def potential_on_grid(self, r_grid, theta_grid, phi_grid):
if self.external_field[0] == 0:
return np.zeros_like(r_grid)
F_r = np.ones_like(r_grid) * self.external_field[0]
F_theta = np.ones_like(r_grid) * self.external_field[1]
F_phi = np.ones_like(r_grid) * self.external_field[2]
x, y, z = Vectors3D.spherical_to_cartesian(r_grid, theta_grid, phi_grid)
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, F_theta, F_phi)
angles_grid = Vectors3D.angle_between_vectors((x, y, z), (F_x, F_y, F_z))
return F_r * r_grid * np.cos(angles_grid)
def potential_on_grid(self, r_grid, theta_grid, phi_grid):
if self.external_field[0] == 0:
return np.zeros_like(r_grid)
F_r = np.ones_like(r_grid) * self.external_field[0]
F_theta = np.ones_like(r_grid) * self.external_field[1]
F_phi = np.ones_like(r_grid) * self.external_field[2]
x, y, z = Vectors3D.spherical_to_cartesian(r_grid, theta_grid, phi_grid)
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, F_theta, F_phi)
angles_grid = Vectors3D.angle_between_vectors((x, y, z), (F_x, F_y, F_z))
return F_r * r_grid * np.cos(angles_grid)
def field(self, r, theta, phi):
r_grid, theta_grid, phi_grid = np.meshgrid(r, theta, phi)
x_grid, y_grid, z_grid = Vectors3D.spherical_to_cartesian(r_grid, theta_grid, phi_grid)
super_x = np.zeros_like(x_grid)
super_y = np.zeros_like(y_grid)
super_z = np.zeros_like(z_grid)
for potential in self.potentials:
F_r, F_theta, F_phi = potential.field(r, theta, phi)
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, F_theta, F_phi)
super_x += F_x
super_y += F_y
super_z += F_z
super_r, super_theta, super_phi = Vectors3D.cartesian_to_spherical(super_x, super_y, super_z)
return super_r, super_theta, super_phi
def field(self, r, theta, phi):
r_grid, theta_grid, phi_grid = np.meshgrid(r, theta, phi)
x_grid, y_grid, z_grid = Vectors3D.spherical_to_cartesian(r_grid, theta_grid, phi_grid)
super_x = np.zeros_like(x_grid)
super_y = np.zeros_like(y_grid)
super_z = np.zeros_like(z_grid)
for potential in self.potentials:
F_r, F_theta, F_phi = potential.field(r, theta, phi)
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, F_theta, F_phi)
super_x += F_x
super_y += F_y
super_z += F_z
super_r, super_theta, super_phi = Vectors3D.cartesian_to_spherical(super_x, super_y, super_z)
return super_r, super_theta, super_phi
def field_cartesian(self, x, y, z):
potential_sign = -1 if self.attractive else 1
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
F_r = -potential_sign * self.a / r_grid**2
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, theta_grid, phi_grid)
return F_x, F_y, F_z
def field_cartesian(self, x, y, z):
potential_sign = -1 if self.attractive else 1
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
F_r = -potential_sign * self.a / r_grid**2
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, theta_grid, phi_grid)
return F_x, F_y, F_z
def field_cartesian(self, x, y, z):
grid = np.ones((np.array(x).size, np.array(y).size, np.array(z).size), dtype=np.float)
ex, ey, ez = Vectors3D.spherical_to_cartesian(self.external_field[0],
self.external_field[1],
self.external_field[2])
F_x = grid * ex
F_y = grid * ey
F_z = grid * ez
return F_x, F_y, F_z
def field_cartesian(self, x, y, z):
grid = np.ones((np.array(x).size, np.array(y).size, np.array(z).size), dtype=np.float)
ex, ey, ez = Vectors3D.spherical_to_cartesian(self.external_field[0],
self.external_field[1],
self.external_field[2])
F_x = grid * ex
F_y = grid * ey
F_z = grid * ez
return F_x, F_y, F_z
def field_cartesian(self, x, y, z):
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
F_r = self.a / r_grid
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, theta_grid, phi_grid)
return F_x, F_y, F_z
def equation(r):
field = self.field(r, theta, 0)
field_x, field_y, field_z = Vectors3D.spherical_to_cartesian(field[0][0][0], field[1][0][0], field[2][0][0])
r_x, r_y, r_z = Vectors3D.spherical_to_cartesian(r, theta, 0)
F_r = field_x * r_x + field_y * r_y + field_z * r_z
return F_r
def field_cartesian(self, x, y, z):
x_grid, y_grid, z_grid = np.meshgrid(x, y, z)
r_grid, theta_grid, phi_grid = Vectors3D.cartesian_to_spherical(x_grid, y_grid, z_grid)
F_r = self.a / r_grid
F_x, F_y, F_z = Vectors3D.spherical_to_cartesian(F_r, theta_grid, phi_grid)
return F_x, F_y, F_z
def equation(r):
field = self.field(r, theta, 0)
field_x, field_y, field_z = Vectors3D.spherical_to_cartesian(field[0][0][0], field[1][0][0], field[2][0][0])
r_x, r_y, r_z = Vectors3D.spherical_to_cartesian(r, theta, 0)
F_r = field_x * r_x + field_y * r_y + field_z * r_z
return F_r
