Numerical Study of Localisation and Event Formation in Variational Dissipative Conservative PDE Systems

This deposit contains the paper “Numerical Study of Localisation and Event Formation in Variational Dissipative–Conservative PDE Systems” by Kevin Ellis Anderson. The paper presents a focused numerical investigation of localisation and event-like behaviour in a class of variational dissipative–conservative partial differential equation systems generated by a single free-energy functional. Using deterministic finite-difference simulations, the study examines instability-driven irreversible energy transfer from an oscillatory sector into auxiliary dissipative degrees of freedom. The simulations demonstrate the formation of spatially localised absorbing regions that irreversibly suppress further oscillatory propagation. Once formed, these regions persist and define discrete interaction outcomes despite the continuous underlying field dynamics. Time-reversal tests confirm that the localisation process is genuinely irreversible and not a numerical artefact. These results provide direct numerical support for analytical stability and localisation criteria established previously and clarify the dynamical origin of event formation in variational dissipative–conservative systems.