Abstract We consider directed polymers in random environment the critical dimension $$d = 2$$ d=2 , focusing on intermediate disorder regime when model undergoes a phase transition. prove that, at criticality, diffusively rescaled field of partition functio...

For efficient use of water, accurate measurement of flow in (field/laboratory) channels is required for many water resource projects. The present work is aimed to study the flow characteristics of a twin plate weir (two sharp-crested plates are placed one behind the other at some distance) under free and submerged flow conditions. Experiments are performed with four spacing of the twin plate we...

trapezoidal channels are frequently used in irrigation networks and other free surface water conveyance systems. the computation of the critical flow depth is one of the primary importance in the design process. it is usually determined by using design charts of iteration techniques. however, researchers have recently proposed formulas that directly provide approximate solutions. this paper pre...