Vortex motions in coupled phase oscillator lattices with inertia under shear stress

We propose a coupled phase oscillator model with inertia and study the vortex motion in the model when the external force is applied at the boundaries. The vortex exhibits a glide motion when the external force is larger than a critical value. We find a transition from the pair annihilation to passing for the collision of the vortex and antivortex when the external force is changed. In the parameter range of the passing, a single vortex exhibits a reciprocal motion, which leads to desynchronization. When the external force is further increased, the multiplication of vortices occurs and the jump of the frequency profile increases. The desynchronization induced by the vortex motion is analogous to the plastic flow induced by the dislocation motion under the shear stress in solids. In perfect crystals without dislocations, the plastic flow hardly occurs. We further show that a vortex ring is generated when a vortex line passes through an impurity region, which corresponds to the Orowan loop in the theory of plasticity.