deerlab.dd_spherepoint¶

dd_spherepoint = <deerlab.model.Model object>¶

One particle distanced from particles uniformly distributed on a sphere

Parameters:

rarray_like: Distance axis, in nanometers.
radiusscalar: Sphere radius.
distscalar: Distance to point.

Returns:

Pndarray: Distance distribution.

Notes

Parameter List

Name	Lower	Upper	Type	Frozen	Unit	Description
`radius`	0.1	20	nonlin	No	nm	Sphere radius
`dist`	0.1	20	nonlin	No	nm	Distance to point

Model

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

where $R$ is the sphere’s radius, and $d$ is the distance from the sphere to the point.

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)