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permeation.py
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permeation.py
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# PERMEATION
# Martin Voegele, 2018-03-20
# Import necessary modulies
import sys
import argparse
import numpy as np
import scipy as sp
import MDAnalysis as mda
## FUNCTIONS ##
def compute_correlation_via_fft(x, y=None):
"""
Correlation of two arrays calculated via FFT.
If only one is given, the autocorrelation of the first one is calculated.
"""
x = np.array(x)
l = len(x)
xft = np.fft.fft(x, 2*l)
if y is None:
yft = xft
else:
y = np.array(y)
yft = np.fft.fft(y, 2*l)
corr = np.real(np.fft.ifft(np.conjugate(xft)*yft))
norm = l - np.arange(l)
corr = corr[:l]/norm
return corr
def compute_msd_via_correlation(x,y=None,z=None):
"""
MSD calculated via FFT-based auto-correlation
"""
y_is_given = y is not None
z_is_given = z is not None
# compute correlation
corrx = compute_correlation_via_fft(x)
# squared distances
dsq = x**2
# repeat correlation for y and z and add y/z components to squared distance
if y_is_given:
corry = compute_correlation_via_fft(y)
dsq += y**2
if z_is_given:
corrz = compute_correlation_via_fft(z)
dsq += z**2
# sum up all squared distances
sumsq = 2*np.sum(dsq)
# initialize MSD
nt = len(x)
msd = np.empty(nt)
msd[0] = 0
# iterate through the time to subtract squared distances
for m in xrange(1,nt):
sumsq = sumsq - dsq[m-1]-dsq[nt-m]
msd[m] = sumsq/(nt-m)
# subtract correlations
msd[1:] -= 2*corrx[1:]
if y_is_given:
msd[1:] -= 2*corry[1:]
if z_is_given:
msd[1:] -= 2*corrz[1:]
return msd
## MAIN ##
# Parse arguments
parser = argparse.ArgumentParser()
parser.add_argument( '-p', dest='prmfile', default='system.prmtop', help="topology file (prmtop)" )
parser.add_argument( '-t', dest='trjfile', default='trajectory.nc', help="trajectory file", nargs='+' )
parser.add_argument( '-o', dest='outfile', default='permeation.dat',help="output file" )
parser.add_argument( '-sel', dest='selection', default='resname WAT and name O', help="selection command" )
parser.add_argument( '-ref', dest='reference', default='resname CNT', help="reference selection command" )
args = parser.parse_args()
vdw_r_c = 1.6 # vdW radius of Carbon [Angstrom]
vol_h2o = 29.7 # volume of a water molecule [Angstrom^3]
# Create the universe
u = mda.Universe(args.prmfile,args.trjfile)
# select water and CNT
water = u.select_atoms(args.selection)
cnt = u.select_atoms(args.reference)
# Initialize all loop variables
num_water = len(water)
num_steps = len(u.trajectory)
t = np.zeros(num_steps)
dn = np.zeros(num_steps)
n = np.zeros(num_steps)
num_inside = np.zeros(num_steps)
volume_cnt = np.zeros(num_steps)
all_z_water = np.zeros([num_water,num_steps],dtype=float)
state_water = np.zeros([num_water,num_steps],dtype=int)
# Loop over the whole trajectory
for ts in u.trajectory:
# simulation time in ps
t[ts.frame] = ts.time
# Wrap all coordinates into a box with the CNT at the center and origin
com_cnt_old = cnt.center_of_mass(pbc=False)
u.atoms.translate(-com_cnt_old+ts.dimensions[:3]*.5)
u.atoms.wrap()
com_cnt_new = cnt.center_of_mass()
u.atoms.translate(-com_cnt_new)
# Check for each water particle whether it is above or below the membrane
upper_water = water.positions[:,2] > 0
lower_water = water.positions[:,2] < 0
state_water[ upper_water, ts.frame ] = 1
state_water[ lower_water, ts.frame ] = -1
# Calculate the principal axis of the CNT
pa = cnt.principal_axes()
# ... and make sure n_z always points upwards
if pa[0][2] < 0:
pa = -pa
# Transform everything to the reference frame of the CNT
tm = np.zeros([4,4])
tm[:3,:3] = pa
u.atoms.transform(tm)
# Calculate z for each water particle
all_z_water[ :, ts.frame ] = water.positions[:,0]
# Calculate the geometry of the CNT
min_cnt = np.min(cnt.positions[:,0])
max_cnt = np.max(cnt.positions[:,0])
len_cnt = max_cnt - min_cnt
r2_cnt = np.average(cnt.positions[:,1]**2+cnt.positions[:,2]**2)
volume_cnt[ts.frame] = np.pi*(np.sqrt(r2_cnt)-vdw_r_c)**2*len_cnt
# Check for each water particle whether it is inside the CNT
abovemin = water.positions[:,0] > min_cnt
belowmax = water.positions[:,0] < max_cnt
incylind = water.positions[:,1]**2 + water.positions[:,2]**2 < r2_cnt
inside_water = abovemin*belowmax*incylind
num_inside[ts.frame] = np.sum(inside_water)
state_water[ inside_water, ts.frame ] = 0
# Calculate n
if ts.frame > 0:
inside_water_before = state_water[:,ts.frame-1] == 0
dz = all_z_water[ inside_water*inside_water_before, ts.frame ] - all_z_water[ inside_water*inside_water_before, ts.frame-1 ]
dn[ts.frame] = np.sum(dz)/len_cnt
n[ts.frame] = n[ts.frame-1] + dn[ts.frame] # np.sum(dn[:ts.frame+1])
# Write the results from the loop
header = "# time [ns], dn, n, # particles inside CNT, volume of CNT [A^3]"
np.savetxt(args.outfile,np.array([t*0.001,dn,n,num_inside,volume_cnt]).T,header=header,fmt=5*'%.8e ')
# Calculate the diffusion coefficient of n (in ps^-1)
msdn = compute_msd_via_correlation(n)
par = np.polyfit(t[0:50]-t[0],msdn[0:50],1,cov=True)
diffc = 0.5*par[0][0]
sigma_diffc = 0.5*par[1][0,0]
print "D_n:", diffc, "+/-", sigma_diffc, "ps^-1"
# Permeabilty (A^3/ps)
perm = diffc*vol_h2o
sigma_perm = sigma_diffc*vol_h2o
print "p_f:", perm, "+/-", sigma_perm, "A^3/ps"