def EISF(self,
q_range=(0., 15.),
subset=None,
weights=None,
random_vectors=15,
first_mode=6):
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.getParticleScalar('b_incoherent')
weights = weights * weights
weights = weights * subset.booleanMask()
total = weights.sumOverParticles()
weights = weights / total
first, last, step = (q_range + (None, ))[:3]
if step is None:
step = (last - first) / 50.
q = N.arange(first, last, step)
f = ParticleProperties.ParticleTensor(self.universe)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
f = f + (1. / mode.inv_relaxation_time) * mode.dyadicProduct(mode)
f = Units.k_B * self.temperature * f / self.friction
eisf = N.zeros(q.shape, N.Float)
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
for a in subset.atomList():
exp = N.exp(-v * (f[a] * v))
N.add(eisf, weights[a] * exp**(q * q), eisf)
return InterpolatingFunction((q, ), eisf / len(random_vectors))
def anisotropicFluctuations(self, first_mode=6):
f = ParticleProperties.ParticleTensor(self.universe)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
array = mode.array
f.array += (array[:, :, N.NewAxis]*array[:, N.NewAxis, :]) \
/ mode.force_constant
if self.temperature is not None:
f.array *= Units.k_B * self.temperature
return f
def anisotropicFluctuations(self, first_mode=6):
"""Returns a Class:MMTK.ParticleTensor containing the thermal
fluctuations for each atom in the universe."""
f = ParticleProperties.ParticleTensor(self.universe)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
array = mode.array
f.array += (array[:, :, N.NewAxis]*array[:, N.NewAxis, :]) \
/ mode.force_constant
f.array *= Units.k_B * self.temperature
return f
def anisotropicFluctuations(self, first_mode=6):
f = ParticleProperties.ParticleTensor(self.universe)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
array = mode.array
f.array += (array[:, :, N.NewAxis]*array[:, N.NewAxis, :]) \
/ mode.frequency**2
s = (2. * N.pi)**2
if self.temperature is not None:
s /= Units.k_B * self.temperature
f.array /= s * self.universe.masses().array[:, N.NewAxis, N.NewAxis]
return f
def EISF(self,
q_range=(0., 15.),
subset=None,
weights=None,
random_vectors=15,
first_mode=6):
"""
:param q_range: the range of angular wavenumber values
:type q_range: tuple
:param subset: the subset of the universe used in the calculation
(default: the whole universe)
:type subset: :class:~MMTK.Collections.GroupOfAtoms
:param weights: the weight to be given to each atom in the average
(default: incoherent scattering lengths)
:type weights: :class:~MMTK.ParticleProperties.ParticleScalar
:param random_vectors: the number of random direction vectors
used in the orientational average
:type random_vectors: int
:param first_mode: the first mode to be taken into account for
the fluctuation calculation. The default value
of 6 is right for molecules in vacuum.
:type first_mode: int
:returns: the Elastic Incoherent Structure Factor (EISF) as a
function of angular wavenumber
:rtype: Scientific.Functions.Interpolation.InterpolatingFunction
"""
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.getParticleScalar('b_incoherent')
weights = weights * weights
weights = weights * subset.booleanMask()
total = weights.sumOverParticles()
weights = weights / total
first, last, step = (q_range + (None, ))[:3]
if step is None:
step = (last - first) / 50.
q = N.arange(first, last, step)
f = ParticleProperties.ParticleTensor(self.universe)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
f = f + (1. / mode.inv_relaxation_time) * mode.dyadicProduct(mode)
f = Units.k_B * self.temperature * f / self.friction
eisf = N.zeros(q.shape, N.Float)
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
for a in subset.atomList():
exp = N.exp(-v * (f[a] * v))
N.add(eisf, weights[a] * exp**(q * q), eisf)
return InterpolatingFunction((q, ), eisf / len(random_vectors))