recruitment gamma

Module: solid

Category: materialprop

Type string: "recruitment gamma"

Parameters

Name	Description	Default	Units
alpha	alpha	2	[]
mu	mu	4	[]
max	max recruitment increase	0	[]

Description

The material type for a gamma recruitment function is recruitment gamma.

For this material the bond recruitment functions is given by

\[ F\left(\Xi\right)=1+r\frac{\gamma\left(\alpha,\Xi/\mu\right)}{\Gamma\left(\alpha,0\right)}\,, \]

where \(\gamma\left(\alpha,z\right)\) and \(\Gamma\left(\alpha,z\right)\) are the lower and upper incomplete gamma functions, respectively. The normalization by \(\Gamma\left(\alpha,0\right)\) ensures that this function is bounded by \(1\le F\left(\Xi\right)\le1+r\).

Example:

<recruitment type="recruitment gamma">
  <alpha>3</alpha>
  <mu>0.4</mu>
  <max>4</max>
</recruitment>