fluopy.kappa_squared

Compute rotational effects expressed by κ².

Functions

simulate_rotational_motion(...)

Simulate rotational motion and return dipole orientations over the lifetime.

kappa_squared(→ numpy.typing.NDArray[numpy.float64])

Calculate dipole orientation factor κ² for arrays of vectors.

integral_kappa_squared(→ float)

Calculate the time-averaged κ² using trapezoidal integration.

sample_kappa_squared_distribution(...)

Sample from the distribution of κ² values utilizing Gaussian kernel-density

Module Contents

fluopy.kappa_squared.simulate_rotational_motion(tau_rot: float, tau_life: float, dt: float = 1e-12, seed: fluopy.fluopy_types.RandomGeneratorSeed = None) → tuple[numpy.typing.NDArray[numpy.float64], numpy.typing.NDArray[numpy.float64]][source]

Simulate rotational motion and return dipole orientations over the lifetime.

Parameters:

  • tau_rot – The rotational diffusion time constant in s.

  • tau_life – The lifetime of the dipole in s.

  • dt – The time step for the simulation in s.

  • seed – Seed.

Returns:

Two arrays containing the dipole orientations over time for two dipoles. Of length int(tau_life / dt).

Return type:

tuple[npt.NDArray[np.float64], npt.NDArray[np.float64]]

fluopy.kappa_squared.kappa_squared(d: numpy.typing.ArrayLike, a: numpy.typing.ArrayLike, r: numpy.typing.ArrayLike) → numpy.typing.NDArray[numpy.float64][source]

Calculate dipole orientation factor κ² for arrays of vectors.

Parameters:

  • d – Donor dipole vectors of shape (N, 3).

  • a – Acceptor dipole vectors of shape (N, 3).

  • r – Unit vector from donor to acceptor of shape (N, 3).

Returns:

The value of κ² calculated from the input vectors.

Return type:

npt.NDArray[np.float64]

fluopy.kappa_squared.integral_kappa_squared(traj1: numpy.typing.ArrayLike, traj2: numpy.typing.ArrayLike, dt: float, r: numpy.typing.ArrayLike | None = None) → float[source]

Calculate the time-averaged κ² using trapezoidal integration.

Parameters:

  • traj1 – Array of dipole orientations for the first dipole. Shape (N, 3).

  • traj2 – Array of dipole orientations for the second dipole. Shape (N, 3).

  • dt – The time step for the simulation in s.

  • r – Unit vector from donor to acceptor. If None, assumes z-axis [0, 0, 1].

Returns:

The time-averaged value of κ².

Return type:

float

fluopy.kappa_squared.sample_kappa_squared_distribution(k2_values: numpy.typing.ArrayLike, size: int = 100, seed: fluopy.fluopy_types.RandomGeneratorSeed = None) → numpy.typing.NDArray[numpy.float64][source]

Sample from the distribution of κ² values utilizing Gaussian kernel-density estimation and logit transformation.

Parameters:

  • k2_values – Array of κ² values between 0 and 4.

  • size – Number of samples to generate.

  • seed – A seed to initialize the BitGenerator.

Returns:

Samples from the κ² distribution.

Return type:

npt.NDArray[np.float64]