def get_free_energy_for_minimize(grid_points):
"""
Calculates total elastic energy for given radius and pressure.
"""
global free_energy_elastic_stretching, \
free_energy_elastic_bending, \
free_energy_elastic_tail, \
free_energy_external, \
current_volume
u_coef = grid_points[:N_COEF_U]
h_coef = grid_points[N_COEF_U:]
u = Chebyshev(u_coef, domain=[0, radius])
h = Chebyshev(h_coef, domain=[0, radius])
r = Chebyshev([radius/2, radius/2], domain=[0, radius])
dh_dr = h.deriv(m=1)
d2h_dr2 = h.deriv(m=2)
du_dr = u.deriv(m=1)
current_volume = get_volume_from_h_coefs(h, radius)
psi_str_to_integrate = \
(du_dr ** 2 + du_dr * dh_dr ** 2 \
+ 0.25 * dh_dr ** 4 \
+ (u // r) ** 2) * r
free_energy_elastic_stretching = np.pi * YOUNGS_MODULUS \
* (psi_str_to_integrate.integ()(radius) \
- psi_str_to_integrate.integ()(0.0))
free_energy_elastic_tail = np.pi * YOUNGS_MODULUS * u(radius) ** 2
psi_bend_to_integrate = \
(d2h_dr2 ** 2 + (dh_dr // r) ** 2) * r
free_energy_elastic_bending = RIGIDITY * np.pi \
* (psi_bend_to_integrate.integ()(radius) \
- psi_bend_to_integrate.integ()(0.0))
# free_energy_elastic_bending = 0.0
free_energy_external = -current_volume * pressure
return free_energy_elastic_stretching \
+ free_energy_elastic_bending \
+ free_energy_elastic_tail \
+ free_energy_external
def h_constraint_der_zero(grid_points):
"""
Boundary condition h'(0) = 0.
"""
h_coef = grid_points[N_COEF_U:]
h = Chebyshev(h_coef, domain=[0, radius])
return h.deriv(m=1)(0.0)
def _derivative(c, m):
cheb = Chebyshev(c)
dcheb = cheb.deriv(m=m)
return dcheb.coef
def _derivative(c, m):
cheb = Chebyshev(c)
dcheb = cheb.deriv(m=m)
return dcheb.coef
