deerlab.dd_sphere¶

dd_sphere = <deerlab.model.Model object>¶

Particles uniformly distributed on a sphere.

Parameters:

rarray_like: Distance axis, in nanometers.
radiusscalar: Sphere radius.

Returns:

Pndarray: Distance distribution.

Notes

Parameter List

Name	Lower	Upper	Type	Frozen	Unit	Description
`radius`	0.1	20	nonlin	No	nm	Sphere radius

Model

$P(r) = \begin{cases} \frac{3r^5}{16R^6} - \frac{9r^3}{4R^4} + \frac{3r^2}{R^3} \quad \text{for} \quad 0 \leq r < 2R \\ 0 \quad \text{for} \quad \text{otherwise} \end{cases}$

where $R$ is the sphere’s radius.

References

[1]

D.R. Kattnig, D. Hinderberger, Analytical distance distributions in systems of spherical symmetry with applications to double electron-electron resonance, JMR, 230, 50-63, 2013

Examples

Example of the model evaluated at the start values of the parameters:

(Source code, png, hires.png, pdf)