The assumption of scale-invariance, when taken in conjunction with the symmetries of the Navier-Stokes equation, is shown to lead to the energy spectrum E(k) = αε 2/3 T k −5/3 , in the limit of infinite Reynolds number. Here ε T is the flux of energy due to inertial transfer, while the prefactor α is determined by an integral over triple correlations of the phases of the system. It is argued that this form of the prefactor provides an answer to the Landau-Kraichnan criticism of the original Kolmogorov (1941) theory (K41).

We propose a novel scheme to trap cold polar molecules on the surface of an insulating substrate (i.e. a chip) by using an inhomogeneous electrostatic field, which is generated by the combination o f a circular charged wire (a ring electrode) and a grounded metal plate. The spatial distributions of the electrostatic field from the above charged wire layout and its Stark potentials for CO molecules are calculated. Our study shows that when the voltage applied to the wire is U = 15 kV, a ring radius is R = 5 mm, the thickness o f the insulating substrate is b = 5 mm, and a wire radius is r = I mm, the maximum efficient trapping potential (i.e., as equivalent temperature) for CO molecules is greater than 141. 7mK7 which is high enough to trap cold polar molecules with a temperature of 50 mK in the low-field-seeking states.

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