Asymptotic expansions,L-values and a new quantum modular form

In 2010, Zagier introduced the notion of a quantum modular form. One of his first examples was the “strange” function F(q) of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan’s mock theta functions. Using these functions and their transformation behaviour, we also compute asymptotic expansions similar to expansions of F(q).     

Polymeric coacervate coating for flame retardant paper

Cellulose - Cellulosic paper (from wood fibers) is a highly flammable material that is used in corrugated carboard, packaging, printing, and construction. While there is significant work focused on...     

Electrochemical caustic generation from sewage

Sewer corrosion caused by hydrogen sulfide generation represents a major issue in sewer management. One commonly used approach for mitigation is the periodic dosing of caustic to the sewer. This creates elevated pH levels that inactivate/kill sulfate reducing bacteria (SRB) present in the biofilms on the sewer pipe. In this study, we investigated the in-situ electrochemical generation of caustic from sewage. The average coulombic efficiency for caustic generation was 53 ± 8% (n = 10) at a current density of 10 mA/cm². The average required cell voltage input was 5.2 ± 0.7 V. Over time, this voltage increased due to a membrane fouling associated increase of the ohmic resistance of the cell. Switching the polarity of the electrodes every four hours was effective to control this fouling and thus retain a stable voltage requirement. This process constitutes a promising reagent-free method for sulfide abatement in sewers.     

The first factor of the class number of the p-th cyclotomic field

Kummer’s conjecture states that the relative class number of the p-th cyclotomic field follows a strict asymptotic law. Granville has shown it unlikely to be true—it cannot be true if we assume the truth of two other widely believed conjectures. We establish a new bound for the error term in Kummer’s conjecture, and more precisely we prove that ${\log(h_p^-)=\frac{p+3}{4} \log p +\frac{p}{2}\log(2\pi)+\log(1-\beta)+O(\log_2 p)}$ , where β is a possible Siegel zero of an ${L(s,\chi), \chi}$ odd.     

Efficient hydrogen peroxide generation from organic matter in a bioelectrochemical system

Hydrogen peroxide (H₂O₂) is an important industrial chemical, but its current production methods are highly energy-intensive. This study presents a novel process for the production of H₂O₂ based on the bioelectrochemical oxidation of wastewater organics at an anode coupled to the cathodic reduction of oxygen to H₂O₂. At an applied voltage of 0.5 V, this system was capable of producing 1.9 ± 0.2 kg H₂O₂/m³/day from acetate at an overall efficiency of 83.1 ± 4.8%. As most of the required energy was derived from the acetate, the system had a low energy requirement of 0.93 kWh/kg H₂O₂.     

Electrochemical regeneration of sulfur loaded electrodes

Electrochemical oxidation of sulfide is a promising technique for its removal from wastewaters. Generally, the main product of this oxidation reaction is elemental sulfur. The latter deposits as a solid on the electrode and deactivates it. Therefore, an efficient and effective regeneration technique of sulfur loaded electrodes is required for the practical implementation of this technology. Here we demonstrate a method for in situ reduction of electrodeposited sulfur on carbon fibre electrodes to sulfide/polysulfides, at low energy input. The intermediary coulombic efficiency (CE) values strongly depend on pH and buffer capacity of the solution. These values were recorded up to 435 ± 5% due to simultaneous chemical dissolution of sulfur to polysulfides under alkaline conditions. This process demonstrates the potential for continuously removing dissolved sulfide from wastewaters at an anode as sulfur and recovering the deposited sulfur based on regular switching between anodic sulfide oxidation and cathodic sulfur reduction.