The Flip Diameter of Rectangulations and Convex Subdivisions

We study the configuration space of rectangulations and convex subdivisions of $n$ points in the plane. It is shown that a sequence of $O(n\log n)$ elementary flip and rotate operations can transform any rectangulation to any other rectangulation on the same set of $n$ points. This bound is the best possible for some point sets, while $\Theta(n)$ operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of $n$ points in the plane.Comment: 17 pages, 12 figures, an extended abstract has been presented at LATIN 201

The impact and mitigation of carbon formation on SOFC anodes arising from biomass gasification tars

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The Flip Diameter of Rectangulations and Convex Subdivisions

We study the configuration space of rectangulations and convex subdivisionsof $n$ points in the plane. It is shown that a sequence of $O(n\log n)$elementary flip and rotate operations can transform any rectangulation to anyother rectangulation on the same set of $n$ points. This bound is the bestpossible for some point sets, while $\Theta(n)$ operations are sufficient andnecessary for others. Some of our bounds generalize to convex subdivisions of$n$ points in the plane.Comment: 17 pages, 12 figures, an extended abstract has been presented at LATIN 201

The Flip Diameter of Rectangulations and Convex Subdivisions

We study the configuration space of rectangulations and convex subdivisions of $n$ points in the plane. It is shown that a sequence of $O(n\log n)$ elementary flip and rotate operations can transform any rectangulation to any other rectangulation on the same set of $n$ points. This bound is the best possible for some point sets, while $\Theta(n)$ operations are sufficient and necessary for others. Some of our bounds generalize to convex subdivisions of $n$ points in the plane

Strategies for carbon and sulfur tolerant solid oxide fuel cell materials, incorporating lessons from heterogeneous catalysis

Solid oxide fuel cells (SOFCs) are a rapidly emerging energy technology for a low carbon world, providing high efficiency, potential to use carbonaceous fuels and compatibility with carbon capture and storage. However, current state-of-the-art materials have low tolerance to sulfur, a common contaminant of many fuels, and are vulnerable to deactivation due to carbon deposition when using carbon-containing compounds. In this review we first study the theoretical basis behind carbon and sulfur poisoning, before examining the strategies towards carbon and sulfur tolerance used so far in the SOFC literature. We then study the more extensive relevant heterogeneous catalysis literature for strategies and materials which could be incorporated into carbon and sulfur tolerant fuel cells