The Hilbert basis method for D-flat directions and the superpotential

We discuss, using the Hilbert basis method, how to efficiently construct a complete basis for D-flat directions in supersymmetric Abelian and non-Abelian gauge theories. We extend the method to discrete (R and non-R) symmetries. This facilitates the construction of a basis of all superpotential terms in a theory with given symmetries.Comment: 11 pages; a related mathematica code can be found at http://einrichtungen.ph.tum.de/T30e/codes/NonAbelianHilbert

Spontaneous Charging of Drops on Lubricant-Infused Surfaces

[Image: see text] When a drop of a polar liquid slides over a hydrophobic surface, it acquires a charge. As a result, the surface charges oppositely. For applications such as the generation of electric energy, lubricant-infused surfaces (LIS) may be important because they show a low friction for drops. However, slide electrification on LIS has not been studied yet. Here, slide electrification on lubricant-infused surfaces was studied by measuring the charge generated by series of water drops sliding down inclined surfaces. As LIS, we used PDMS-coated glass with micrometer-thick silicone oil films on top. For PDMS-coated glass without lubricant, the charge for the first drop is highest. Then it decreases and saturates at a steady state charge per drop. With lubricant, the drop charge starts from 0, then it increases and reaches a maximum charge per drop. Afterward, it decreases again before reaching its steady-state value. This dependency is not a unique phenomenon for lubricant-infused PDMS; it also occurs on lubricant-infused micropillar surfaces. We attribute this dependency of charge on drop numbers to a change in surface conductivity and depletion of lubricant. These findings are helpful for understanding the charge process and optimizing solid–liquid nanogenerator devices in applications