Reto Muller investigated a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold $M$ with the harmonic map flow of a map $\phi$ from $M$ to some closed target closed manifold $N$, given by $\frac{\partial}{\partial t} g = - 2 Ric + 2 \alpha \nabla \phi \bigotimes \nabla \phi, \frac{\partial}{\partial t}\phi = \tau_{g}\phi $, where $\alpha$ is a positive coupling constant. This new flow shares many good properties with the Ricci flow.