Papers › Crystal Ball: A Simple Model for Phase Transitions on a Classical Spherical Lattice
Crystal Ball: A Simple Model for Phase Transitions on a Classical Spherical Lattice
Aidan Bachmann, Pierre-Alexandre Gourdain, Eric G. Blackman
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When compressed, certain lattices undergo phase transitions that may allow nuclei to gain significant kinetic energy. To explore the dynamics of this phenomenon, we develop a framework to study Coulomb coupled N-body systems constrained to a parametric surface, focusing specifically on the case of a sphere, as in the Thomson problem. We initialize N total Boron nuclei as point particles on the surface of a sphere, allowing the particles to equilibrate via Coulomb scattering with a viscous damping term. To simulate a phase transition, we remove Nᵣₘ particles, forcing the system to rearrange into a new equilibrium. We develop a scaling relation for the average peak kinetic energy attained by a single particle as a function of N and Nᵣₘ. For certain values of N, we find an order of magnitude energy gain when increasing Nᵣₘ from 1 to 6, indicating that it may be possible to engineer a lattice that maximizes the energy output.
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