def V_twiddle_sq_R(k_vector):
k = AS.k_mag(k_vector)
#q_vector = np.asarray(kprime_vector)- np.asarray(k_vector)
#calculate the angle of incidence
inc = acos(k_vector[0] / (k))
vs_new = v_sound(inc)
# k will cancel out
return abs(hbar * (vs_new - vs) / (2 * math.pi))**2
def Gamma(k_vector, vg):
return Gamma_GBS(k_vector, AS.kprimes_y(k_vector, D), vg, n_1D,
D) * 1E-9 #what's this function for?
def Gamma_GBS(k_vector, kprime_vectors, vg, n_1D, D):
return AS.GammaArray(k_vector, kprime_vectors, V1_twiddle_sq_Delta, vg, n_1D, D, 1) \
+ AS.GammaArray(k_vector, kprime_vectors, V1_twiddle_sq_S, vg, n_1D, D, 1)\
+ AS.GammaArray(k_vector, kprime_vectors, V1_twiddle_sq_R, vg, n_1D, D, 1)
def V1_twiddle_sq_R(k_vector, kprime_vector):
k = AS.k_mag(k_vector)
q_vector = np.asarray(kprime_vector) - np.asarray(k_vector)
return abs(AS.hbar * omega_k(k_vector) * gamma(k_vector) * \
b * ((2 * q_vector[0]) / (q_vector[0]**2 + q_vector[1]**2)))**2
def V1_twiddle_sq_S(k_vector, kprime_vector):
k = AS.k_mag(k_vector)
q_vector = np.asarray(kprime_vector) - np.asarray(k_vector)
return abs(AS.hbar * omega_k(k_vector) * gamma(k_vector) * \
(b / (1 - nu)) * ((q_vector[0] * q_vector[1]**2)\
/ (q_vector[0]**2 + q_vector[1]**2)**2)) ** 2
def V1_twiddle_sq_Delta(k_vector, kprime_vector):
k = AS.k_mag(k_vector)
q_vector = np.asarray(kprime_vector) - np.asarray(k_vector)
return abs(AS.hbar * omega_k(k_vector) * gamma(k_vector) * \
((b * (1 - 2 * nu)) / (1 - nu)) * (q_vector[1]\
/ (q_vector[0]**2 + q_vector[1]**2)))**2
def omega_k(k_vector):
k = AS.k_mag(k_vector)
return vs * k
omega_list = []
vg_list = []
tau_list = []
trans_list = []
tbc_list = []
kappa_list = []
#%% Spectral plots
T = 300
for k in k_mags:
omega_list.append(
omega_k([k, 0, 0])
) # omega and vg are supposed to be only a function of k, not k_vector. This is tacky and needs to be fixed!
vg_list.append(vg_k([k, 0, 0]))
tau_list.append(AS.tau_spectral(Gamma, k, vg_k, 50))
trans_list.append(AS.transmissivity(k, vg_k, n_1D, Gamma, 50))
tbc_list.append(AS.tbc_spectral(k, vg_k, omega_k, T, Gamma, n_1D, 50))
kappa_list.append(AS.kL_spectral(Gamma, k, vg_k, omega_k, T, 50))
#
#
plt.figure()
plt.xlabel(r'$k \; \mathrm{(m^{-1})}$', fontsize=16)
plt.ylabel(r'$\tau \; \mathrm{(ns)}$', fontsize=16)
plt.plot(k_mags, tau_list)
plt.savefig('tiltBoundary_D1e-9_2.pdf', dpi=400, bbox_inches='tight')
plt.show(block=False)
#
#plt.figure()
#plt.xlabel(r'$k \; \mathrm{(m^{-1}}$')
#plt.ylabel(r'$t$')
def Vn_twiddle_sq_E13(k_vector, kprime_vector):
k = AS.k_mag(k_vector)
q_vector = np.asarray(kprime_vector) - np.asarray(k_vector)
return abs(hbar * omega_k(k_vector) * gamma(k) * (b * q_vector[1]) /
(2 * (q_vector[0]**2 + q_vector[1]**2)))**2
def omega_k(k_vector):
if np.size(k_vector) > 1:
k = AS.k_mag(k_vector)
else:
k = k_vector
return vs * k
def Gamma_rot(k_vector, vg):
return Gamma_GBS_rot(k_vector, AS.kprimes_y(k_vector, D),
AS.kprimes_z(k_vector, D), vg, n_1D, D) * 1E-9
def Gamma_GBS_rot(k_vector, kprime_yvectors, kprime_zvectors, vg, n_1D, D):
return AS.GammaArray(k_vector, kprime_yvectors, V_twiddle_sq_n, vg, n_1D, D, 1) \
+ AS.GammaArray(k_vector, kprime_zvectors, V_twiddle_sq_m, vg, n_1D, D, 2) \
+ V_twiddle_sq_R(k_vector)
# plt.show(block=False)
#%%
# Calculation of spectral tau and kappa
omega_list = []
vg_list = []
tau_list = []
kappa_list = []
trans_list = []
T = 300
for k in k_mags:
omega_list.append(
omega_k([k, 0, 0])
) # omega and vg are supposed to be only a function of k, not k_vector. This is tacky and needs to be fixed!
vg_list.append(vg_k([k, 0, 0]))
tau_list.append(AS.tau_spectral(Gamma_rot, k, vg_k, 50))
trans_list.append(AS.transmissivity(k, vg_k, n_1D, Gamma_rot, 50))
#kappa_list.append(AS.kL_spectral(Gamma_rot, k, vg_k, omega_k, T, 50))
plt.figure()
plt.xlabel(r'$k \; \mathrm{(m^{-1})}$', fontsize=16)
plt.ylabel(r'$\tau \; \mathrm{(ns)}$', fontsize=16)
plt.plot(k_mags, tau_list)
plt.savefig('twistBoundary_D1e-9.pdf', dpi=400, bbox_inches='tight')
plt.show(block=False)
#plt.figure
#plt.xlabel(r'$k \; \mathrm{(m^{-1})}$', fontsize=16)
#plt.ylabel(r'$\kappa_\mathrm{L} \; \mathrm{(W/m/K)}$', fontsize=16)
#plt.plot(k_mags, kappa_list)
#plt.savefig('twistKappa_D1e-9.pdf', dpi=400, bbox_inches = 'tight')