def density_diagram(disp_rel,
K,
W,
R1,
R1min,
R1max,
c2,
c0,
vA,
just_dots=False):
# Plot omega/k against rho_1/rho_0 for eigenmodes
Wmin = cT(c0, vA)
Wmax = vA
R1_range = np.linspace(R1min, R1max, 51)
W_range = np.linspace(Wmin, Wmax, 51)
# Global font change
font = {'size': 15}
matplotlib.rc('font', **font)
plt.figure(num=None, figsize=(10, 11), facecolor='w', edgecolor='k')
ax = plt.subplot()
if just_dots == True:
#Plot the dots
W_array = tool.point_find(disp_rel, R1_range, W_range, args=(None))
ax.plot(R1_range, W_array, '.', color='b')
ax.set_xlim(0, R1_range[-1])
ax.set_ylim(Wmin, Wmax)
def dispersion_diagram(mode_options,
chosen_mode,
disp_rel,
K,
W,
R1,
just_dots=False):
# Dispersion diagram for eigenmodes given by mode_options.
# Can only do R1=1.5, 1.8, 2.0.
# Create sublists of modes
kink_mode_options = []
saus_mode_options = []
slow_surf_mode_options = []
fast_surf_mode_options = []
fast_kink_mode_options = []
fast_saus_mode_options = []
slow_body_1_mode_options = []
slow_body_2_mode_options = []
slow_body_3_mode_options = []
slow_body_mode_options = []
fast_body_1_mode_options = []
fast_body_2_mode_options = []
fast_body_3_mode_options = []
for mode in mode_options:
if 'kink' in mode:
kink_mode_options.append(mode)
if 'saus' in mode:
saus_mode_options.append(mode)
if 'slow' in mode and 'surf' in mode:
slow_surf_mode_options.append(mode)
if 'fast' in mode and 'surf' in mode:
fast_surf_mode_options.append(mode)
if 'fast' in mode and 'kink' in mode:
fast_kink_mode_options.append(mode)
if 'fast' in mode and 'saus' in mode:
fast_saus_mode_options.append(mode)
if 'fast' in mode and 'body-1' in mode:
fast_body_1_mode_options.append(mode)
if 'fast' in mode and 'body-2' in mode:
fast_body_2_mode_options.append(mode)
if 'fast' in mode and 'body-3' in mode:
fast_body_3_mode_options.append(mode)
if 'slow' in mode and 'body-1' in mode:
slow_body_1_mode_options.append(mode)
if 'slow' in mode and 'body-2' in mode:
slow_body_2_mode_options.append(mode)
if 'slow' in mode and 'body-3' in mode:
slow_body_3_mode_options.append(mode)
if 'slow' in mode and 'body' in mode:
slow_body_mode_options.append(mode)
# Set plotting range
Kmin = 0.
Kmax = 23. #10.
Wmin = 0.
Wmax = sf.c2
K_range = np.linspace(Kmin, Kmax, 51)
W_range = np.linspace(Wmin, Wmax, 51)
# Global font change
font = {'size': 15}
matplotlib.rc('font', **font)
# Initialise plot
plt.figure(num=None, figsize=(10, 11), facecolor='w', edgecolor='k')
ax = plt.subplot()
# line colours - g=chosen, b=body, r=surface
def colour(mode):
colours = []
if mode in fast_surf_mode_options:
for i in range(len(mode_options)):
if i <= 7:
if mode_options[i] == mode:
colours.append('g')
elif mode_options[
i] in slow_surf_mode_options + fast_surf_mode_options:
colours.append('r')
else:
colours.append('b')
elif i >= 14:
if mode_options[i] == mode:
colours.append('g')
elif mode_options[
i] in slow_surf_mode_options + fast_surf_mode_options:
colours.append('r')
else:
colours.append('b')
else:
for i in range(len(mode_options)):
if mode_options[i] == mode:
colours.append('g')
elif mode_options[
i] in slow_surf_mode_options + fast_surf_mode_options:
colours.append('r')
else:
colours.append('b')
return colours
# line styles - '--'=kink, '-'=sausage
def ls(mode):
linestyles = []
if mode in fast_surf_mode_options:
for i in range(8):
if mode_options[i] in kink_mode_options:
linestyles.append('--')
else:
linestyles.append('-')
for i in range(8, len(mode_options)):
if mode_options[i - 1] in kink_mode_options:
linestyles.append('--')
else:
linestyles.append('-')
else:
for i in range(len(mode_options)):
if mode_options[i] in kink_mode_options:
linestyles.append('--')
else:
linestyles.append('-')
