amep.utils.domain_length

amep.utils.domain_length(s_fac: ndarray, q: ndarray, qmin: float | None = None, qmax: float | None = None) → float

Calculate the domain length from the structure factor. Takes the structure factor as a function of the wave numbers as well as the corresponding wave numbers.

Notes

The domain length is defined as

\[L(t) = 2\pi\frac{\int_{q_{\rm min}}^{q_{\rm max}}{\rm d}q\,S(q,t)}{\int_{q_{\rm min}}^{q_{\rm max}}{\rm d}q\,qS(q,t)}\]

and has been used in Refs. [1] [2] [3] [4] for example.

References

[1]

R. Wittkowski, A. Tiribocchi, J. Stenhammar, R. J. Allen, D. Marenduzzo, and M. E. Cates, Scalar Φ4 Field Theory for Active-Particle Phase Separation, Nat. Commun. 5, 4351 (2014). https://doi.org/10.1038/ncomms5351

[2]

A. K. Omar, K. Klymko, T. GrandPre, P. L. Geissler, and J. F. Brady, Tuning Nonequilibrium Phase Transitions with Inertia, J. Chem. Phys. 158, 42 (2023). https://doi.org/10.1063/5.0138256

[3]

J. Stenhammar, D. Marenduzzo, R. J. Allen, and M. E. Cates, Phase Behaviour of Active Brownian Particles: The Role of Dimensionality, Soft Matter 10, 1489 (2014). https://doi.org/10.1039/C3SM52813H

[4]

V. M. KENDON, M. E. CATES, I. PAGONABARRAGA, J.-C. DESPLAT, and P. BLADON, Inertial Effects in Three-Dimensional Spinodal Decomposition of a Symmetric Binary Fluid Mixture: A Lattice Boltzmann Study, J. Fluid Mech. 440, 147 (2001). https://doi.org/10.1017/S0022112001004682

Parameters:

• s_fac (np.ndarray) – structure factor corresponding to the given q-values

• q (np.ndarray) – The wave number corresponding to the structure factor

• qmin (float or None, optional) – Lower integration limit. The default is None.

• qmax (float or None, optional) – Upper integration limit. The default is None.

Returns:

l – Domain length as inverse expectation value of q.

Return type:

float

Examples

>>> import amep
>>> traj = amep.load.traj("../examples/data/continuum.h5amep")
>>> frame = traj[3]
>>> C = frame.data('c')
>>> X, Y = frame.grid
>>> sq2d, qx, qy = amep.continuum.sf2d(C, X, Y)
>>> fig, axs = amep.plot.new(figsize=(3.6,3))
>>> mp = amep.plot.field(axs, C, X, Y)
>>> cax = amep.plot.add_colorbar(
...     fig, axs, mp, label=r'$c(x,y)$'
... )
>>> axs.set_xlabel(r'$x$')
>>> axs.set_ylabel(r'$y$')
>>> fig.savefig('./figures/utils/utils-domain_length_1.png')
>>>

>>> sq, q = amep.utils.sq_from_sf2d(sq2d, qx, qy)
>>> fig, axs = amep.plot.new()
>>> axs.plot(q[1:], sq[1:])
>>> axs.set_xlabel(r'$q$')
>>> axs.set_ylabel(r'$S(q)$')
>>> fig.savefig('./figures/utils/utils-domain_length_2.png')
>>>

>>> L = amep.utils.domain_length(sq, q)
>>> print(L)
10.400560044952304
>>>