Abstract: A characteristic of the defocusing cubic nonlinear Schrodinger equation (NLSE), when defined so that the space variable is the multi-dimensional square torus, is that there exist solutions that start with arbitrarily small norms Sobolev norms and evolve to develop arbitrarily large modes at later times; this phenomenon is recognized as a weak energy transfer to high modes for the NLSE. In this talk, we will discuss research that shows that when the system is considered on an irrational torus, energy transfer is diminished.