Computes the mean squared displacement of particles along a trajectory. It takes the periodic boundary counditions into account.
The purpose of this program is to compute the mean squared displacement (MSD) of a series of equivalent particles that have positions evolving in time.
The MSD we calculate is defined as
where q is the three-dimension position vector. It is averaged over all sites, i, and origins of time, t0.
In a nutshell, the MSD at time t is the ensemble average of the squared Euclidean distance between two positions separated by time t
Written by Maximilien Levesque, while in postdoc in the group of Mathieu Salanne at
UPMC Univ Paris 06, CNRS, ESPCI, UMR 7195, PECSA, F-75005 Paris, France
- Marie Jardat, UPMC, PECSA, Paris, France, for discussions, extensive testing and bug reports of the beta (unshared) versions.
- Xudong Zhao, UPMC, PECSA, Paris, France, for providing test cases and for discussions.
You need to install scons, which is a newer and better and easier equivalent to the much complicated make.
Please visit the scons website for download, or you should better use the repositories of your own distribution:
Under Ubuntu: sudo apt-get install scons
Under Fedora: sudo yum install scons
and so on for other distros.
Once you're in the directory where you downloaded meanSquaredDisplacement, just type
$ scons
In a nutshell, scons will look at the file called SConstruct I built for you and compile everything smartly.
Of course, you may compile the simple fortran file(s) by yourself if you prefer the complicated ways.
All you need is a file, whatever its name, containing all your positions in a format
x(1,t) y(1,t) z(1,t)
x(2,t) y(2,t) z(2,t)
x(i,t) y(i,t) z(i,t)
...
x(Nat,t) y(Nat,t) z(Nat,t)
x(1,t+1) y(1,t+1) z(1,t+1)
x(2,t+1) y(2,t+1) z(2,t+1)
x(i,t+1) y(i,t+1) z(i,t+1)
...
x(Nat,t+1) y(Nat,t+1) z(Nat,t+1)
...
...
x(Nat,t+Nstep) y(Nat,t+Nstep) z(Nat,t+Nstep)
where Nat is the total number of atoms you have in your supercell,
and Nstep is the number of timesteps in your trajectory.
In other words, you print the coordinates of all sites for a given timestep, then for the next one, etc.
You do not print blank lines anywhere. You can add as many spaces you want between the columns.
At the end, you must have 3 columns and Nat x Nstep rows.
That's all you need.
Note that if you have one-dimensional (two-dimensional) positions at each time step, you'll have to add 2 (1) column filled with zero.
The executable is waiting for arguments:
Lx, the length of the supercell in x direction, in the same units as the positionsLyLzNat, defined abovefilenameof the trajectory in the format discussed above.
So, you have to execute:
$ meanSquaredDisplacement 56.0 37.43 288.1 800 ./analysis/MSD/positions.out
Execution of meanSquaredDisplacement will result in a single file: msd.out.
This file has a very simple ASCII format:
1 1.12931233
2 1.24034134
3 1.5908O123
...
Nstep 123987.12383
where the first column is the timestep, and the second column is the mean squared displacement.
Both timesteps and mean squared displacement are in units of your simulation.
If your trajectory file contains milliseconds (ms) and (Angstroms), msd.out will be in ms Angstroms².
This program has been thoroughly tested and validated. I would not share a tool that is not production ready. I am very confident in this program. Nevertheless, this program may contain bugs or restrictions that would lead to unexpected results. Please, read carefully this readme file, and test it thoroughly on data for which you already know the results.
Comments, bug reports or even thanks ;) are welcome!