dd_shellsphere

Particles distributed on a sphere inside a spherical shell

Syntax

info = dd_shellsphere()
P = dd_shellsphere(r,param)
Parameters
  • r - Distance axis (N-array)
  • param - Model parameters
Returns
  • P - Distance distribution (N-array)
  • info - Model information (struct)

Model

../_images/model_scheme_dd_sphereshell.png

P(r) = \frac{3}{16R_1^3(R_2^3 - R_1^3)}\begin{cases} 12r^3R_1^2 - r^5 \quad \text{for} \quad 0\leq r < \min(2R_1,R_2 - R_1) \\ 8r^2(R_2^3 - R_1^3) - 3r(R_2^2 - R_1^2)^2 - 6r^3(R_2 - R_1)(R_2 + R_1) \quad \text{for} \quad R_2-R_1 \leq r < 2R_1 \\ 16r^2R_1^3 \quad \text{for} \quad 2R_1\leq r < R_2 - R_1 \\ r^5 - 6r^3(R_2^2 + R_1^2) + 8r^2(R_2^3 + R_1^3) - 3r(R_2^2 - R1_2)^2 \quad \text{for} \quad \max(R_2-R_1,2R_1) \leq r < R_1+R_2 \\ 0 \quad \text{for} \quad \text{otherwise} \end{cases}

with

R_1 = R

R_2 = R + w_1

Variable Symbol Default Lower Upper Description
param(1) R 1.5 0.1 20 Sphere radius
param(2) w 0.5 0.1 20 Shell thickness

Example using default parameters:

../_images/model_dd_shellsphere.png

Description

info = dd_shellsphere()

Returns an info structure containing the specifics of the model:

  • info.model - Full name of the parametric model.
  • info.nparam - Total number of adjustable parameters.
  • info.parameters - Structure array with information on individual parameters.
P = dd_shellsphere(r,param)

Computes the distance distribution model P from the axis r according to the parameters array param. The required parameters can also be found in the info structure.

References

[1] D.R. Kattnig, D. Hinderberger, Journal of Magnetic Resonance, 230 (2013), 50-63. DOI: 10.1016/j.jmr.2013.01.007