Work

One-dimensional inelastic collapse of four particles: asymmetric collision sequences and spherical billiard reduction

Year: 2025

Type: article

Abstract: We consider a one-dimensional system of four inelastic hard spheres, colliding with a fixed restitution coefficient r, and we study the inelastic collapse phenomenon for such a particle system. We study a periodic, asymmetric collision pattern, proving that it can be realized, despite its instability. We prove that we can associate to the four-particle dynamical system another dynamical system of smaller dimension, acting on { 1 , 2 , 3 } × S 2 , and that encodes the collision orders of each trajectory. We provide different representations of this new dynamical system, and study numerically its ω-limit sets. In particular, the numerical simulations suggest that the orbits of such a system might be quasi-periodic.

Source: Nonlinearity

DOI: 10.1088/1361-6544/adc9ee

Authors: Théophile Dolmaire, Eleni Hübner-Rosenau

Institutions: University of L'Aquila, University of Regensburg

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Deutsche Forschungsgemeinschaft, Università degli Studi dell'Aquila, Rheinische Friedrich-Wilhelms-Universität Bonn, Hausdorff Research Institute for Mathematics