Mathematical modelling of the catalyst layer of a polymer-electrolyte fuel cell

In this paper we derive a mathematical model for the cathode catalyst layer of a polymer electrolyte fuel cell. The model explicitly incorporates the restriction placed on oxygen in reaching the reaction sites, capturing the experimentally observed fall in the current density to a limiting value at low cell voltages. Temperature variations and interfacial transfer of O2 between the dissolved and gas phases are also included. Bounds on the solutions are derived, from which we provide a rigorous proof that the model admits a solution. Of particular interest are the maximum and minimum attainable values. We perform an asymptotic analysis in several limits inherent in the problem by identifying important groupings of parameters. This analysis reveals a number of key relationships between the solutions, including the current density, and the composition of the layer. A comparison of numerically computed and asymptotic solutions shows very good agreement. Implications of the results are discussed and future work is outlined

Delegation, Deference and Difference: In Search of a Principled Approach to Implementing and Administering Aboriginal Rights

In 2017, the Supreme Court of Canada (SCC) decided two duty to consult cases, heard together: Clyde River (Hamlet) v. Petroleum Geo-Services Inc. and Chippewas of the Thames First Nation v. Enbridge Pipelines Inc. (“the 2017 cases”). Within the issue of whether the duty to consult had been satisfied, key points of contention focused on who is responsible for discharging the duty to consult Indigenous Peoples, including assessing the adequacy of the consultation. The cases presented the particular situation of a regulatory agency (the National Energy Board or NEB) that had final approval authority, without the involvement of the Crown “proper” (understood as a minister of the Crown or cabinet). In other words, can the duty be satisfied without the Crown participating in the process and assessing its adequacy? The Court’s answer: “While the Crown always owes the duty to consult, regulatory processes can partially or completely fulfill this duty.” A second, equally contentious issue was about what is required of a regulatory agency in assessing the obligation to consult when this obligation rests with it. Embedded within this issue is the question: what is the degree of specificity or formality with which the existing or claimed Aboriginal or treaty rights must be treated for the duty to assess adequacy to be discharged