Constructing Amplitudes from Their Soft Limits

The existence of universal soft limits for gauge-theory and gravity amplitudes has been known for a long time. The properties of the soft limits have been exploited in numerous ways; in particular for relating an n-point amplitude to an (n-1)-point amplitude by removing a soft particle. Recently, a procedure called inverse soft was developed by which "soft" particles can be systematically added to an amplitude to construct a higher-point amplitude for generic kinematics. We review this procedure and relate it to Britto-Cachazo-Feng-Witten recursion. We show that all tree-level amplitudes in gauge theory and gravity up through seven points can be constructed in this way, as well as certain classes of NMHV gauge-theory amplitudes with any number of external legs. This provides us with a systematic procedure for constructing amplitudes solely from their soft limits.Comment: minor change

Elucidating the Pd Active Sites of Bimetallic Gold-palladium Catalysts Using Chemisorption and Titration Techniques

A bimetallic nanoparticle catalyst combines two different metals on an oxide support, which can increase the selectivity towards useful products that may be too tightly bound to a monometallic catalyst. To explore the surface properties of such a system, we made a group of four PdAu bimetallic catalysts with varying gold mass loadings to compare with a parent Pd catalyst. The parent catalyst was synthesized using ion exchange, and gold was added to this parent Pd catalyst using incipient wetness impregnation (IWI) to create four bimetallic catalysts. All catalysts were characterized using H2 and CO chemisorption in tandem with O2 and H2 titration methods. The measured dispersion of the parent catalyst ranged from 60-72% which is consistent with previous measurements for catalysts synthesized with the same loading and synthesis technique. This dispersion value implies an average Pd particle diameter of about 1.8 nm. Each bimetallic catalyst was characterized using chemisorption and titration methods and the fractional gold coverage was found to be about 70%, independent of the gold loading. In parallel with the chemisorption and titration measurements, we used ICP-OES analysis to determine the gold content in the bimetallic catalysts, but these results were inconsistent with the quantities of gold used in the IWI synthesis

The Solution to the Sorites Paradox

The solution to the Sorites Paradox is discussed