Tracking Particles with Large Displacements using Energy Minimization

TL;DR

This paper introduces an energy minimization-based particle tracking method capable of accurately tracking particles with large displacements, especially in deforming materials, surpassing traditional squared-displacement approaches in reliability.

Contribution

The novel method extends particle tracking capabilities to large displacements by minimizing strain energy, applicable to highly deformed materials, and includes a MATLAB implementation with strain estimation.

Findings

More reliable than squared-displacement methods for large, correlated displacements.

Applicable to particles in materials undergoing large deformations.

Provides strain tensor estimates for each tracked particle.

Abstract

We describe a method to track particles undergoing large displacements. Starting with a list of particle positions sampled at different time points, we assign particle identities by minimizing the sum across all particles of the trace of the square of the strain tensor. This method of tracking corresponds to minimizing the stored energy in an elastic solid or the dissipated energy in a viscous fluid. Our energy-minimizing approach extends the advantages of particle tracking to situations where particle imaging velocimetry and digital imaging correlation are typically required. This approach is much more reliable than the standard squared-displacement minimizing approach for spatially-correlated displacements that are larger than the typical interparticle spacing. Thus, it is suitable for particles embedded in a material undergoing large deformations. On the other hand, squared-displacement minimization is more effective for particles undergoing uncorrelated random motion. In the Supplement, we include a flexible MATLAB particle tracker that implements either approach. This implementation returns an estimation of the strain tensor for each particle, in addition to its identification.