Kowakae Higashi-Osaka 577-8502, Japan
[3] School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

Rights-holder(s): Andrew J. Archer, Tomonari Dotera and Alastair M. Rucklidge

Publication Year: 2022

Description: 

There are two files in this dataset (gzipped text files):
dft_5_stable_bronze_mean_a_33_b_23_tol_6e-6.dat.gz (86MB)
dft_6_stable_EDRT_a_43_b_27.dat.gz (161MB)

Each file consists of a list of density values at the grid points, on a 1:sqrt(3) periodic domain. The "pixels" are not square.

dft_5_stable_bronze_mean_a_33_b_23_tol_6e-6.dat.gz:
with a=33 and b=23, we have m = 2*a-b = 43
the grid is 2048 x 2048
There are three columns: x, y, density
x ranges from 0 to 540.09010675130412 = 86 * 2pi * 2047/2048                  (86=2*m)
y ranges from 0 to 311.82116851951918 = 86 * 2pi * 2047/2048 / sqrt(3) 
Each group of lines with common x values is separated by a line with a single '#'
The parameter values of the calculation are:
sigma, C_2, C_4, C_6, C_8 = 0.95, -2.3455, 1.2638, -0.20667, 0.010136
rhobar = 9.6

dft_6_stable_EDRT_a_43_b_27.dat.gz
with a=43 and b=27, we have m = 2*a-b = 59
the grid is 4096 x 4096 and the layout of data is as with the first file, but the (x,y) values are not included, and the blank line every 4096 is not present
the order of the data is the same as the first file.
x ranges from 0 to 118 * 2pi * 4095/4096                 (118=2*m)
y ranges from 0 to 118 * 2pi * 4095/4096 / sqrt(3) 
The parameter values of the calculation are:
sigma, C_2, C_4, C_6, C_8 = 0.85, -1.4516, 0.69075, -0.098040, 0.0044548
rhobar = 9.4

Cite as: 

A. J. Archer, T. Dotera, and A. M. Rucklidge (2022), Dataset for ``Rectangle--triangle soft-matter quasicrystals with hexagonal symmetry'', University of Leeds. [Dataset]. https://doi.org/10.5518/1188.

Related publication: 

A. J. Archer, T. Dotera, and A. M. Rucklidge (2022), ``Rectangle--triangle soft-matter quasicrystals with hexagonal symmetry'', Physical Review E, 
Accepted.

Contact: 
Andrew J. Archer A.J.Archer@lboro.ac.uk and Alastair M. Rucklidge A.M.Rucklidge@leeds.ac.uk

2. TERMS OF USE
---------------

Copyright 2022 A. J. Archer, T. Dotera, and A. M. Rucklidge. 
This dataset is
licensed under a Creative Commons Attribution 4.0 International Licence: https://creativecommons.org/licenses/by/4.0/.


3. PROJECT AND FUNDING INFORMATION
----------------------------------

Title: Quasicrystals: how and why do they form?

Dates: August 2017 -- July 2021

Funding organisation: EPSRC

Grant no.: EP/P015689/1 and EP/P015611/1

Title: Advanced study of softmatter quasicrystals and quasiperiodic tiling theory

Dates: April 2019 -- March 2022

Funding organisation: Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research (KAKEN), Japan.

Grant no.: 19K03777

4. CONTENTS
-----------
File listing

There are two files in this dataset (gzipped text files):
dft_5_stable_bronze_mean_a_33_b_23_tol_6e-6.dat.gz (86MB)
dft_6_stable_EDRT_a_43_b_27.dat.gz (161MB)

Each file consists of a list of density values at the grid points, on a 1:sqrt(3) periodic domain. The "pixels" are not square.

dft_5_stable_bronze_mean_a_33_b_23_tol_6e-6.dat.gz:
with a=33 and b=23, we have m = 2*a-b = 43
the grid is 2048 x 2048
There are three columns: x, y, density
x ranges from 0 to 540.09010675130412 = 86 * 2pi * 2047/2048                  (86=2*m)
y ranges from 0 to 311.82116851951918 = 86 * 2pi * 2047/2048 / sqrt(3) 
Each group of lines with common x values is separated by a line with a single '#'
The parameter values of the calculation are:
sigma, C_2, C_4, C_6, C_8 = 0.95, -2.3455, 1.2638, -0.20667, 0.010136
rhobar = 9.6

dft_6_stable_EDRT_a_43_b_27.dat.gz
with a=43 and b=27, we have m = 2*a-b = 59
the grid is 4096 x 4096 and the layout of data is as with the first file, but the (x,y) values are not included, and the blank line every 4096 is not present
the order of the data is the same as the first file.
x ranges from 0 to 118 * 2pi * 4095/4096                 (118=2*m)
y ranges from 0 to 118 * 2pi * 4095/4096 / sqrt(3) 
The parameter values of the calculation are:
sigma, C_2, C_4, C_6, C_8 = 0.85, -1.4516, 0.69075, -0.098040, 0.0044548
rhobar = 9.4

5. METHODS
----------

The density profiles are (local) minima of the Dynamic Density Functional Theory free energy, and are found by Picard iteration. The iteration 
is initialised with a profile constructed by superposing the Fourier modes needed for each type of quasicrystal.