def test_max_langevin_fixed_point(self):
"""
Estimating the intrinsic velocity of a dissipative soliton
"""
default_params = {"m": 3, "r": 30}
# active Brownian motion
ds = velocity(tau=3.8, delta_t=0.05, R=3e-4, seed=0)
v = ds.simulate(1000000, v0=np.zeros(1))
v0 = max_langevin_fixed_point(v[:, 0], **default_params)
self.assertTrue(abs(ds.deterministic - v0) < 0.0001)
# Brownian motion
ds = velocity(tau=2.0 / 0.3 - 3.8, delta_t=0.05, R=3e-4, seed=0)
v = ds.simulate(1000000, v0=np.zeros(1))
v0 = max_langevin_fixed_point(v[:, 0], **default_params)
self.assertTrue(v0 < 0.001)
def test_estimate_friedrich_coefficients(self):
"""
Estimate friedrich coefficients
"""
default_params = {"m": 3, "r": 30}
# active Brownian motion
ds = velocity(tau=3.8, delta_t=0.05, R=3e-4, seed=0)
v = ds.simulate(1000000, v0=np.zeros(1))
coeff = _estimate_friedrich_coefficients(v[:, 0], **default_params)
self.assertTrue(abs(coeff[-1]) < 0.0001)
# Brownian motion
ds = velocity(tau=2.0 / 0.3 - 3.8, delta_t=0.05, R=3e-4, seed=0)
v = ds.simulate(1000000, v0=np.zeros(1))
coeff = _estimate_friedrich_coefficients(v[:, 0], **default_params)
self.assertTrue(abs(coeff[-1]) < 0.0001)
def test_dimensionality(self):
ds = velocity(tau=1.0/0.3)
Nt = 10
v = ds.simulate(Nt)
self.assertEqual(v.shape, (Nt, 2),
'The default configuration should return velocities from a two-dimensional dissipative soliton.')
v = ds.simulate(Nt, v0=np.zeros(3))
self.assertEqual(v.shape, (Nt, 3),
'The returned vector should reflect the dimension of the initial condition.')
def test_equlibrium_velocity(self):
"""
Test accuracy of integrating the deterministic dynamics for equilibrium velocity [6, p. 116]
"""
ds = velocity(tau=1.01/0.3, R=0)
v0 = ds.deterministic
Nt = 100 # Number of time steps
v = ds.simulate(Nt, v0=np.array([v0, 0.]))
return np.testing.assert_array_almost_equal(v[:,0]-v0, np.zeros(Nt),
decimal=8)
def test_equlibrium_velocity(self):
"""
Test accuracy of integrating the deterministic dynamics for equilibrium velocity [6, p. 116]
"""
ds = velocity(tau=1.01 / 0.3, R=0)
v0 = ds.deterministic
Nt = 100 # Number of time steps
v = ds.simulate(Nt, v0=np.array([v0, 0.]))
return np.testing.assert_array_almost_equal(v[:, 0] - v0,
np.zeros(Nt),
decimal=8)
def test_dimensionality(self):
ds = velocity(tau=1.0 / 0.3)
Nt = 10
v = ds.simulate(Nt)
self.assertEqual(
v.shape, (Nt, 2),
'The default configuration should return velocities from a two-dimensional dissipative soliton.'
)
v = ds.simulate(Nt, v0=np.zeros(3))
self.assertEqual(
v.shape, (Nt, 3),
'The returned vector should reflect the dimension of the initial condition.'
)
def test_relaxation_dynamics(self):
"""
Test accuracy of integrating the deterministic dynamics [6, p. 116]
"""
ds = velocity(tau=1.01/0.3, R=0)
v0 = 1.01 * ds.deterministic
Nt = 100 # Number of time steps
v = ds.simulate(Nt, v0=np.array([v0, 0.]))
k3t = ds.kappa_3 * ds.tau
k3st = ds.kappa_3**2 * ds.tau
a0 = v0 / ds.kappa_3
acceleration = lambda t: ds.kappa_3 * (a0 * np.sqrt(k3t - 1) * np.exp(k3st * t) /
np.sqrt(np.exp(2.0 * k3st * t) * ds.Q * a0**2 +
np.exp(2.0 * ds.kappa_3 * t) * (k3t - 1 - ds.Q * a0**2)))
t = ds.delta_t * np.arange(Nt)
return np.testing.assert_array_almost_equal(v[:,0], np.vectorize(acceleration)(t),
decimal=8)
def test_relaxation_dynamics(self):
"""
Test accuracy of integrating the deterministic dynamics [6, p. 116]
"""
ds = velocity(tau=1.01 / 0.3, R=0)
v0 = 1.01 * ds.deterministic
Nt = 100 # Number of time steps
v = ds.simulate(Nt, v0=np.array([v0, 0.]))
k3t = ds.kappa_3 * ds.tau
k3st = ds.kappa_3**2 * ds.tau
a0 = v0 / ds.kappa_3
acceleration = lambda t: ds.kappa_3 * (a0 * np.sqrt(k3t - 1) * np.exp(
k3st * t) / np.sqrt(
np.exp(2.0 * k3st * t) * ds.Q * a0**2 + np.exp(
2.0 * ds.kappa_3 * t) * (k3t - 1 - ds.Q * a0**2)))
t = ds.delta_t * np.arange(Nt)
return np.testing.assert_array_almost_equal(
v[:, 0], np.vectorize(acceleration)(t), decimal=8)
def test_intrinsic_velocity_at_default_bifurcation_point(self):
"""
The intrinsic velocity of a dissipative soliton at the Drift bifurcation point is zero.
"""
ds = velocity(tau=1.0 / 0.3)
self.assertEqual(ds.deterministic, 0.0)
def test_intrinsic_velocity_at_default_bifurcation_point(self):
"""
The intrinsic velocity of a dissipative soliton at the Drift bifurcation point is zero.
"""
ds = velocity(tau=1.0/0.3)
self.assertEqual(ds.deterministic, 0.0)
