def f_left(f, t, q1, q2, p1, p2, p3, params):
k = params.boltzmann_constant
E_upper = params.E_band
T = params.initial_temperature
mu = params.initial_mu
t = params.current_time
omega = 2. * np.pi * params.AC_freq
if (params.source_type == 'AC'):
vel_drift_x_in = params.vel_drift_x_in * np.sin(omega * t)
elif (params.source_type == 'DC'):
vel_drift_x_in = params.vel_drift_x_in
else:
raise NotImplementedError('Unsupported source_type')
if (params.p_space_grid == 'cartesian'):
p_x = p1
p_y = p2
elif (params.p_space_grid == 'polar2D'):
p_x = p1 * af.cos(p2)
p_y = p1 * af.sin(p2)
else:
raise NotImplementedError('Unsupported coordinate system in p_space')
fermi_dirac_in = (1. / (af.exp(
(E_upper - vel_drift_x_in * p_x - mu) / (k * T)) + 1.))
x, y = coords.get_cartesian_coords(q1, q2)
y_contact_start = params.contact_start
y_contact_end = params.contact_end
cond = ((y >= y_contact_start) & \
(y <= y_contact_end) \
)
f_left = cond * fermi_dirac_in + (1 - cond) * f
af.eval(f_left)
return (f_left)
N_q2_2 = domain_2.N_q2
q1_2 = domain_2.q1_start + (0.5 + np.arange(N_q1_2)) * (domain_2.q1_end - \
domain_2.q1_start)/N_q1_2
q2_2 = domain_2.q2_start + (0.5 + np.arange(N_q2_2)) * (domain_2.q2_end - \
domain_2.q2_start)/N_q2_2
dq1_2 = (domain_2.q1_end - domain_1.q1_start) / N_q1_1
dq2_2 = (domain_2.q2_end - domain_1.q2_start) / N_q2_1
q2_meshgrid_2, q1_meshgrid_2 = np.meshgrid(q2_2, q1_2)
q1_meshgrid_2 = af.from_ndarray(q1_meshgrid_2)
q2_meshgrid_2 = af.from_ndarray(q2_meshgrid_2)
x, y = coords_2.get_cartesian_coords(q1_meshgrid_2, q2_meshgrid_2)
x_2 = x.to_ndarray()
y_2 = y.to_ndarray()
# Stich domains
#N_q1 = N_q1_1
#N_q2 = N_q2_1 + N_q2_2
#q1_start = 0.
#q1_end = domain_1.q1_end
#q2_start = 0.
#q2_end = domain_1.q2_end + domain_2.q2_end
#dq1 = (q1_end - q1_start)/N_q1
#dq2 = (q2_end - q2_start)/N_q2
def initialize_f(q1, q2, p1, p2, p3, params):
PETSc.Sys.Print("Initializing f")
k = params.boltzmann_constant
params.mu = 0. * q1 + params.initial_mu
params.T = 0. * q1 + params.initial_temperature
params.vel_drift_x = 0. * q1
params.vel_drift_y = 0. * q1
params.phi = 0. * q1
params.mu_ee = params.mu.copy()
params.T_ee = params.T.copy()
params.vel_drift_x = 0. * q1 + 0e-3
params.vel_drift_y = 0. * q1 + 0e-3
params.j_x = 0. * q1
params.j_y = 0. * q1
params.E_band = params.band_energy(p1, p2)
params.vel_band = params.band_velocity(p1, p2)
E_upper = params.E_band + params.charge[0] * params.phi
if (params.p_space_grid == 'cartesian'):
p_x = p1
p_y = p2
elif (params.p_space_grid == 'polar2D'):
p_x = p1 * af.cos(p2)
p_y = p1 * af.sin(p2)
else:
raise NotImplementedError('Unsupported coordinate system in p_space')
# Initialize to zero
f = 0 * q1 * p1
# Parameters to define a gaussian in space (representing a 2D ball)
A = domain.N_p2 # Amplitude (required for normalization)
sigma_x = 0.05 # Standard deviation in x
sigma_y = 0.05 # Standard deviation in y
x_0 = 0. # Center in x
y_0 = 0. # Center in y
# TODO: This will work with polar2D p-space only for the moment
# Particles lying on the ball need to have the same velocity (direction)
#theta_0_index = (5*N_p2/8) - 1 # Direction of initial velocity
theta_0_index = int(5 * domain.N_p2 / 8) # Direction of initial velocity
print("Initial angle : ")
af.display(p2[theta_0_index])
# Load shift indices for all 4 boundaries into params. Required to perform
# mirroring operations along boundaries at arbitrary angles.
params.shift_indices_left, params.shift_indices_right, \
params.shift_indices_bottom, params.shift_indices_top = \
compute_shift_indices(q1, q2, p1, p2, p3, params)
x, y = coords.get_cartesian_coords(q1, q2)
# f[theta_0_index, :, :] = A + A*af.exp(-( (x-x_0)**2/(2*sigma_x**2) + \
# (y-y_0)**2/(2*sigma_y**2)
# )
# )
f = (1. / (af.exp(
(E_upper - params.vel_drift_x * p_x - params.vel_drift_y * p_y -
params.mu) / (k * params.T)) + 1.))
af.eval(f)
return (f)