Interaction potential between parabolic rotator and an outside particle

At micro/nanoscale, the interaction potential between parabolic rotator and a particle located outside the rotator is studied on the basis of the negative exponential pair potential (1/R)ⁿ between particles. Similar to two-dimensional curved surfaces, we confirm that the potential of the three-dimensional parabolic rotator and outside particle can also be expressed as a unified form of curvatures; that is, it can be written as the function of curvatures. Furthermore, we verify that the driving forces acting on the particle may be induced by the highly curved micro/nano-parabolic rotator. Curvatures and the gradient of curvatures are the essential elements forming the driving forces. Through the idealized numerical experiments, the accuracy of the curvature-based potential is preliminarily proved.