def mag_oscillation(KE=.001):
# print(KE)
# p_phi1 = (KE/10.)**.5 #give half the KE to p_phi1
# p_phi2 = -p_phi1
# p_tht = 0.
# T_long = 2*numpy.pi/((5./3.)**.5)
p_phi1 = (KE / 18.)**.5
p_phi2 = p_phi1
p_tht = -2 * p_phi1
T_long = 2 * numpy.pi / ((7.)**.5)
calced_KE = p_phi1**2 * 5 + p_phi2**2 * 5 + 2 * p_tht**2
print(calced_KE, KE)
print(p_tht**2 / 2)
print(T_long)
init_state = numpy.array([0, 0, 0, 0, p_phi1, p_phi2, p_tht])
sim_path = utils.RK4_adapt(double_dipole_eqs,
init_state,
T_long * 2,
max_steps=10**6,
precision=10**-6)
t_vals = utils.read_column(sim_path, 0)
phi1_vals = numpy.array(utils.read_column(sim_path, 1))
phi2_vals = numpy.array(utils.read_column(sim_path, 2))
tht_vals = numpy.array(utils.read_column(sim_path, 3))
print(phi1_vals[-1] - tht_vals[-1])
pyplot.plot(t_vals, phi1_vals)
pyplot.plot(t_vals, phi2_vals)
pyplot.plot(t_vals, tht_vals)
pyplot.show()
def plot_path_from_point(state0):
start = numpy.array(state0)
figure, subplots = pyplot.subplots(1, 2)
# print(start[-2:])
path = utils.RK4_adapt(reduced_double_dipole,
start,
6.,
max_steps=10**6,
precision=10**-7)
t_vals = utils.read_column(path, 0)
phid_vals = numpy.array(utils.read_column(path, 1))
phit_vals = numpy.array(utils.read_column(path, 2))
tht_vals = numpy.array(utils.read_column(path, 3))
pphid_vals = numpy.array(utils.read_column(path, 4))
pphit_vals = numpy.array(utils.read_column(path, 5))
ptht_vals = numpy.array(utils.read_column(path, 6))
force_r = numpy.array(map(rf_red, path))
ratio = numpy.array(map(lambda arr: arr[2] / arr[3], path))
# subplots[0].plot(t_vals ,phid_vals)
# subplots[0].plot(t_vals ,phit_vals)
# subplots[0].plot(t_vals ,tht_vals)
subplots[0].plot(t_vals, force_r)
# subplots[0].plot(t_vals ,ratio) #between phit and tht
subplots[1].plot(t_vals, pphid_vals)
subplots[1].plot(t_vals, pphit_vals)
subplots[1].plot(t_vals, ptht_vals)
pyplot.show()
def random_point_examine():
#phd, pht, tht, pd, pt, ptht
state0p, state0m = utils.reduced_state_gen()
figure, subplots = pyplot.subplots(2, 2)
states = [state0p, state0m]
print(state0p)
for state0_ind in range(2):
start = numpy.array(states[state0_ind])
print(start[-2:])
# print(start[-2:])
path = utils.RK4_adapt(reduced_double_dipole,
start,
20.,
max_steps=10**6,
precision=10**-7)
t_vals = utils.read_column(path, 0)
phid_vals = numpy.array(utils.read_column(path, 1))
phit_vals = numpy.array(utils.read_column(path, 2))
tht_vals = numpy.array(utils.read_column(path, 3))
pphid_vals = numpy.array(utils.read_column(path, 4))
pphit_vals = numpy.array(utils.read_column(path, 5))
ptht_vals = numpy.array(utils.read_column(path, 6))
force_r = numpy.array(map(rf_red, path))
subplots[state0_ind, 0].plot(t_vals, phid_vals)
subplots[state0_ind, 0].plot(t_vals, phit_vals)
subplots[state0_ind, 0].plot(t_vals, tht_vals)
subplots[state0_ind, 0].plot(t_vals, force_r)
subplots[state0_ind, 1].plot(t_vals, pphid_vals)
subplots[state0_ind, 1].plot(t_vals, pphit_vals)
subplots[state0_ind, 1].plot(t_vals, ptht_vals)
pyplot.show()
def setUp(self):
x0 = random.random()
p0 = (1 - x0**2)**.5
self.stateI = numpy.array([0., x0, p0])
self.path_out = utils.RK4_adapt(base_SHO,
self.stateI,
2 * numpy.pi * (1. + 10**-7),
max_steps=2000,
precision=10**-8)
def test_period_check(self):
stateI = numpy.array([0., 0., 1.])
print('pre starting')
path_out = utils.RK4_adapt(base_SHO,
stateI,
2 * numpy.pi,
max_steps=500,
precision=10**-6)
print(path_out[-1][0] - 2 * numpy.pi, path_out[-1][1])
self.assertTrue((path_out[-1][0] - 2 * numpy.pi) < 10**-5)
self.assertTrue(abs(path_out[-1][1]) < 10**-5)
def spinning_period_sim():
samples = 200
fine_res = 150
fineT = 2.5 / 12.
maxT = 18. / 12.
