# quaternion to be used for disturbing the orientation of each body
quaternion_shift = Quaternion(np.array([1,0,0,0]))
# for each step in the Markov chain, disturb each body's location and orientation and obtain the new list of r_vectors
# of each blob. Calculate the potential of the new state, and accept or reject it according to the Markov chain rules:
# 1. if Ej < Ei, always accept the state 2. if Ej < Ei, accept the state according to the probability determined by
# exp(-(Ej-Ei)/kT). Then record data.
# Important: record data also when staying in the same state (i.e. when a sample state is rejected)
for step in range(read.initial_step, read.n_steps):
blob_index = 0
for i, body in enumerate(bodies): # distrub bodies
body.location_new = body.location + np.random.uniform(-max_translation, max_translation, 3) # make small change to location
quaternion_shift = Quaternion.from_rotation(np.random.normal(0,1,3) * max_angle_shift)
body.orientation_new = quaternion_shift * body.orientation
sample_r_vectors[blob_index : blob_index + bodies[i].Nblobs] = body.get_r_vectors(body.location_new, body.orientation_new)
blob_index += body.Nblobs
# calculate potential of proposed new state
sample_state_energy = many_body_potential_pycuda.compute_total_energy(bodies,
sample_r_vectors,
periodic_length = periodic_length,
debye_length_wall = read.debye_length_wall,
repulsion_strength_wall = read.repulsion_strength_wall,
debye_length = read.debye_length,
repulsion_strength = read.repulsion_strength,
weight = weight,
blob_radius = blob_radius)
# accept or reject the sample state and collect data accordingly
if np.random.uniform(0.0, 1.0) < np.exp(-(sample_state_energy - current_state_energy) / kT):
# for each step in the Markov chain, disturb each body's location and orientation and obtain the new list of r_vectors
# of each blob. Calculate the potential of the new state, and accept or reject it according to the Markov chain rules:
# 1. if Ej < Ei, always accept the state 2. if Ej < Ei, accept the state according to the probability determined by
# exp(-(Ej-Ei)/kT). Then record data.
# Important: record data also when staying in the same state (i.e. when a sample state is rejected)
for step in range(read.initial_step, read.n_steps):
blob_index = 0
for i, body in enumerate(bodies): # distrub bodies
body.location_new = body.location + np.random.uniform(
-max_translation, max_translation,
3) # make small change to location
quaternion_shift = Quaternion.from_rotation(
np.random.normal(0, 1, 3) * max_angle_shift)
body.orientation_new = quaternion_shift * body.orientation
sample_r_vectors[blob_index:blob_index +
bodies[i].Nblobs] = body.get_r_vectors(
body.location_new, body.orientation_new)
blob_index += body.Nblobs
# calculate potential of proposed new state
sample_state_energy = many_body_potential_pycuda.compute_total_energy(
bodies,
sample_r_vectors,
periodic_length=periodic_length,
debye_length_wall=read.debye_length_wall,
repulsion_strength_wall=read.repulsion_strength_wall,
debye_length=read.debye_length,
repulsion_strength=read.repulsion_strength,
weight=weight,
blob_radius=blob_radius)
# accept or reject the sample state and collect data accordingly
def slip_extensile_rod(body):
'''
Creates slip for a extensile rod. The slip is along the
axis pointing to the closest end. We assume the blobs
are equispaced.
In this version the slip is constant.
'''
# Slip speed
speed = -20.0
# Identify blobs at the extremities depending on the resolution
if body.Nblobs == 14:
Nblobs_covering_ends = 0
Nlobs_perimeter = 0
elif body.Nblobs == 86:
Nblobs_covering_ends = 1
Nlobs_perimeter = 6
elif body.Nblobs == 324:
Nblobs_covering_ends = 6
Nlobs_perimeter = 12
slip = np.empty((body.Nblobs, 3))
# Get rod orientation
r_vectors = body.get_r_vectors()
# Compute end-to-end vector
if body.Nblobs > 14:
axis = r_vectors[body.Nblobs - 2 * Nblobs_covering_ends -
2] - r_vectors[Nlobs_perimeter - 2]
else:
axis = r_vectors[body.Nblobs - 1] - r_vectors[0]
length_rod = np.linalg.norm(axis) + 2.0 * body.blob_radius
# axis = orientation vector
axis = axis / np.sqrt(np.dot(axis, axis))
# Choose the portion of the surface covered with a tangential slip
length_covered = 0.8
lower_bound = length_rod / 2.0 - length_covered
upper_bound = length_rod / 2.0
# Create slip
slip_blob = []
for i in range(body.Nblobs):
# Blobs at the extremities are passive
if (Nblobs_covering_ends >
0) and (i >= body.Nblobs - 2 * Nblobs_covering_ends):
slip_blob = [0., 0., 0.]
else:
dist_COM_along_axis = np.dot(r_vectors[i] - body.location, axis)
if (dist_COM_along_axis > lower_bound) and (dist_COM_along_axis <=
upper_bound):
slip_blob = -speed * axis
elif (dist_COM_along_axis < -lower_bound) and (dist_COM_along_axis
>= -upper_bound):
slip_blob = speed * axis
else:
slip_blob = [0., 0., 0.]
slip[i] = slip_blob
return slip
