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SofteningLength: Because Newton's law of Gravitation diverges as the relative separations |r'-r| tends to zero, it is common to add a positive constant λ also known as the "softening length", i.e. :
SingLe determines the appropriate value of this Softening Length λ for a given disc local structure (thickness 2h and vertical stratification ρ), in the axially symmetric, flat disc limit, preserving at best the Newtonian character of the gravitational potential and associated forces. Mass density ρ(z) is assumed to be locally expandable in the z-direction according to:
APPLawD (Accurate Disk Potentials for Power Law Surface densities) determines the gravitational potential in the equatorial plane of a flat axially symmetric disk (inside and outside) with finite size and power law surface density profile. Potential values are computed on the basis of the density splitting method, where the residual Poisson kernel is expanded over the modulus of the complete elliptic integral of the first kind. In contrast with classical multipole expansions of potential theory, the residual series converges linearly inside sources, leading to very accurate potential values for low order truncations of the series. The code is easy to use, works under variable precision, and is written in Fortran 90 with no external dependencies.