Implement mittag_leffler model

[henrikjacobsenfys]

Disclaimer: The code was written by Claude and looked through by me. The description below was written by me.

This implements the diffusion model that was requested at the summer school, eqs. 41 and 42 in this paper

A. N. Hassani, L. Haris, M. Appel, T. Seydel, A. M. Stadler and G. R. Kneller,
Multiscale relaxation dynamics and diffusion of myelin basic protein in solution studied by
quasielastic neutron scattering, J. Chem. Phys. 156, 025102 (2022),
doi:10.1063/5.0077100.

A factor pi is missing in the equation, which is fixed here. Eq. 42 is also a special case of $\tau_R=1$, here we allow any value of $\tau_R$.

It is implemented as a ModelComponent for the per-Q calculation and as a DiffusionModel since in the paper $\epsilon=DQ^2$. It is modelled after the existing DeltaLorentz diffusion model, so the only new things are the equations - all the architecture is essentially copy/pasted. (I don't think it should be put into a shared base class when we have only two models that are similar).

The tests verify numerical correctness by comparing with the Laplace transform given earlier in the paper.

The notebook reproduces several of the figures of the paper, indicating that everything works as it should.

[codecov]

Codecov Report

❌ Patch coverage is 92.80206% with 28 lines in your changes missing coverage. Please review.
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Files with missing lines	Patch %	Lines
..._model/diffusion_model/mittag_leffler_diffusion.py	90.57%	16 Missing and 12 partials ⚠️

Additional details and impacted files

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  Coverage           ?   98.10%           
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  Files              ?       59           
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Flag	Coverage Δ
unittests	98.10% <92.80%> (?)

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Files with missing lines	Coverage Δ
src/easydynamics/__init__.py	100.00% <100.00%> (ø)
src/easydynamics/sample_model/__init__.py	100.00% <100.00%> (ø)
...c/easydynamics/sample_model/components/__init__.py	100.00% <100.00%> (ø)
...odel/components/diffusion_damped_mittag_leffler.py	100.00% <100.00%> (ø)
...ydynamics/sample_model/diffusion_model/__init__.py	100.00% <100.00%> (ø)
src/easydynamics/utils/utils.py	98.88% <100.00%> (ø)
..._model/diffusion_model/mittag_leffler_diffusion.py	90.57% <90.57%> (ø)

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[rozyczko]

damping can silently become 0, producing NaN at x = 0 with no exception.

_evaluate_values computes

omega = np.abs(x_vals) / width
epsilon = damping / width
modulus_squared = omega**2 + epsilon**2
...
denominator = modulus_squared * (
    (modulus_squared**alpha + 1) * modulus_squared ** (-alpha / 2) + 2 * np.cos(phase)
)
return scale * numerator / (np.pi * width * denominator)

diffusion_coefficient's setter only rejects < 0, not == 0.
if float(diffusion_coefficient) < 0),
and its Parameter is constructed with min=0.0, so D = 0 is a possible value, accessible from the public API.

Q has no positivity check anywhere in the validation conditionals

Suggested fix: validate the effective epsilon/modulus_squared in _evaluate_values itself, or at least reject Q = 0 in _validate_and_convert_Q/DiffusionModelBase.Q and reject diffusion_coefficient == 0 in the setter.

[rozyczko]

Try running the attached script to see the issue

pr244_nan_repro.py

[henrikjacobsenfys]

Thanks, finally found a bit of time to fix it