data_out = open('./%d.txt' % time.time(), 'w')
start = time.time()
energies = []
for frac in range(1, samples):
if frac <= fine_res:
T_0 = (fineT / fine_res) * frac
else:
T_0 = fineT + (frac - fine_res) * (maxT - fineT) / (samples -
fine_res)
energies.append(T_0)
# T_0 = .5
print(T_0)
Pd = (T_0 / 10.)**.5
init = numpy.array([0.0, 0.0, 0.0, 0.0, Pd, 0., 0.0])
sim_path = utils.RK4_adapt(reduced_double_dipole,
init,
.05,
max_steps=10**6,
precision=10**-10)
S_0 = sim_path[-1]
S_0[0] = 0.0
# S_0 = init
# print(S_0)
return_times = utils.return_times_finder(reduced_double_dipole,
S_0,
max_steps=10**6,
precision=10**-10,
max_time=75)
# print(return_times)
# print([val[0]/return_times[0][0] for val in return_times])
period = utils.fit_slope_and_chisqr(return_times)
print(period)
S_0 = list(S_0)
S_0.append(period[0])
S_0.append(period[1])
data_out.write(('%f ' * 8) % tuple(S_0[1:]))
data_out.write('\n')
print(' ')
data_out.close()
# periods = utils.read_column(S_0, -2)
# matplotlib.plot(energies, periods)
# pyplot.show()
print('took %d seconds' %
(time.time() - start)) # print(len(sim_path), T_0)
def simulate_energy(energy):
# p_phi1 = (energy/10.)**.5 #give half the KE to p_phi1
# p_phi2 = -p_phi1
# p_tht = 0.
# T_long = 2*numpy.pi/((5./3.)**.5)
p_phi1 = (energy / 12.)**.5
p_phi2 = p_phi1
p_tht = -2 * p_phi1
T_long = 2 * numpy.pi / ((6.)**.5)
init_state = numpy.array([0, 0, 0, 0, p_phi1, p_phi2, p_tht])
return utils.RK4_adapt(double_dipole_eqs,
init_state,
T_long * 2,
max_steps=10**6,
precision=10**-6)
def orbital_period_sim():
samples = 100
# coarse_res = 50
# coarseT = 0./12.
maxT = 1. / 3.
data_out = open('./%d.txt' % time.time(), 'w')
start = time.time()
for frac in range(1, samples):
# if frac <=coarse_res:
# T_0 = (coarseT/coarse_res)*frac
# else:
# T_0 = coarseT + (frac-coarse_res)*(maxT-coarseT)/(samples-coarse_res)
T_0 = (maxT / samples) * frac
# T_0 = .5
print(T_0)
P_tht = (2. * T_0 / 7.)**.5
init = numpy.array([0.0, 0.0, 0.0, 0.0, 0.0, -P_tht / 2., P_tht])
sim_path = utils.RK4_adapt(reduced_double_dipole,
init,
.01,
max_steps=10**6,
precision=10**-10)
S_0 = sim_path[-1]
S_0[0] = 0.0
# S_0 = init
# print(S_0)
return_times = utils.return_times_finder(reduced_double_dipole,
S_0,
max_steps=10**6,
precision=10**-9,
max_time=75)
# print(return_times)
# print([val[0]/return_times[0][0] for val in return_times])
period = utils.fit_slope_and_chisqr(return_times)
print(period)
S_0 = list(S_0)
S_0.append(period[0])
S_0.append(period[1])
data_out.write(('%f ' * 8) % tuple(S_0[1:]))
data_out.write('\n')
print(' ')
data_out.close()
print('took %d seconds' %
(time.time() - start)) # print(len(sim_path), T_0)
def spinning_period_sim():
samples = 150
maxT = 2. / 12.
data_out = open('./%d.txt' % time.time(), 'w')
start = time.time()
for frac in range(1, samples):
T_0 = (maxT / samples) * frac
# T_0 = .5
print(T_0)
Pd = (T_0 / 10.)**.5
init = numpy.array([0.0, 0.0, 0.0, 0.0, Pd, 0., 0.0])
sim_path = utils.RK4_adapt(reduced_double_dipole,
init,
.05,
max_steps=10**6,
precision=10**-10)
S_0 = sim_path[-1]
S_0[0] = 0.0
# S_0 = init
# print(S_0)
return_times = utils.return_times_finder(reduced_double_dipole,
S_0,
max_steps=10**6,
precision=10**-10,
max_time=75)
# print(return_times)
# print([val[0]/return_times[0][0] for val in return_times])
period = utils.fit_slope_and_chisqr(return_times)
print(period)
S_0 = list(S_0)
S_0.append(period[0])
S_0.append(period[1])
data_out.write(('%f ' * 8) % tuple(S_0[1:]))
data_out.write('\n')
print(' ')
data_out.close()
print('took %d seconds' %
(time.time() - start)) # print(len(sim_path), T_0)
def simulate_initial(init_state, T_long=(24 * numpy.pi / ((7.)**.5))):
return utils.RK4_adapt(reduced_double_dipole,
init_state,
T_long,
max_steps=10**6,
precision=10**-6)