Disclinations in crystalline materials are point defects that are responsible for rotational kinematic incompatibility. They are characterised by the so-called Frank angle, measuring the severity of the lattice mismatch. The variational setting and semi-discrete modelling of a systems of disclinations is developed in [1] resorting to the Airy stress function. In this talk, we present this variational setup and show the energetic equivalence of a disclination dipole with an edge dislocation, recovering the energy expansion of Cermelli–Leoni (SIMA 2005) around minimisers. Moreover, we present results on the dynamics of disclinations in a two-dimensional domain [2]. Disclinations move by energy minimisation, in a similar fashion as dislocations do. We study the well-posedness of the ODE governing the motion of a system of disclinations, with particular attention to the simple, yet illuminating cases of one disclination alone or two disclinations in the domain. An analysis of collision times is performed, and we also show how to account for the possible presence of preferred directions of motion determined by the crystalline structure. Finally, we show numerical evidence of this dynamics. This is work in collaboration with Pierluigi Cesana (Kyushu University), Lucia De Luca (CNR, Rome), and Alfio Grillo and Andrea Pastore (Politecnico di Torino). REFERENCES [1] Cesana P., De Luca L., Morandotti M., Semi-discrete modeling of systems of wedge disclinations and edge dislocations via the Airy stress function method. SIAM J. Math. Anal., 56(1), pp. 79–136, 2024. [2] Cesana P., Grillo A., Morandotti M., Pastore A., Dissipative dynamics of Volterra disclinations, 2025, submitted.