He is best known for his excellent contributions to the theory of crystal growth, surface dynamics, low-dimensional magnetism, as well as spatially modulated, commensurate and incommensurate structures in solids.
It provides a theoretical basis for understanding numerous experimental observations on commensurate and incommensurate structures, as well as accompanying phase transitions, in magnets, alloys, adsorbates, and other solids.
However, the integer frequencies can be selected to be incommensurate to any order so that the error can be controlled meeting any precision requirement in theory.
Event simulation also has the advantage of greater flexibility, handling design features difficult to handle with cycle simulation, such as asynchronous logic and incommensurate clocks.
Since the numerical value of an irrational number can not be stored exactly in a computer, an approximation of the incommensurate frequencies by all rational numbers is required in implementation.
If two of these frequencies form an irrational fraction (i.e. they are incommensurate), the trajectory is no longer closed, and the limit cycle becomes a limit torus.
The integer frequencies are not strictly incommensurate, resulting in an error between the multi-dimensional integral and the transformed one-dimensional integral.