return linestyles
# Basic, but much fast plot to get an idea of the solutions.
if just_dots == True:
#Plot the dots
W_array = tool.point_find(disp_rel, K_range, W_range, args=(None))
ax.plot(K_range, W_array, '.', color='b')
else:
# Do the full plot
if R1 == 1.5:
if chosen_mode in fast_surf_mode_options:
K_guess = [1., 1., 10.12, 8.74, 5.98, 5.98, 3.68, 1.84, 6., 6.]
W_guess = [
0.64, 0.72, 0.863, 0.867, 0.855, 0.885, 0.885, 0.920,
1.01567, 1.05754
]
step = [
0.01, 0.01, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.01,
0.01
]
K_start = [
0.0001, 0.0001, 2., 1.6, 1.2, 0.9, 0.6, 0.2, 4.22, 0.67
]
K_end = [
Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, 4.2, Kmax, Kmax
]
K_fast_body_circles = [-10, 0.67]
W_fast_body_circles = [sf.c2] * len(K_fast_body_circles)
K_transition_circles = [4.2]
W_transition_circles = [sf.c0]
else:
K_guess = [
1., 1., 8.74, 8.74, 5.98, 5.98, 3.68, 1.84, 1.84, 6.44,
9.2, 15.18, 19.78, 22.01
]
W_guess = [
0.473, 0.547, 0.719463, 0.733764, 0.722183, 0.746659,
0.741942, 0.749326, 1.085, 1.131, 1.181, 1.154, 1.156,
1.181
]
step = [
0.01, 0.01, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01
]
K_start = [
0.0001, 0.0001, 2.3, 1.8, 1.3, 1., 0.8, 0.3, 0.47, 4.51,
8.55, 12.55, 16.5, 20.53
]
K_end = [
Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax,
Kmax, Kmax, Kmax, Kmax
]
K_fast_body_circles = [0.47, 4.51, 8.55, 12.55, 16.5, 20.53]
W_fast_body_circles = [sf.c2] * len(K_fast_body_circles)
K_transition_circles = []
W_transition_circles = []
elif R1 == 1.8:
if chosen_mode in fast_surf_mode_options:
K_guess = [1., 1., 10.12, 8.74, 5.98, 5.98, 3.68, 1.84, 6., 6.]
W_guess = [
0.64, 0.72, 0.863, 0.867, 0.855, 0.885, 0.885, 0.920,
1.01567, 1.05754
]
step = [
0.01, 0.01, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.01,
0.01
]
K_start = [
0.0001, 0.0001, 2., 1.6, 1.2, 0.9, 0.6, 0.2, 4.752, 0.365
]
K_end = [
Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, 4.752, Kmax, Kmax
]
K_fast_body_circles = [-10, 0.365]
W_fast_body_circles = [sf.c2] * len(K_fast_body_circles)
K_transition_circles = [4.752]
W_transition_circles = [sf.c0]
else:
K_guess = [
1., 1., 8.74, 8.74, 5.98, 5.98, 3.68, 1.84, 1.84, 6.44,
9.2, 15.18, 19.78, 22.01
]
W_guess = [
0.473, 0.547, 0.719463, 0.733764, 0.722183, 0.746659,
0.741942, 0.749326, 1.085, 1.131, 1.181, 1.154, 1.156,
1.181
]
step = [
0.01, 0.01, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01
]
K_start = [
0.0001, 0.0001, 2.3, 1.8, 1.3, 1., 0.8, 0.3, 0.336, 4.306,
8.346, 12.318, 16.309, 20.342
]
K_end = [
Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax,
Kmax, Kmax, Kmax, Kmax
]
K_fast_body_circles = [
0.336, 4.306, 8.346, 12.318, 16.309, 20.342
]
W_fast_body_circles = [sf.c2] * len(K_fast_body_circles)
K_transition_circles = []
W_transition_circles = []
elif R1 == 2.:
if chosen_mode in fast_surf_mode_options:
K_guess = [1., 1., 11.96, 6., 4., 4., 2., 2., 6., 6.]
