Ana Granados

In Situ Determination of MEA Resistance and Electrode Diffusivity of a Fuel Cell

This paper describes a novel method to determine the membrane electrode assembly (MEA) resistance and electrode diffusion (MRED) coefficient for a fuel cell (the MRED method) under in situ conditions. It is shown that theMRED method allows the determination of (i) the ohmic resistance of an MEA and (ii) the mass-transport coefficient of the electrodes. The method is based on the galvanostatic discharge of a fuel cell with interrupted reactant supply. Application of the method to the cathode of a polymer electrolyte membrane fuel cell is demonstrated, and the experimental results are analyzed using a theoretical model based on a simple one-dimensional diffusion process using Ficks law. Comparison of the experimental O 2 mass-transport coefficient with theoretical values indicates that diffusion in the active layer is mass-transport limiting.

Gromov hyperbolicity of planar graphs

We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given. A weaker version of this conjecture stating that every tessellation graph of ℝ2 with rectangular tiles is non-hyperbolic is given and partially answered. If this conjecture were true, many tessellation graphs of ℝ2 with tiles which are parallelograms would be non-hyperbolic.

CONFORMAL IMAGES OF BOREL SETS

For any holomorphic map in the unit disk, the set of radial limits at a Borel set on the unit circle is a Suslin-analytic set. Here it is proved that, for a conformal map, this set is, in fact, Borel. As a consequence, the sets of accessible boundary points, of cut points and of transition points are Borel. In addition, it is shown that the set of end points is a

Gromov Hyperbolicity in Mycielskian Graphs

G_{\delta}

Isoperimetric inequalities in graphs and surfaces

-set.

Gromov hyperbolicity of periodic planar graphs

Since the characterization of Gromov hyperbolic graphs seems a too ambitious task, there are many papers studying the hyperbolicity of several classes of graphs. In this paper, it is proven that every Mycielskian graph G M is hyperbolic and that δ ( G M ) is comparable to diam ( G M ) . Furthermore, we study the extremal problems of finding the smallest and largest hyperbolicity constants of such graphs; in fact, it is shown that 5 / 4 ≤ δ ( G M ) ≤ 5 / 2 . Graphs G whose Mycielskian have hyperbolicity constant 5 / 4 or 5 / 2 are characterized. The hyperbolicity constants of the Mycielskian of path, cycle, complete and complete bipartite graphs are calculated explicitly. Finally, information on δ ( G ) just in terms of δ ( G M ) is obtained.

Quasi-isometries and isoperimetric inequalities in planar domains

Let M be the set of metric spaces that are either graphs with bounded degree or Riemannian manifolds with bounded geometry. Kanai proved the quasi-isometric stability of several geometric properties (in particular, of isoperimetric inequalities) for the spaces in M. Kanai proves directly these results for graphs with bounded degree; in order to prove the general case, he uses a graph (an e-net) associated to a Riemannian manifold with bounded geometry. This paper studies the stability of isoperimetric inequalities under quasi-isometries between non-exceptional Riemann surfaces (endowed with their Poincare metrics). The present work proves the stability of the linear isoperimetric inequality for planar surfaces (genus zero surfaces) without the condition on bounded geometry. It is also shown the stability of any non-linear isoperimetric inequality.