We have studied electron tunneling across the gap between two electrodes as the gap is varied by electrodeposition and etching. The tunneling current tends to change in a stepwise fashion, corresponding to a discrete change of the gap width. The stepwise change is due to the discrete nature of atoms and a series of structural relaxations of the atoms at the electrodes between stable configurations upon deposition and etching. By stabilizing the tunneling current on various steps using a feedback loop, we have demonstrated that stable molecular-scale gaps can be fabricated with subangstrom precision.

The precorrected-FFT acceleration technique is successfully applied in the boundary element method for the simulation of 3-D acoustic radiation problems. The constant triangular element is employed in the simulation. The computational cost, the consumed memory and the accuracy of the current method are demonstrated and analyzed through the simulation of the acoustic radiation from a pulsating sphere. Both the surface and the exterior field dimensionless acoustic pressures are presented to show the precision of this method.