Efficient Atlasing and Search of Configuration Spaces of Point-Sets Constrained by Distance Intervals

TL;DR

This paper presents algorithms and software for efficiently characterizing and exploring the configuration spaces of point-sets constrained by distance intervals, with applications in material assembly and molecular modeling.

Contribution

It introduces new algorithms and theoretical insights for sampling and analyzing configuration spaces constrained by distance intervals, enhancing understanding of their structure and properties.

Findings

Algorithms enable efficient sampling of configuration spaces.

Applications include computing free energy and assembly kinetics.

Survey of experimental results demonstrates effectiveness.

Abstract

For configurations of point-sets that are pairwise constrained by distance intervals, the EASAL software implements a suite of algorithms that characterize the structure and geometric properties of the configuration space. The algorithms generate, describe and explore these configuration spaces using generic rigidity properties, classical results for stratification of semi-algebraic sets, and new results for efficient sampling by convex parametrization. The paper reviews the key theoretical underpinnings, major algorithms and their implementation. The paper outlines the main applications such as the computation of free energy and kinetics of assembly of supramolecular structures or of clusters in colloidal and soft materials. In addition, the paper surveys select experimental results and comparisons.