To the naked eye, turbulent flows exhibit whirls of many different sizes. To each size, or scale, corresponds a fraction of the total energy resulting from a cascade in five dimensions: scale, time, and three-dimensional space. Understanding this process is critical to strategies for modeling geophysical and industrial flows. By tracking the flow regions containing energy in different scales, w...

We derive the five–dimensional effective action of strongly coupled heterotic string theory for the complete (1, 1) sector of the theory by performing a reduction, on a Calabi–Yau three–fold, of M–theory on S1/Z2. A crucial ingredient for a consistent truncation is a non–zero mode of the antisymmetric tensor field strength which arises due to magnetic sources on the orbifold planes. The correct...

We show the universal seesaw in the extra dimension setup, where three extra vector-like fields exist in the 5D bulk with heavy masses. We take the framework of the left-right symmetric model. The universal seesaw formula is easily obtained as a replacement of the vector-like mass in 4D case Mi to 2M∗ tan[πRMi] (M∗: 5D Planck scale, Mi: vector-like bulk mass, and R: compactification radius). Th...