Determining the Inter-Particle Force-Laws in Amorphous Solids from a Visual Image

TL;DR

This paper introduces a new algorithm that determines inter-particle force laws in amorphous solids using only particle positions and pressure measurements, correcting for experimental errors.

Contribution

The authors propose a novel visual-based algorithm to infer force-laws in amorphous systems, accommodating multiple particle types and correcting measurement errors.

Findings

Successfully determines force-law coefficients from visual data.

Handles multiple particle types with Laurent polynomial models.

Includes error correction to improve experimental accuracy.

Abstract

We consider the problem of how to determine the force laws in an amorphous system of interacting particles. Given the positions of the centers of mass of the constituent particles we propose a new algorithm to determine the inter-particle force-laws. Having $n$ different types of constituents we determine the coefficients in the Laurent polynomials for the $n(n+1)/2$ possibly different force-laws. A visual providing the particle positions in addition to a measurement of the pressure is all that is required. The algorithm proposed includes a part that can correct for experimental errors in the positions of the particles. Such a correction of unavoidable measurement errors is expected to benefit many experiments in the field.