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 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 = wavevector2d(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 = wavevector2d(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
