July module of the month: Minimal distance segment to segment with Karush-Kuhn-Tucker conditions

 

Description

The module minDist2segments_KKT returns the minimal distance between two line segments. It uses the Karush-Kuhn-Tucker conditions (KKT) for the minimization under constraints.

Practical application

We would use the present module to avoid topology violation in an entangled polymer system. To preserve topology in a system of entangled polymers we need to determine the minimal distance between two bonds. Once is done we can apply either a soft potential either a hard potential to avoid a crossing of the two bonds. Here, we propose to determine the minimal distance between two segments with the help of the Karush-Kuhn-Tucker conditions.

This module is a part of an E-CAM pilot project at the ENS Lyon, focused on the implementation of contact joint to resolve excluded volume constraints

Background information

A detailed derivation of the minimal distance between two segments using the Karush-Kuhn-Tucker conditions is available at  https://gitlab.e-cam2020.eu:10443/carrivain/mindist2segments_kkt/-/blob/master/minDist2segments_KKT.pdf

This module is used by other ongoing work, such as module velocities_resolve_EV, that resolves the excluded volume constraint  with a velocity formulation.

Source code

The source code and more information can be found at minDist2segments_KKT GitLab repository.

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