def test_compute_modes():
obj = _fake_mesh_conductor("unit_disc")
DC_n = thermal_noise.compute_current_modes(
obj, T=300, resistivity=1e-8, thickness=1e-3, mode="DC"
)
AC_n = thermal_noise.compute_current_modes(
obj, freqs=np.array((0,)), T=300, resistivity=1e-8, thickness=1e-3, mode="AC"
)
points = np.array([[0.1, 0, 0.2], [-0.1, 0.1, -0.2]])
obj.set_basis("vertex")
DC_Bn_covar = thermal_noise.noise_covar(obj.B_coupling(points), DC_n)
AC_Bn_covar = thermal_noise.noise_covar(obj.B_coupling(points), AC_n)
assert_allclose(DC_Bn_covar, AC_Bn_covar[:, :, :, 0])
DC_Bn_covar_dir = thermal_noise.noise_covar_dir(obj.B_coupling(points), DC_n)
AC_Bn_covar_dir = thermal_noise.noise_covar_dir(obj.B_coupling(points), AC_n)
assert_allclose(DC_Bn_covar_dir, AC_Bn_covar_dir[:, :, :, 0])
DC_Bn_var = thermal_noise.noise_var(obj.B_coupling(points), DC_n)
AC_Bn_var = thermal_noise.noise_var(obj.B_coupling(points), AC_n)
assert_allclose(DC_Bn_var, AC_Bn_var[:, :, 0])
thermal_noise.visualize_current_modes(obj.mesh, DC_n, scale=0.5, Nmodes=3)
def test_vs_analytic():
obj = _fake_mesh_conductor("unit_disc")
mesh = obj.mesh
mesh.vertices, mesh.faces = trimesh.remesh.subdivide(mesh.vertices, mesh.faces)
# Fix the simulation parameters
d = 100e-6 # thickness
sigma = 3.7e7 # conductivity
res = 1 / sigma # resistivity
T = 300 # temperature
kB = 1.38064852e-23 # Boltz
mu0 = 4 * np.pi * 1e-7 # permeability of freespace
# Compute the AC-current modes and visualize them
vl, u = thermal_noise.compute_current_modes(
obj=mesh, T=T, resistivity=res, thickness=d, mode="AC", return_eigenvals=True
)
# Define field points on z axis
Np = 10
z = np.linspace(0.2, 1, Np)
fp = np.array((np.zeros(z.shape), np.zeros(z.shape), z)).T
B_coupling = magnetic_field_coupling(
mesh, fp, analytic=True
) # field coupling matrix
# Compute noise variance
B = np.sqrt(thermal_noise.noise_var(B_coupling, vl))
# Next, we compute the DC noise without reference to the inductance
vl_dc, u_dc = thermal_noise.compute_current_modes(
obj=mesh, T=T, resistivity=res, thickness=d, mode="DC", return_eigenvals=True
)
# Compute noise variance
B_dc = np.sqrt(thermal_noise.noise_var(B_coupling, vl_dc))
# Calculate Bz noise using analytical formula and plot the results
r = 1
Ban = (
mu0
* np.sqrt(sigma * d * kB * T / (8 * np.pi * z ** 2))
* (1 / (1 + z ** 2 / r ** 2))
)
assert_allclose(B_dc[:, 2], B[:, 2, 0])
assert_allclose(Ban, B[:, 2, 0], rtol=5e-2)
vl = compute_current_modes(
obj=mesh,
T=T,
resistivity=1 / sigma,
thickness=d,
mode="AC",
return_eigenvals=False,
)
# scene = mlab.figure(None, bgcolor=(1, 1, 1), fgcolor=(0.5, 0.5, 0.5),
# size=(800, 800))
# visualize_current_modes(mesh,vl[:,:,0], 8, 1)
vl[:, 0] = np.zeros(vl[:, 0].shape) # fix DC-component
Btemp = noise_var(B_coupling, vl)
B[i] = Btemp[:, :, 0]
scene = mlab.figure(None, bgcolor=(1, 1, 1), fgcolor=(0.5, 0.5, 0.5), size=(800, 800))
s = mlab.triangular_mesh(*mesh.vertices.T, mesh.faces)
scene.scene.z_minus_view()
surface = scene.children[0].children[0].children[0].children[0]
surface.actor.property.representation = "wireframe"
surface.actor.mapper.scalar_visibility = False
scene.scene.camera.position = [0.0, 0.0, -5.530686305704514]
scene.scene.camera.focal_point = [0.0, 0.0, 0.0]
scene.scene.camera.view_angle = 30.0
scene.scene.camera.view_up = [0.0, 1.0, 0.0]
scene.scene.camera.clipping_range = [3.485379442647469, 8.118646600290083]
scene.scene.camera.compute_view_plane_normal()
None, bgcolor=(1, 1, 1), fgcolor=(0.5, 0.5, 0.5), size=(800, 800)
)
s = mlab.triangular_mesh(*mesh.vertices.T, mesh.faces)
