Fully Algebraic Description of the Static Level Sets for the System of Two Particles under a Van der Waals Potential

• Main Authors: Romero, Carlos Barrón, Hernández, Arturo Cueto, Monroy-Pérez, Felipe
• Format: Journal Article
• Language: English
• Published: 27-11-2012
• Subjects: Mathematics - Mathematical Physics; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.1211.6488

We study the equipotential surfaces around of a two particle system in 3-d
under a pairwise good potential as the one of Van der Waals. The level sets are
completely determined by the solutions of polynomials of at most fourth degree
that can be solved by standard algebraic methods. The distribution of real
positive roots determines the level sets and provides a complete description of
the map for the equipotential zones. Our methods can be generalized to a family
of polynomials with degree multiple of 2, 3, or 4. Numerical simulations of 2-d
and 3-d pictures depicting the true orbits and equipotential zones are
provided.