1155092080 / bec3p

bec3p

All the codes are from https://arxiv.org/pdf/1412.7152.pdf

The code as packaged here contains a Makefile that has been tested using gcc 4.5.2 on a 64-bit Linux host. The C++ code also compiles as a Visual Studio 2010 console application project on Windows 7 64-bit. This archive contains the following files:

00readme.txt - This file Makefile - UNIX/Linux makefile stdafx.h - C/C++ header file (mainly for Visual Studio) parameters3.h - C/C++ header file with configurable parameters bec3p.c++ - C/C++ program file parameters3.f90 - Fortran 90 header file bec3p.f90 - Fortran 90 program file animate.sh - Shell (bash) script to create animated GIFs video.sh - Shell (bash) script to convert animations into MP4

WARNING: This program produces a large number of output files. It may be a good idea to run this program in an empty folder to avoid clobbering existing data.

Compilation using Makefile provided

Adjust run-time parameters in parameters.h or parameters.f90 as desired, then compile the code using:

make all - compiles both the C++ and Fortran versions make bec3p - compiles the Fortran version make bec3pc - compiles the C++ version

Test run

To run the program enter, ./bec3p - Fortran executable or ./bec3pc - C++ executable

The sample parameter files (parameters.h and parameters.f90) set the number of iterations to 50000 and the grid size to 20x20x20. With these settings, the program takes approximately 5 minutes to run on a typical computer. It produces 3x3 output files every 100 iterations, i.e. 4509 files.

Visualisation

The output files from the program can be converted to GIF and MPEG-4 formats using the scripts provided; more details below.

./animate.sh -o bec3p_out.gif

The bec3_out.gif file can be viewed in a browser window or using the 'animate' utility of the ImageMagick suite, which is preinstalled in many Linux distributions.

./video.sh -i bec2p_out.gif -o bec3p_out.mp4

The bec30_out.mp4 can be viewed in Windows Media Player or VLC media player.

Detailed description

Our self-gravitating BEC code has several components. A stand-alone executable compiled from FORTRAN (bec3p.f90) or C++ (bec3p.c++) source performs the simulation. User-definable parameters are in header files (parameters3.f90 or parameters3.h). A change in parameters necessitates recompiling the executables, but this is quickly accomplished using the supplied make file (Makefile). The simulation code creates data files at set intervals, specifically formatted to facilitate plotting using the gnuplot utility. A UNIX style shell script (animate.sh) is provided that uses gnuplot to create animations in the form of animated GIF files. Finally, yet another shell script (video.sh) can be used to convert these GIF files into MPEG-4 video animations.

For additional details, see arXiv:1207.5249.

The structure of the main source file (bec3p.f90 or bec3p.c++) is as follows:

• The main program (or _tmain function in the C++ imlementation) initializes parameters and executes the main simulation loop.

• The function init creates the initial distribution. This is the only user-modifiable subroutine in the main program file; in the test implementation, it creates a naive initial distribution inspired by the Lane-Emden equation.

• The function get_U computes the potential term (without rotation) in the Gross-Pitaevskii equation, as given in Eq. (3).

• The functions calc_rhs_x, calc_rhs_y and calc_rhs_z compute the right-hand side of the Gross-Pitaevskii equation (1).

• The function solve_x, solve_y and solve_z solve for the left-hand side of the Gross-Pitaevskii equation according to the scheme represented by Eq. (4).

• The function thomas solves a tridiagonal system of linear equations using the Thomas algorithm.

• The function get_normsimp obtains a numerical approximation of the integral of the mod square of the wave function using Simpson's formula.

• The functions movieX, movieY and movieZ generate output after a set number of iterations (controlled by the variable nstep2) that is set in parameters3.h or parameters3.f90 in a format that is suitable for use with gnuplot.

• The function get_phi computes the gravitational potential corresponding to the current values of \psi using the relaxation method.

• The function get_density computes the density |\psi|^2.

Output files produced by the program include the following:

• The files densZnnnnnnn.dat contain values of density |\psi|^2, sorted and grouped to facilitate plotting with gnuplot in the plane perpendicular to the Z-axis (i.e., the XY plane). Similarly, the files densXnnnnnnn.dat and densYnnnnnnn.dat contain density values sorted and grouped for plotting in the plane perpendicular to the X and Y-axis.

• The files gravZnnnnnnn.dat, gravXnnnnnnn.dat and gravYnnnnnnn.dat contain values of the gravitational potential, arranged similarly.

• The files phasZnnnnnnn.dat, phasXnnnnnnn.dat and phasYnnnnnnn.dat contain values of the complex phase of \psi, again arranged as before.

The shell script animate.sh provides simple visualization. By default, this script create an animated GIF of density values, in the plane perpendicular to the Z-axis and across the origin, with the color range normalized to the 1000th iteration step. Running

animate.sh -h

prints a brief help message that lists all the options of this script; in particular, the option -p that allows the user to change the plane for visualization and the option -t that allows the user to change the plot type. The script can also output an animated plot of the estimated Keplerian rotational velocity (option -t vrot), for circular orbits centered around the origin in the XY plane.

Finally, the shell script video.sh can be used to convert animated GIF output into MPEG-4 video. For this script to work, the utilities ffmpeg and mplayer must be installed on the workstation where the script is being used.