scene.scene.z_minus_view()
surface = scene.children[0].children[0].children[0].children[0]
surface.actor.property.representation = "wireframe"
surface.actor.mapper.scalar_visibility = False
scene.scene.camera.position = [0.0, 0.0, -4.515786458791532]
scene.scene.camera.focal_point = [0.0, 0.0, 0.0]
scene.scene.camera.view_angle = 30.0
scene.scene.camera.view_up = [0.0, 1.0, 0.0]
scene.scene.camera.clipping_range = [4.229838328573525, 4.886628590046963]
scene.scene.camera.compute_view_plane_normal()
scene.scene.render()
Bvar = noise_var(B_coupling, vl)
Bn[i] = np.sqrt(Bvar[:, 2, 0])
if i == 0:
u0 = u
if i == 1:
u1 = u
if i == 2:
u2 = u
print(i)
figw = 3.75
plt.figure(figsize=(figw, 5))
plt.loglog(1 / u0 * 1e3, linewidth=2, label="N = %i" % Nfaces[0])
s = mlab.triangular_mesh(*mesh.vertices.T, mesh.faces)
scene.scene.z_minus_view()
surface = scene.children[0].children[0].children[0].children[0]
surface.actor.property.representation = "wireframe"
surface.actor.mapper.scalar_visibility = False
scene.scene.isometric_view()
scene.scene.render()
Np = 30
x = np.linspace(-0.95, 0.95, Np)
fp = np.array((x, np.zeros(x.shape), np.zeros(x.shape))).T
B_coupling = magnetic_field_coupling(mesh, fp, analytic=True)
B = noise_var(B_coupling, vl)
a = 0.5
L = 2
rat = L / (2 * a)
Gfact = (
1
/ (8 * np.pi)
* (
(3 * rat ** 5 + 5 * rat ** 3 + 2) / (rat ** 2 * (1 + rat ** 2) ** 2)
+ 3 * np.arctan(rat)
)
)
Ban = np.sqrt(Gfact) * mu0 * np.sqrt(kB * T * sigma * d) / a
plt.figure(figsize=(5, 5))
Ngrid = 21 xx = np.linspace(np.min(mesh.vertices[:, 0]), np.max(mesh.vertices[:, 0]), Ngrid) yy = np.linspace(np.min(mesh.vertices[:, 1]), np.max(mesh.vertices[:, 1]), Ngrid) zz = np.max(mesh.vertices[:, 2]) + np.array([0.1, 0.2, 0.3, 0.4, 0.5]) X, Y, Z = np.meshgrid(xx, yy, zz, indexing="ij") x = X.ravel() y = Y.ravel() z = Z.ravel() fp = np.vstack((x, y, z)).T B_coupling = magnetic_field_coupling(mesh, fp, analytic=True) Bvar = noise_var(B_coupling, vl) * 1e30 #%% cmap = "inferno" vmin = 1e-2 vmax = 30 levels = np.linspace(vmin, vmax, 5) Bzcov = np.sqrt(Bvar[:, 0, 0]) Bgrid = Bzcov.reshape((Ngrid, Ngrid, 5))
T=T,
resistivity=1 / sigma,
thickness=d,
mode="AC",
freqs=freqs,
return_eigenvals=False,
)
#%%
Np = 25
z = np.linspace(0.05, 1, Np)
fp = np.array((np.zeros(z.shape), np.zeros(z.shape), z)).T
B_coupling = magnetic_field_coupling(mesh, fp, analytic=True)
Bf = np.sqrt(noise_var(B_coupling, vl))
plt.figure(figsize=(5, 5))
plt.loglog(freqs, Bf[:, 2, :].T * 1e15, linewidth=2)
plt.grid()
plt.ylim(0.1, 100)
plt.gca().spines["right"].set_visible(False)
plt.gca().spines["top"].set_visible(False)
plt.legend(frameon=False)
plt.xlabel("Frequency (Hz)")
plt.ylabel(r"$B_z$ noise (fT/rHz)")
plt.tight_layout()
f_interp = np.linspace(0, 120, 500)
cutf = np.zeros(Np)
scene = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
visualize_current_modes(mesh, vl[:, :, 0], 42, 5, contours=True)
# Define field points on z axis
Np = 30
z = np.linspace(0.1, 1, Np)
fp = np.array((np.zeros(z.shape), np.zeros(z.shape), z)).T
B_coupling = magnetic_field_coupling(mesh, fp,
analytic=True) # field coupling matrix
# Compute noise variance
B = np.sqrt(noise_var(B_coupling, vl))
# Calculate Bz noise using analytical formula and plot the results
r = 1
Ban = (mu0 * np.sqrt(sigma * d * kB * T / (8 * np.pi * z**2)) *
(1 / (1 + z**2 / r**2)))
plt.figure()
plt.subplot(2, 1, 1)
plt.semilogy(z, Ban, label="Analytic")
plt.semilogy(z, B[:, 2, 0], "x", label="Numerical")
plt.legend(frameon=False)
plt.xlabel("Distance d/R")
plt.ylabel("DC noise Bz (T/rHz)")
plt.subplot(2, 1, 2)