def choosewavevector(Numofq, ndim):
""" Choose Wavevector in dynamic structure factor """
if ndim == 3:
return wavevector3d(Numofq)
elif ndim == 2:
return wavevector2d(Numofq)
def slowS4(self, outputfile, X4time, dt = 0.002, a = 1.0, results_path = '../../analysis/dynamics'):
""" Compute four-point dynamic structure factor at peak timescale of dynamic susceptibility
Based on overlap function Qt and its corresponding dynamic susceptibility QtX4
a is the cutoff for the overlap function, default is 1.0 (EAM) and 0.3(LJ) (0.3<d>)
X4time is the peaktime scale of X4
dt is the timestep in MD simulations
Dynamics should be calculated before computing S4
Only considered the particles which are slow
"""
print ('-----------------Compute dynamic S4(q) of slow particles --------------')
if not os.path.exists(results_path):
os.makedirs(results_path)
X4time = int(X4time / dt / self.TimeStep)
twopidl = 2 * pi / self.Boxlength[0]
if self.Boxlength[0] <= 40.0:
Numofq = int(self.Boxlength[0] / twopidl)
else:
Numofq = int(self.Boxlength[0] / 2 / twopidl)
wavevector = wavevector3d(Numofq) #Only S4(q) at low wavenumber range is interested
qvalue, qcount = np.unique(wavevector[:, 0], return_counts = True)
sqresults = np.zeros((len(wavevector[:, 0]), 3)) #the first row accouants for wavenumber
for n in range(self.SnapshotNumber - X4time):
RII = np.square(self.Positions[n + X4time] - self.Positions[n]).sum(axis = 1)
RII = np.where(np.sqrt(RII) <= a, 1, 0)
sqtotal = np.zeros((len(wavevector[:, 0]), 2))
for i in range(self.ParticleNumber):
medium = twopidl * (self.Positions[n][i] * wavevector[:, 1:]).sum(axis = 1)
sqtotal[:, 0] += np.sin(medium) * RII[i]
sqtotal[:, 1] += np.cos(medium) * RII[i]
sqresults[:, 1] += np.square(sqtotal).sum(axis = 1) / self.ParticleNumber
sqresults[:, 2] += sqtotal[:, 1]
sqresults[:, 0] = wavevector[:, 0]
sqresults[:, 1] = sqresults[:, 1] / (self.SnapshotNumber - X4time)
sqresults[:, 2] = np.square(sqresults[:, 2] / (self.SnapshotNumber - X4time)) / self.ParticleNumber
sqresults = pd.DataFrame(sqresults)
results = np.array(sqresults.groupby(sqresults[0]).mean())
results[:, 1] = results[:, 0] - results[:, 1] / qcount
qvalue = twopidl * np.sqrt(qvalue)
results = np.column_stack((qvalue, results))
names = 'q S4a(q) S4b(q)'
np.savetxt(results_path + outputfile, results, fmt='%.6f', header = names, comments = '')
print ('--------- Compute S4(q) of slow particles over ------')
return results
def fastS4(self, outputfile, a = 1.0, dt = 0.002, X4timeset = 0, results_path = '../../analysis/dynamics'):
""" Compute four-point dynamic structure factor at peak timescale of dynamic susceptibility
Based on overlap function Qt and its corresponding dynamic susceptibility QtX4
a is the cutoff for the overlap function, default is 1.0 (EAM) and 0.3(LJ) (0.3<d>)
dt is the timestep of MD simulations
X4timeset is the peaktime scale of X4, if 0 will use the calculated one
Dynamics should be calculated before computing S4
Only considered the particles which are fast
The Qt and X4 should be calculated first
"""
print ('-----------------Compute dynamic S4(q) of fast particles --------------')
if not os.path.exists(results_path):
os.makedirs(results_path)
#-----------calculte overall dynamics first----------------
results = np.zeros(((self.SnapshotNumber - 1), 3))
names = 't Qt QtX4'
cal_Qt = pd.DataFrame(np.zeros((self.SnapshotNumber-1))[np.newaxis, :])
deltat = np.zeros(((self.SnapshotNumber - 1), 2), dtype = np.int) #deltat, deltatcounts
for n in range(self.SnapshotNumber - 1): #time interval
RII = self.Positions[n + 1:] - self.Positions[n]
distance = np.square(RII).sum(axis = 2)
RII_Qt = (np.sqrt(distance) >= a).sum(axis = 1)
cal_Qt = pd.concat([cal_Qt, pd.DataFrame(RII_Qt[np.newaxis, :])])
cal_Qt = cal_Qt.iloc[1:]
deltat[:, 0] = np.array(cal_Qt.columns) + 1 #Timeinterval
deltat[:, 1] = np.array(cal_Qt.count()) #Timeinterval frequency
results[:, 0] = deltat[:, 0] * self.TimeStep * dt
results[:, 1] = cal_Qt.mean() / self.ParticleNumber
results[:, 2] = ((cal_Qt**2).mean() - (cal_Qt.mean())**2) / self.ParticleNumber
np.savetxt(results_path + 'Dynamics.' + outputfile, results, fmt='%.6f', header = names, comments = '')
#-----------calculte S4(q) of fast particles----------------
twopidl = 2 * pi / self.Boxlength[0]
if self.Boxlength[0] <= 40.0:
Numofq = int(self.Boxlength[0] / twopidl)
else:
Numofq = int(self.Boxlength[0] / 2 / twopidl)
wavevector = wavevector3d(Numofq) #Only S4(q) at low wavenumber range is interested
qvalue, qcount = np.unique(wavevector[:, 0], return_counts = True)
sqresults = np.zeros((len(wavevector[:, 0]), 3)) #the first row accouants for wavenumber
if X4timeset:
X4time = int(X4timeset / dt / self.TimeStep)
else:
X4time = deltat[results[:, 2].argmax(), 0]
for n in range(self.SnapshotNumber - X4time):
RII = np.square(self.Positions[n + X4time] - self.Positions[n]).sum(axis = 1)
RII = np.where(np.sqrt(RII) >= a, 1, 0)
sqtotal = np.zeros((len(wavevector[:, 0]), 2))
for i in range(self.ParticleNumber):
medium = twopidl * (self.Positions[n][i] * wavevector[:, 1:]).sum(axis = 1)
sqtotal[:, 0] += np.sin(medium) * RII[i]
sqtotal[:, 1] += np.cos(medium) * RII[i]
sqresults[:, 1] += np.square(sqtotal).sum(axis = 1) / self.ParticleNumber
sqresults[:, 2] += sqtotal[:, 1]
sqresults[:, 0] = wavevector[:, 0]
sqresults[:, 1] = sqresults[:, 1] / (self.SnapshotNumber - X4time)
sqresults[:, 2] = np.square(sqresults[:, 2] / (self.SnapshotNumber - X4time)) / self.ParticleNumber
sqresults = pd.DataFrame(sqresults)
results = np.array(sqresults.groupby(sqresults[0]).mean())
results[:, 1] = results[:, 0] - results[:, 1] / qcount
qvalue = twopidl * np.sqrt(qvalue)
results = np.column_stack((qvalue, results))
names = 'q S4a(q) S4b(q)'
np.savetxt(results_path + outputfile, results, fmt='%.6f', header = names, comments = '')
print ('--------- Compute S4(q) of fast particles over ------')
return results