models_theory

This class contains a recopilatory of diffusion models used in ANDI. The class is organized in three subclasses, each corresponding to a different dimensionality of the output trajectory.

Currently the library containts the following models:

Function	Dimensions	Description
bm	(1D)	Brownian motion
fbm	(1D/2D/3D)	Fractional browian motion, simulated via the stochastic Python library
ctrw	(1D/2D/3D)	Continuous time random walks
lw	(1D/2D/3D)	Levy walks
attm	(1D/2D/3D)	Annealed transit time
sbm	(1D/2D/3D)	Scaled brownian motion

The class is organized as follows:

• For every model in the previous list, there exists a function models_theory.name_walk which generates diffusion following that model. All functions have the same inputs and outputs:

  Inputs

  • T (int): lenght of the trajectory. Gets transformed to int if input is float.
  • alpha (float): anomalous exponent
  • D ({1,2,3}): dimension of the walk.

  Outputs

  • numpy.array of lenght DxT.

  This is the recommended way of generating trajectories.

• For every dimension, there exists a subclass models_theory._dimensionD, which gives access to the walk generators in each dimensions. Every walk is a function of these subclasses. This allows to access more features of the diffusion models:

  • ctrw
    • regular_time (bool): if true, regularizes the trajectory so that every element in the output corresponds to a time step. If false, returns the positions and times at which steps were done.
  • attm:
    • regime ({1,2,3}): allows to chose the regime of ATTM model. See the original paper Phys. Rev. Lett. 112, 150603 (2014) for further details.
  • sbm:
    • sigma (float): variance of the noise generator (similar to a local diffusion coefficient).

To learn more on the use of this class, please visit this tutorial.