arim.scat

Scattering functions and helpers

In a nutshell: use scat_factory() to create a Scattering2d object.

Single frequency scattering matrices are defined formally as:

S_LL[j, i] = scat_func_LL(phi_in[i], phi_out[j], frequency) for i, j in 0..numangles-1

where phi_in and phi_out are linearly spaced 1d array between -pi (included) and pi (excluded), as returned by make_angles(). NB: S_LL[phi_out_idx, phi_in_idx]

Multiple frequency scattering matrices are defined formally as:

S_LL[k, j, i] = scat_func_LL(phi_in[i], phi_out[j], frequencies[k])

arim.scat.SCAT_KEYS = frozenset(('LL', 'LT', 'TL', 'TT'))

Keys for the different kinds of scattering. The first letter is the mode of the incident wave; the second letter is the mode of the scattered wave. In this module, functions that take an argument to_compute expects a subset of these keys.

CrackCentreScat(crack_length, ...[, ...])	Scattering of a crack at its centre.
CrackTipScat(longitudinal_vel, transverse_vel)	Crack tip diffraction
PointSourceScat(longitudinal_vel, transverse_vel)	Scattering of an unphysical point source.
ScatFromData(frequencies[, scat_matrix_LL, ...])	Scattering functions from a set of data.
Scattering2d()	Base object for computing the scattering functions in 2D.
Scattering2dFromFunc()	Wrapper for scattering functions that take as three first arguments 'inc_theta', 'out_theta' and 'frequency', and that accepts an argument 'to_compute'.
SdhScat(radius, longitudinal_vel, transverse_vel)	Scattering for side-drilled hole
crack_2d_scat(inc_theta, out_theta, ...[, ...])	Scattering matrix of the centre of a crack.
crack_tip_2d(inc_theta, out_theta, ...[, ...])	Analytical model of the diffraction of elastic waves by a crack tip.
interpolate_matrices(scattering_matrices)	Convert a dictionary containing scattering matrices to a dictionary containing functions that interpolate the values of the scattering matrices.
interpolate_matrix(scattering_matrix)	Returns a function that takes as input the incident angles and the scattering angles.
make_angles(numpoints)	Return angles for scattering matrices.
make_angles_grid(numpoints)	Return angles for scattering matrices as a grid of incident and outgoing angles.
rotate_matrices(scat_matrices, phi)	Call rotate_matrix() on each matrix in a dict.
rotate_matrix(scat_matrix, phi)	Return the scattering matrix S' of the scatterer rotated by an angle phi, knowing the scattering matrix S of the unrotated scatterer.
scat_factory(kind, material, *args, **kwargs)	Creates a Scattering2d object in a simple way
sdh_2d_scat(inc_theta, out_theta, frequency, ...)	Scattering coefficients for a side-drilled hole in 2D