Depinning dynamics

The previous examples dealt more with static properties of the interface. The MD_rigid_rototrasl.py module allows you to integrate the overdamped equation of motion (see introduction) and follow the trajectory of a cluster in time. See the example folder molecular_dynamics for more details and inputs.

An example of interesting time evolution is the depinning of a cluster under the action of external drivers, like a torque and a force applied on its center of mass (CM). If these drivers are above a critical threshold, the cluster will depin and starting to translate and rotate.

The animation below shows the evolution of the cluster during the depining, with each particle coloured according to its potential energy. The applied torque is in the counter-clockwise direction and the force along \(x\).

_images/trajectory.gif — Depinning cluster under the action of torque and force. The color of each particle indicates the substrate potential energy, increasing from blue to yello. Arrows in dicate the force acting on each particle (the legth is proportional to the magnitude).

From the output file, we can also plot the evolution of the total energy of the cluster as a function of time.

_images/energy.png — Energy per particle as a function of time

As the drivers in this example are not much larger than the critical value, the motion is characterised by an intermittent dynamics reminiscent of stick-slip (strincly speaking, there cannot be stick-slip in a rigid system under a constant force), as highlight by the evolution of the \(x\) coordinate of the CM below. In the limit of large drives, the cluster will move in an almost-smooth fashion, as the force imposed by the substrate will be negligible.

_images/x_trajectory.png — Position of the cluster CM along x as a function of time

Note how the amplitude of the “slips” is not constant, but decreases with time, toward an almost smooth sliding. This is due to the coupling of rotation and translation: as the cluster rotates the depth of the energy landscape decreases, thus making the applied force effectively larger, closer to the smooth sliding limit.