Fig 1.
Dependence of the singlet yield on the strength of the applied magnetic field.
Singlet yield is minimized for low level magnetic fields. Hyperfine constants are chosen as A1x = −0.234, A1y = −0.234, A1z = 0.117 all in mT. These values are chosen in the spirit of [25].
Fig 2.
One proton model field optimization.
Identification of magnetic parameters for a one-proton model with hyperfine constants A1x = −0.234, A1y = −0.234, and A1z = 0.117. Epoch stands for iteration parameter n. A: Minimization of the cost function. B: Magnetic parameter evolution. C: Final value of the cost function versus distance of initial iteration from the optimal parameter.
Fig 3.
One proton model hyperfine optimization.
Identification of hyperfine paramters for a one-proton model. The cost function minimum is reached for diagonal hyperfine constants A1x = −0.054, A1y = −0.198 and A1z = 0.131 and using a regularization parameter λ = 10−5. A: Cost function minimization with or without regularization. B: Hyperfine parameter evolution.
Fig 4.
Identification of the magnetic field and hyperfine parameters for a one-proton model.
Identification of the magnetic field and hyperfine parameters for a one-proton model. The cost function minimum is reached for hyperfine constants A1x = −0.089, A1y = −0.053, A1z = 0.155 for a magnetic field (ux, uy, uz) = (-4.92, -19.33, -18.81) μT. A: Cost function minimization with or without regularization. B: Magnetic field parameter evolution. C: Hyperfine parameter evolution.
Fig 5.
Quantum yield as a function of magnetic field for two-proton model.
Hyperfine constants are chosen as A1x = 0.03, A1y = −0.64, A1z = 0.17, A2x = −0.10, A2y = 0.0, A2z = 0.05 all in mT.
Fig 6.
Identification of magnetic parameters for a two-proton model.
Iterative method decreases quantum yield to its minimum value represented by the dose-response model. This minimum corresponds to fields (ux, uy, uz) = (2.4, −17.3, −1.7) μT. Negative uz indicates opposite direction as coordinate frame. Field azimuthal symmetry is lost for this model. A: Cost function minimization for different values of the regularization parameter. B: Magnetic field parameter evolution.
Fig 7.
Identification of magnetic parameters for a two-proton model.
Iterative method decreases the quantum yield to its minimum value represented by the dose-response model. Optimal values of the hyperfine parameters are A1x = 0, A1y = 0, A1z = −0.004, A2x = −0.2, A2y = 0, A2z = 0.52. A: Cost function minimization with regularization. B: First proton hyperfine parameter evolution. C: Second proton hyperfine parameter evolution.
Fig 8.
Identification of hyperfine and field parameters for a two-proton model.
Quantum yield decreases significantly compared to static response model and reaches the minimum for hyperfine parameters A1x = 0.081, A1y = −0.186, A1z = 0.104, A2x = −0.232, A2y = 0.119, A2z = 0.848 and field (ux, uy, uz) = (−12.9, −3.7, −8.1) μT. A: Cost function minimization with and without regularization. B: Field parameter evolution. C: First proton hyperfine parameter evolution.D: Second proton hyperfine parameter evolution.