How do perennial rivers in high alpine areas maintain year round flows? We have several perennial rivers in my country that originate out of high altitude alpine glacier melt. I can understand snow or glacier melting in the summer to increase the flows but it is observed that flows do not come to a  complete halt during peak winter as well even though temperatures maybe below freezing point. Upon investigation it was revealed that a process called calving(presumably pressure differences)  is responsible for glacier breakdown but wikipedia claims that the mathematics of this process is still in development. 
Is it possible to get an expert answer on this phenomenon ?
Not claiming to be an expert, but I think the process you're referring to is called pressure melt. This effect occurs when the pressure at the bottom of the glacier is high enough to either shift the melting point slightly (melting point decreases by 0.7$\,^{\circ}$C per km of ice according to this link, which provides some more background information on processes and conditions inside glaciers), which combined with frictional energy from the constant movement of the glacier, and, in some regions, geothermal energy causes a constant supply of liquid water. Since these discharges are usually concentrated under the ice (also the principle behind the formation of eskers), leading to large discharges at a few emergence points with enough energy to prevent them from freezing over.