W_guess = [
0.64, 0.72, 0.877, 0.836, 0.826, 0.847, 0.83, 0.915,
1.01567, 1.05754
]
step = [
0.01, 0.01, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.01,
0.01
]
K_start = [
0.0001, 0.0001, 2., 1.6, 1.2, 0.9, 0.6, 0.2, 5.24, 0.001
]
K_end = [
Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, 5.2, Kmax, Kmax
]
K_fast_body_circles = []
W_fast_body_circles = []
K_transition_circles = [5.2]
W_transition_circles = [sf.c0]
else:
K_guess = [
1., 1., 8.74, 8.74, 5.98, 5.98, 3.68, 1.84, 2., 6., 9.,
14.73, 19.8, 23.4
]
W_guess = [
0.473, 0.547, 0.719463, 0.733764, 0.722183, 0.746659,
0.741942, 0.749326, 1.16675, 1.156, 1.17, 1.1547, 1.16,
1.16
]
step = [
0.01, 0.01, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.01,
0.01, 0.01, 0.01, 0.01, 0.01
]
K_start = [
0.0001, 0.0001, 2.3, 1.8, 1.3, 1., 0.8, 0.3, 0.0001, 4.1,
8.2, 12.2, 16.2, 20.2
]
K_end = [
Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax, Kmax,
Kmax, Kmax, Kmax, Kmax
]
K_fast_body_circles = [-10, 4.1, 8.2, 12.2, 16.2, 20.2]
W_fast_body_circles = [sf.c2] * len(K_fast_body_circles)
K_transition_circles = []
W_transition_circles = []
else:
raise ValueError('R1 can only take the values 1.5, 1.8, 2.0')
# line width
lw = 1.5
disp_modes = range(len(K_guess))
for i in disp_modes:
K_values, root_array = tool.line_trace(disp_rel, K_guess[i],
W_guess[i], step[i],
K_start[i], K_end[i],
(None))
ax.plot(K_values,
root_array,
color=colour(chosen_mode)[i],
linewidth=lw,
linestyle=ls(chosen_mode)[i])
for i in range(len(K_fast_body_circles)):
ax.plot(K_fast_body_circles[i],
W_fast_body_circles[i],
marker='o',
markerfacecolor='None',
markeredgecolor=colour(chosen_mode)[i + 8],
markeredgewidth=lw,
markersize=8)
for i in range(len(K_transition_circles)):
ax.plot(K_transition_circles[i],
W_transition_circles[i],
marker='o',
markerfacecolor='None',
markeredgecolor=colour(chosen_mode)[i + 8],
markeredgewidth=lw,
markersize=8)
# Labels, annotations etc...
ax.set_ylabel(r'$v_{ph}/c_0$', fontsize=20)
ax.set_xlabel(r'$k x_0$', fontsize=20)
ax.set_xlim(K_range[0], K_range[-1])
ax.set_ylim(0., 1.41)
if chosen_mode in fast_surf_mode_options:
ax.fill_between((Kmin - 0.1, Kmax + 0.1), (sf.c2, sf.c2),
(1.42, 1.42),
edgecolor='gray',
linestyle='-.',
color='None',
hatch='/',
linewidth=2)
#ax.plot([K_range[0], K_range[-1]], [sf.vA, sf.vA], color = '0.5', linestyle='--', linewidth=2)
ax.annotate(r'$v_A$',
xy=(K_range[-1] + 0.03, sf.vA - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
ax.plot([K_range[0], K_range[-1]], [sf.vA, sf.vA],
color='0.5',
linestyle='-.',
linewidth=2)
ax.plot([K_range[0], K_range[-1]], [sf.cT, sf.cT],
color='0.5',
linestyle='-.',
linewidth=2)
ax.annotate(r'$c_T$',
xy=(K_range[-1] + 0.03, sf.cT - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
ax.plot([K_range[0], K_range[-1]], [sf.c0, sf.c0],
color='0.5',
linestyle='-.',
linewidth=2)
ax.annotate(r'$c_0$',
xy=(K_range[-1] + 0.03, sf.c0 - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
#ax.plot([K_range[0], K_range[-1]], [sf.c2, sf.c2], color = '0.5', linestyle='--', linewidth=2)
# ax.annotate(r'$c_2$', xy=(K_range[-1] + 0.03, sf.c2 - 0.01), xycoords='data', annotation_clip=False, fontsize=20)
ax.plot([K_range[0], K_range[-1]],
[sf.c1(R1), sf.c1(R1)],
color='0.5',
