Hidden semi-group structure in crystals

The ordering and Mِbius technique has been applied to a variety of inverse problems in physics, such as inverse blackbody problem, inverse heat capacity problem and inverse Fermi system problem. The present work shows the recent progress of this methodology to inverse cohesion problem for inter-atomic potentials in bulk materials, and to inverse adhesion problem for inter-atomic potentials across interface. The key step in this methodology is to explore the semi-group structure in the system under consideration.