Metallic mesoporous nanocomposites for electrocatalysis

We describe the fabrication, characterization, and applications of ultrathin, free-standing mesoporous metal membranes uniformly decorated with catalytically active nanoparticles. Platinum-plated nanoporous gold leaf (Pt-NPG) made by confining a plating reaction to occur within the pores of dealloyed silver/gold leaf is 100 nm thick and contains an extremely high, uniform dispersion of 3 nm diameter catalytic particles. This nanostructured composite holds promise as a prototypical member of a new class of fuel cell electrodes, showing good electrocatalytic performance at low platinum loading (less than 0.05 mg cm-2), while also maintaining long-term stability against coarsening and aggregation of catalytic nanoparticles.     

Nanoporous metals with controlled multimodal pore size distribution

A simple two-step dealloying strategy is described to make free-standing metal membranes with hierarchical porous architecture. This structure has a bimodal pore size distribution composed of large porosity channels and small porosity channel walls, where each pore size can be tailored independently of the others. A new gas-phase electroless plating technique was also developed here that could be used to uniformly fill porous structures with pore size as small as 10 nm.     

Numerical Quadrature over the Surface of a Sphere

Large‐scale simulations in spherical geometries require associated quadrature formulas. Classical approaches based on tabulated weights are limited to specific quasi‐uniform distributions of relatively low numbers of nodes. By using a radial basis function‐generated finite differences (RBF‐FD)‐based approach, the proposed algorithm creates quadrature weights for N arbitrarily scattered nodes in only operations.     

Improved bounds for the randomized decision tree Complexity of recursive majority

We consider the randomized decision tree complexity of the recursive 3‐majority function. We prove a lower bound of for the two‐sided‐error randomized decision tree complexity of evaluating height h formulae with error . This improves the lower bound of given by Jayram, Kumar, and Sivakumar (STOC'03), and the one of given by Leonardos (ICALP'13). Second, we improve the upper bound by giving a new zero‐error randomized decision tree algorithm that has complexity at most . The previous best known algorithm achieved complexity . The new lower bound follows from a better analysis of the base case of the recursion of Jayram et al. The new algorithm uses a novel “interleaving” of two recursive algorithms. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 612–638, 2016     

The toric ideal of a graphic matroid is generated by quadrics

Describing minimal generating sets of toric ideals is a well-studied and difficult problem. Neil White conjectured in 1980 that the toric ideal associated to a matroid is generated by quadrics corresponding to single element symmetric exchanges. We give a combinatorial proof of White’s conjecture for graphic matroids.     

Cutting of single-walled carbon nanotubes by ozonolysis

Cutting of single-walled carbon nanotubes (SWNT) has been achieved by extensive ozonolysis at room temperature. Perfluoropolyether (PFPE) was selected as a medium for cutting SWNT due to its high solubility for ozone (O3). A mixture of 9 wt % of O3 in O2 was bubbled through a homogeneous suspension of pristine SWNT in PFPE, at room temperature. The intense disorder mode in the Raman spectra of ozonated SWNT indicates that extensive reaction with the sidewalls of SWNT occurs during ozonolysis. Atomic force microscopy (AFM) images of SWNT, before and after ozonolysis, provided a measure of the extent of the cutting effects. Monitoring of the evolved gases for both pristine and purified SWNT indicates CO2 was produced during the ozonolysis process with a dependence on both system pressure and temperature. During heating, FTIR analysis of gases released indicated that carbon oxygen groups on the sidewalls of SWNT are released as CO2. SWNT was found to be extensively cut after an ozone treatment with a yield of approximately 80% of the original carbon.