Recursive generation of IPR fullerenes

We describe a new construction algorithm for the recursive generation of all non-isomorphic IPR fullerenes. Unlike previous algorithms, the new algorithm stays entirely within the class of IPR fullerenes, that is: every IPR fullerene is constructed by expanding a smaller IPR fullerene unless it belongs to limited class of irreducible IPR fullerenes that can easily be made separately. The class of irreducible IPR fullerenes consists of 36 fullerenes with up to 112 vertices and 4 infinite families of nanotube fullerenes. Our implementation of this algorithm is faster than other generators for IPR fullerenes and we used it to compute all IPR fullerenes up to 400 vertices.Comment: 19 pages; to appear in Journal of Mathematical Chemistr

Fullerenes with distant pentagons

For each $d>0$, we find all the smallest fullerenes for which the least distance between two pentagons is $d$. We also show that for each $d$ there is an $h_d$ such that fullerenes with pentagons at least distance $d$ apart and any number of hexagons greater than or equal to $h_d$ exist. We also determine the number of fullerenes where the minimum distance between any two pentagons is at least $d$, for $1 \le d \le 5$, up to 400 vertices.Comment: 15 pages, submitted for publication. arXiv admin note: text overlap with arXiv:1501.0268

Petrographic survey of lunar regolith breccias

Regolith breccias from the Moon and from parent bodies of some meteorites may provide samples of ancient regoliths which have been frozen in time. If these rocks were essentially closed at some earlier time and that time can be determined, then these rocks provide a record of conditions in the solar system at that point in time. A survey of regolith breccias in the Apollo collection was conducted concentrating initially on Apollo 15 and 16. All available thin sections for 32 regolith breccias from Apollo 15 and 19 breccias from Apollo 16 were surveyed. These are most of the returned regolith breccias larger than 1 cm from these two mission. For comparison several fragmental matrix breccias which do not strictly qualify as regolith breccias were investigated. The criteria for classification as a regolith breccia is the presence of identifiable soil components such as glass spheres or agglutinates. The breccias are classified according to their intergranular porosity. In addition the fracture porosity is noted, and the relative abundance of agglutinates and spheres. Several petrographic trends are also noted. Identifiable regolith material decreases with decreasing intergranular porosity while fracture porosity increases. This relative lack of maturity of regolith breccias mayreflect their generally earlier formation age an the maturity of the regolith at that earlier time

On Birthing Dancing Stars: The Need for Bounded Chaos in Information Interaction

While computers causing chaos is acommon social trope, nearly the entirety of the history of computing is dedicated to generating order. Typical interactive information retrieval tasks ask computers to support the traversal and exploration of large, complex information spaces. The implicit assumption is that they are to support users in simplifying the complexity (i.e. in creating order from chaos). But for some types of task, particularly those that involve the creative application or synthesis of knowledge or the creation of new knowledge, this assumption may be incorrect. It is increasingly evident that perfect order—and the systems we create with it—support highly-structured information tasks well, but provide poor support for less-structured tasks.We need digital information environments that help create a little more chaos from order to spark creative thinking and knowledge creation. This paper argues for the need for information systems that offerwhat we term ‘bounded chaos’, and offers research directions that may support the creation of such interface