polyTEM.spatial.domain.DomainCollection

class polyTEM.spatial.domain.DomainCollection(domains: list | None = None, pixel_res=None, savedir='')

Bases: object

A collection of one or more Domains

Variables:

  • domains – list of Domain objects

  • savedir – path to save directory

  • pixel_resolution – nm/pixel

  • parallel_dtheta – list of scipy random variable class generated from rv_histogram, which contains the distribution for probability P(dtheta|r), where r is the list index (i.e. parallel_dtheta[1] = P(dtheta | r=1) in the direction parallel to the nematic director of the centroid)

  • perpendicular_dtheta – same as DomainCollection.parallel_dtheta but in the perpendicular direction

  • Ld_par – orientation correlation length in the parallel direction (in pixels)

  • Ld_perp – orientation correlation length in the perpendicular direction (in pixels)

histogram_dtheta()

computes parallel_dtheta and perpendicular_dtheta

plot_orientation_change()

plots the pdf from histogram_dtheta

Private attributes:

_parallel_dtheta_values, _perpendicular_dtheta_values _expected_val_par, _expected_val_perp _model_Ld_par, _model_Ld_perp _orientation_correlation_length_bounds

__init__(domains: list | None = None, pixel_res=None, savedir='')

Methods

__init__([domains, pixel_res, savedir])

frank_elastic_relation([freqs])

Calculate an estimate for the Frank elastic relations by taking the average

from_crystalstack(crystal_stack[, savedir, ...])

Creates DomainsCollection from CrystalStack

histogram_dtheta()

Histograms the orientation change as a function of distance in the directions parallel and perpendicular to the nematic director of at the domain centroid

load(savefile)

orientation_correlation_length([min_dist, ...])

Calculates the orientation correlation length given by the exponential decay fit of the expected value <2cos^2(Delta heta)-1>

plot_orientation_change(distances[, ...])

Plots the pdf of the probability $P(Delta heta | r)$ in the directions parallel and perpendicular to the nematic director of the domain centroid.

plot_orientation_correlation()

save(savefile)

Save as json.
_remove_unpicklable()

Returns a copy of the DomainCollection, but with unpicklable attributes set to None

Current List of unserializable attributes:

parallel_dtheta and perpendicular_dtheta: scipy.stats distributions cannot be serialized

frank_elastic_relation(freqs=array([0.14, 0.15755102, 0.17510204, 0.19265306, 0.21020408, 0.2277551, 0.24530612, 0.26285714, 0.28040816, 0.29795918, 0.3155102, 0.33306122, 0.35061224, 0.36816327, 0.38571429, 0.40326531, 0.42081633, 0.43836735, 0.45591837, 0.47346939, 0.49102041, 0.50857143, 0.52612245, 0.54367347, 0.56122449, 0.57877551, 0.59632653, 0.61387755, 0.63142857, 0.64897959, 0.66653061, 0.68408163, 0.70163265, 0.71918367, 0.73673469, 0.75428571, 0.77183673, 0.78938776, 0.80693878, 0.8244898, 0.84204082, 0.85959184, 0.87714286, 0.89469388, 0.9122449, 0.92979592, 0.94734694, 0.96489796, 0.98244898, 1.]))

Calculate an estimate for the Frank elastic relations by taking the average of the Fourier Transform of the orientation correlation function

Let R = autocorrelation function = $langle n(r) cdot n(r’)

angle$. <br>

Then the Fourier transform of R is: egin{equation} mathscr{F}{R}(k) = 1 -

rac{1}{K_B k_y^2 + K_Sk_x^2}

end{equation}

If we use R_parallel and R_perpendicular instead we get: egin{align}

mathscr{F}{R_{parallel}}(k) = 1 -

rac{1}{K_B k_y^2}

mathscr{F}{R_{perp}}(k) = 1 -

rac{1}{K_S k_x^2}

end{align} and the Frank Elastic relations egin{align}

K_Bk_y^2 &=

rac{1}{1-mathscr{F}{R_{parallel}}}

K_Sk_x^2 &=

rac{1}{1-mathscr{F}{R_{perp}}}

end{align}

Returns:

freqs Ks_kx^2 Kb_ky^2

classmethod from_crystalstack(crystal_stack, savedir='', alpha=0.2, cluster_df=None, num_threads=1)

Creates DomainsCollection from CrystalStack

for 1400 domains, this takes 12 seconds on 1 core if no cluster_df is given. Takes 6 seconds if cluster_df is provided (Polygons pre computed) So I probably don’t need to speed it up. but the multiprocessing is written for num_threads>1 just in case.

Parameters:

  • crystal_stack – CrystalStack object

  • savedir – directory for savefiles

  • alpha – parameter to extract shape of domain, see Domain.make_domain()

  • cluster_df – optional, backwards compatibility with cluster_dfs made by pytem.spatial_analysis.create_polygons()

  • num_threads – integer, num_threads == 1 core does not use multiprocessing, else sets the number of cores used

histogram_dtheta()

Histograms the orientation change as a function of distance in the directions parallel and perpendicular to the nematic director of at the domain centroid

orientation_correlation_length(min_dist=0, max_dist=20, plot=False)

Calculates the orientation correlation length given by the exponential decay fit of the expected value <2cos^2(Delta heta)-1>

plot_orientation_change(distances: list, dtheta_min=-5, dtheta_max=5)

Plots the pdf of the probability $P(Delta heta | r)$ in the directions parallel and perpendicular to the nematic director of the domain centroid.

Parameters:

  • distances – list of integer distances to plot

  • dtheta_min – int

  • dtheta_max – int

save(savefile)

Save as json. However, scipy.stats.distributions cannot be serialized, so DomainCollection.parallel_dtheta and DomainCollection.perpendicular_dtheta cannot be saved. Instead, we will only save _parallel_dtheta_values and _perpendicular_dtheta_values, and the rv_histogram will be recreated upon loading