Levitating frogs, machine learning and elliptic integrals

TL;DR

This paper calculates the stability region of a diamagnet levitated by a magnetic field using machine learning techniques, specifically automatic differentiation, to handle elliptic integrals involved in the analysis.

Contribution

It introduces the application of automatic differentiation to compute elliptic integrals for analyzing magnetic levitation stability regions.

Findings

Successfully calculated the stability region of a diamagnet in a magnetic field.

Demonstrated the effectiveness of machine learning techniques in complex physical calculations.

Provided a new computational approach for elliptic integral evaluations in physics.

Abstract

We present the calculation of the stability region of a perfect diamagnet levitated in a magnetic field created by a circular current loop. We make use of the machine learning technique of automatic differentiation to illustrate the calculations with the elliptic integrals involved.