linestyle='-.',
linewidth=2)
if R1 == 2.:
ax.annotate(r'$c_1=c_2$',
xy=(K_range[-1] + 0.03, sf.c1(R1) - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
else:
ax.annotate(r'$c_1$',
xy=(K_range[-1] + 0.03, sf.c1(R1) - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
ax.annotate(r'$c_2$',
xy=(K_range[-1] + 0.03, sf.c2 - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
else:
K_range_for_fill = np.append(K_range, K_range[-1] + 0.1)
ax.fill_between((Kmin - 0.1, Kmax + 0.1), (sf.c0, sf.c0),
(sf.vA, sf.vA),
edgecolor='gray',
linestyle='-.',
color='None',
hatch='/',
linewidth=2)
ax.fill_between((Kmin - 0.1, Kmax + 0.1), (sf.c2, sf.c2),
(1.42, 1.42),
edgecolor='gray',
linestyle='-.',
color='None',
hatch='/',
linewidth=2)
#ax.plot([K_range[0], K_range[-1]], [sf.vA, sf.vA], color = '0.5', linestyle='--', linewidth=2)
ax.annotate(r'$v_A$',
xy=(K_range[-1] + 0.03, sf.vA - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
ax.plot([K_range[0], K_range[-1]], [sf.cT, sf.cT],
color='0.5',
linestyle='-.',
linewidth=2)
ax.annotate(r'$c_T$',
xy=(K_range[-1] + 0.03, sf.cT - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
#ax.plot([K_range[0], K_range[-1]], [sf.c0, sf.c0], color = '0.5', linestyle='--', linewidth=2)
ax.annotate(r'$c_0$',
xy=(K_range[-1] + 0.03, sf.c0 - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
#ax.plot([K_range[0], K_range[-1]], [sf.c2, sf.c2], color = '0.5', linestyle='--', linewidth=2)
# ax.annotate(r'$c_2$', xy=(K_range[-1] + 0.03, sf.c2 - 0.01), xycoords='data', annotation_clip=False, fontsize=20)
ax.plot([K_range[0], K_range[-1]],
[sf.c1(R1), sf.c1(R1)],
color='0.5',
linestyle='-.',
linewidth=2)
if R1 == 2.:
ax.annotate(r'$c_1=c_2$',
xy=(K_range[-1] + 0.03, sf.c1(R1) - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
else:
ax.annotate(r'$c_1$',
xy=(K_range[-1] + 0.03, sf.c1(R1) - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
ax.annotate(r'$c_2$',
xy=(K_range[-1] + 0.03, sf.c2 - 0.01),
xycoords='data',
annotation_clip=False,
fontsize=20)
# Plot a green circle where the chosen mode is
ax.plot(K, W, 'go', markersize=10)
# Specify density ratio R1 := rho_1 / rho_0
# R1 = 1.5 # Higher denisty on left than right
# R1 = 1.8
# R1 = 1.9 # Disp_diagram will only work for R1=1.5, 1.8, 2.0
R1 = 2. # Symmetric slab
# Reduce number of variables in dispersion relation
disp_rel_partial = partial(sf.disp_rel_asym, R1=R1)
# find eigenfrequencies W (= omega/k) within the range Wrange for the given parameters.
Wrange1 = np.linspace(0., sf.cT, 11)
Wrange2 = np.linspace(sf.cT, sf.c0, 401)
Wrange3 = np.linspace(sf.c0, sf.c2, 11)
Woptions_slow_surf = np.real(
tool.point_find(disp_rel_partial, np.array(K), Wrange1,
args=None).transpose())
Woptions_slow_body = np.real(
tool.point_find(disp_rel_partial, np.array(K), Wrange2,
args=None).transpose())
Woptions_fast = np.real(
tool.point_find(disp_rel_partial, np.array(K), Wrange3,
args=None).transpose())
# Remove W values that are very close to characteristic speeds - these are spurious solutions
tol = 1e-2
indices_to_rm = []
for i, w in enumerate(Woptions_slow_surf):
spurious_roots_diff = abs(
np.array([w, w - sf.c0, w - sf.c1(R1), w - sf.c2, w - sf.vA]))
if min(spurious_roots_diff) < tol or w < 0 or w > sf.cT:
indices_to_rm.append(i)