def recompute_alpha(sph_start, sph_end, t_start, t_end, mag_params):
"""
From a change in energy we can calculate what the effective damping
was. For more details see [Albuquerque2001,
http://dx.doi.org/10.1063/1.1355322].
alpha' = - (1/(M**2)) *( dE/dt / spaceintegral( (dm/dt**2 )))
No space integral is needed because we are working with 0D LLG.
"""
Ms = mag_params.Ms
dt = t_end - t_start
# Estimate dEnergy / dTime
dE = llg_state_energy(sph_end, mag_params) \
- llg_state_energy(sph_start, mag_params)
dEdt = dE / dt
# Estimate dMagentisation / dTime then take sum of squares
dm = [
m2 - m1
for m1, m2 in zip(utils.sph2cart(sph_start), utils.sph2cart(sph_end))
]
dmdt_sq_sum = sum([(dm_i / dt)**2 for dm_i in dm])
# dE should be negative so the result should be positive.
return -(1 / (Ms**2)) * (dEdt / dmdt_sq_sum)
def recompute_alpha(sph_start, sph_end, t_start, t_end, mag_params):
"""
From a change in energy we can calculate what the effective damping
was. For more details see [Albuquerque2001,
http://dx.doi.org/10.1063/1.1355322].
alpha' = - (1/(M**2)) *( dE/dt / spaceintegral( (dm/dt**2 )))
No space integral is needed because we are working with 0D LLG.
"""
Ms = mag_params.Ms
dt = t_end - t_start
# Estimate dEnergy / dTime
dE = llg_state_energy(sph_end, mag_params) \
- llg_state_energy(sph_start, mag_params)
dEdt = dE / dt
# Estimate dMagentisation / dTime then take sum of squares
dm = [m2 - m1 for m1, m2 in
zip(utils.sph2cart(sph_start), utils.sph2cart(sph_end))]
dmdt_sq_sum = sum([(dm_i / dt)**2 for dm_i in dm])
# dE should be negative so the result should be positive.
return - (1/(Ms**2)) * (dEdt / dmdt_sq_sum)
def test_dfdm():
ms = [utils.sph2cart([1.0, 0.0, pi/18]),
utils.sph2cart([1.0, 0.0, 0.0001*pi]),
utils.sph2cart([1.0, 0.0, 0.999*pi]),
utils.sph2cart([1.0, 0.3*2*pi, 0.5*pi]),
utils.sph2cart([1.0, 2*pi, pi/18]),
]
for m in ms:
yield check_dfdm, m
def test_dfdm():
ms = [
utils.sph2cart([1.0, 0.0, pi / 18]),
utils.sph2cart([1.0, 0.0, 0.0001 * pi]),
utils.sph2cart([1.0, 0.0, 0.999 * pi]),
utils.sph2cart([1.0, 0.3 * 2 * pi, 0.5 * pi]),
utils.sph2cart([1.0, 2 * pi, pi / 18]),
]
for m in ms:
yield check_dfdm, m
def zeeman_energy(sph, mag_params):
""" Ez = - mu0 * (M.Happ)
"""
Ms = mag_params.Ms
Happ = mag_params.Hvec
mu0 = mag_params.mu0
m = utils.sph2cart(sph)
return -1 * mu0 * Ms * sp.dot(m, Happ)
def zeeman_energy(sph, mag_params):
""" Ez = - mu0 * (M.Happ)
"""
Ms = mag_params.Ms
Happ = mag_params.Hvec
mu0 = mag_params.mu0
m = utils.sph2cart(sph)
return -1 * mu0 * Ms * sp.dot(m, Happ)
def test_llg_residuals():
m0_sph = [0.0, pi/18]
m0_cart = utils.sph2cart(tuple([1.0] + m0_sph))
# m0_constrained = list(m0_cart) + [None] # ??ds
residuals = [(llg_cartesian_residual, m0_cart),
#(llg_spherical_residual, m0_sph),
# (llg_constrained_cartesian_residual, m0_constrained),
]
for r, i in residuals:
yield check_residual, r, i
def test_llg_residuals():
m0_sph = [0.0, pi / 18]
m0_cart = utils.sph2cart(tuple([1.0] + m0_sph))
# m0_constrained = list(m0_cart) + [None] # ??ds
residuals = [
(llg_cartesian_residual, m0_cart),
#(llg_spherical_residual, m0_sph),
# (llg_constrained_cartesian_residual, m0_constrained),
]
for r, i in residuals:
yield check_residual, r, i
def magnetocrystalline_anisotropy_energy(sph, mag_params):
""" Eca = K1 (m.e)^2"""
K1 = mag_params.K1
m_cart = utils.sph2cart(sph)
return K1 * (1 - sp.dot(m_cart, mag_params.easy_axis)**2)
def magnetocrystalline_anisotropy_energy(sph, mag_params):
""" Eca = K1 (m.e)^2"""
K1 = mag_params.K1
m_cart = utils.sph2cart(sph)
return K1 * (1 - sp.dot(m_cart, mag_params.easy_axis)**2)