This program is to get well-aligned density profiles from trajectory with multi-components in molecular dynamics using convolution method under periodic boundary condition
numpyandscipy: for numerical calculationsmdtraj(> version 1.9.1): to read trajectory and structure file
Molecular dynamics is a good tool to simply simulate complex systems such as two phases (solid-liquid, liquid-liquid, liquid-gas) of single or multi-components. From two equilibrated phases in a single cell, we can get density or concentration profiles at time frames for single or multi-components. The problem is that the density profile has instantaneous values, thus we need to average the profiles to get coexistance properties to draw phase diagram such as concenteration - temperature space. During the simulation, because of mass transfer between two phases and fluctuation of interace position, alignment method is necessary to reduce any flucutations.
The idea is to implement convolution method in not only signal processing but also density profile. In engineering field, the method is widely used to get delay time between two identical (sound, light, or electrical) wave signal but different tranvelling time (or travelling distance) from source to detector. Even though very noisy environment may prevent to figure where the signals show, the convolution method amazingly works in obtaning the delay time for signal processing. This strategy may work in this density profile due to following analogy:
| interpretation | wave signal | density profile |
|---|---|---|
| object1 | wave packet with travelling time t1 |
density profile with travelling distance d1 |
| object2 | wave packet with travelling time t2 |
density profile with travelling distance d2 |
| delay time or shift distance | t2-t1 |
d2-d1 |
| In real, | wave packet mixed with noise by environment | density profile with statistical noise due to small number of molecules |
| In theory, | wave packet with sum of sine functions | density profile composing sum of two tangent functions (rough interface) or two step functions (very flat interface) |
Once we know all shift distances between any density profiles by convolution, we can align the density profiles accurately by shifting along the normal direction on interface plane (assummed 2D-plane), and then get well averaged density profile to get accurate density or concentration of phases. Note that we use theoretical density profile with two step functions as standard to get optimal shift distance.
Basically, slicing method is necessary to get local densities of slabs which are parallel to interface plane. The thickness of slab is the half resolution to get optimal shifting distance for density profile. Thus, to get good result, small slab thickness is good choice.
On the other side, if the small aggregation in the phase exists or your molecules are big enough, convolution might not work unless you increase slab thickness. For very small slab thickness, the density profile would be descrete, which leads wrong optimal shift distances. Thus, we recommend to check the effect of thickness of slab on density profile and coexistance properties.
(coming soon...)
currently, I assume the system has only two phases under periodic boundary condition. If your system is in single phase (mixing) or three or more phases, please find alternative way by modifying this code or making your own code. Also, your system should be large enough for density profile to be flat in each phase. If you have too wide area for interface in the density profile, the result (finding optimal shift distance) would be highly affected by a theoretical density profile, step function. Although the step function is far from a copy of realistic density profiles, the assumption that the flat region makes much more hits than that in interface region makes working. Instead of step function, tangent function probably may be good reference for convolution processing to get optimal shift distance in that the function reflects interface region.
v1.0.0 upload my home code to github for polymer/ionic liquid system. (see tutorial for such a three-component system - cation, anion, and neutral polymer)
v1.1.0 add function for optimizing parameters tangent functions as a reference during convolution
Please cite the following article for convolution method:
A simulation method for the phase diagram of complex fluid mixtures, Hyuntae Jung and Arun Yethiraja, The Journal of Chemical Physics 2018, 148:24 https://aip.scitation.org/doi/abs/10.1063/1.5033958