Pyrite oxidation under initially neutral pH conditions and in the presence of Acidithiobacillus ferrooxidans and micromolar hydrogen peroxide

Hydrogen peroxide (H2O2) at a micromolar level played a role in the microbial surface oxidation of pyrite crystals under initially neutral pH. When the mineral-bacteria system was cyclically exposed to 50 μM H2O2, the colonization of Acidithiobacillus ferrooxidans onto the mineral surface was markedly enhanced, as compared to the control(no added H2O2). This can be attributed to the effects of H2O2 on increasing the roughness of the mineral surfaces, as well as the acidity and Fe2+ concentration at the mineral-solution interfaces. All of these effects tended to create more favourable nanoto micro-scale environments in the mineral surfaces for the cell adsorption. However, higher H2O2 levels inhibited the attachment of cells onto the mineral surfaces, possibly due to the oxidative stress in the bacteria when they approached the mineral surfaces where high levels of free radicals are present as a result of Fenton-like reactions. The more aggressive nature of H2O2 as an oxidant caused marked surface flaking of the mineral surface. The XPS results suggest that H2O2 accelerated the oxidation of pyrite-S and consequently facilitated the overall corrosion cycle of pyrite surfaces. This was accompanied by pH drop in the solution in contact with the pyrite cubes

On the Sublinear Convergence Rate of Multi-Block ADMM

The alternating direction method of multipliers (ADMM) is widely used in solving structured convex optimization problems. Despite of its success in practice, the convergence properties of the standard ADMM for minimizing the sum of $N$ $(N\geq 3)$ convex functions with $N$ block variables linked by linear constraints, have remained unclear for a very long time. In this paper, we present convergence and convergence rate results for the standard ADMM applied to solve $N$-block $(N\geq 3)$ convex minimization problem, under the condition that one of these functions is convex (not necessarily strongly convex) and the other $N-1$ functions are strongly convex. Specifically, in that case the ADMM is proven to converge with rate $O(1/t)$ in a certain ergodic sense, and $o(1/t)$ in non-ergodic sense, where $t$ denotes the number of iterations. As a by-product, we also provide a simple proof for the $O(1/t)$ convergence rate of two-block ADMM in terms of both objective error and constraint violation, without assuming any condition on the penalty parameter and strong convexity on the functions