Ovoids and spreads of finite classical generalized hexagons and applications

One intuitively describes a generalized hexagon as a point-line geometry full of ordinary hexagons, but containing no ordinary n-gons for n<6. A generalized hexagon has order (s,t) if every point is on t+1 lines and every line contains s+1 points. The main result of my PhD Thesis is the construction of three new examples of distance-2 ovoids (a set of non-collinear points that is uniquely intersected by any chosen line) in H(3) and H(4), where H(q) belongs to a special class of order (q,q) generalized hexagons. One of these examples has lead to the construction of a new infinite class of two-character sets. These in turn give rise to new strongly regular graphs and new two-weight codes, which is why I dedicate a whole chapter on codes arising from small generalized hexagons. By considering the (0,1)-vector space of characteristic functions within H(q), one obtains a one-to-one correspondence between such a code and some substructure of the hexagon. A regular substructure can be viewed as the eigenvector of a certain (0,1)-matrix and the fact that eigenvectors of distinct eigenvalues have to be orthogonal often yields exact values for the intersection number of the according substructures. In my thesis I reveal some unexpected results to this particular technique. Furthermore I classify all distance-2 and -3 ovoids (a maximal set of points mutually at maximal distance) within H(3). As such we obtain a geometrical interpretation of all maximal subgroups of G2(3), a geometric construction of a GAB, the first sporadic examples of ovoid-spread pairings and a transitive 1-system of Q(6,3). Research on derivations of this 1-system was followed by an investigation of common point reguli of different hexagons on the same Q(6,q), with nice applications as a result. Of these, the most important is the alternative construction of the Hölz design and a subdesign. Furthermore we theoretically prove that the Hölz design on 28 points only contains Hermitian and Ree unitals (previously shown by Tonchev by computer). As these Hölz designs are one-point extensions of generalized quadrangles, we dedicate a final chapter to the characterization of the affine extension of H(2) using a combinatorial property

A theoretical and experimental spectroscopy study on methanol and ethanol conversion over H-SAPO-34

The elucidation of the structure-activity relation of zeolites or zeotype materials remains very challenging. Recent advances in both theoretical and experimental techniques provide new opportunities to study these complex materials and any catalytic reaction occurring inside. In order to establish new active reaction routes, the knowledge of formed intermediates is crucial. The characterization of such intermediates can be done using a variety of spectroscopic techniques. In this contribution, methanol and ethanol conversion over H-SAPO-34 is investigated using IR and UV-VIS measurements. Calculated adsorption enthalpies of methanol and ethanol in a large SAPO 44T finite cluster show the stronger adsorption of the larger alcohol by 14 kJ mol-1. Dispersion contributions are found to be crucial. IR spectra are calculated for the clusters containing the adsorbed alcohols and matched with experimental data. In addition, the cluster is also loaded with singly methylated cationic hydrocarbons as these are representative reaction intermediates. A detailed normal mode analysis is performed, enabling to separate the framework-guest contributions. Based on the computed data in situ DRIFT experimental peaks could be assigned. Finally, contemporary DFT functionals such as CAM-B3LYP seem promising to compute gas phase UV-VIS spectra

Exploring new frontiers in modeling complex zeolite-catalyzed reactions using advanced molecular dynamics techniques

We show the potential of advanced molecular dynamics techniques to obtain insight into the complex MTO process by thoroughly studying proton mobility and mapping free energy surfaces of reaction steps at high temperature. The applied methodology can be used to unravel any complex zeolitic process at the nanometer scale level

Shape-selective diffusion of olefins in 8-ring solid acid microporous zeolites

[EN] The diffusion of olefins through 8-ring solid acid microporous zeolites is investigated using molecular dynamics simulations techniques and using a newly developed flexible force field. Within the context of the methanol-to-olefin (MTO) process and the observed product distribution, knowledge of the diffusion paths is essential to obtain molecular level control over the process conditions. Eight-ring zeotype materials are favorably used for the MTO process as they give a selective product distribution toward low-carbon olefins. To investigate how composition, acidity, and flexibility influence the diffusion paths of ethene and propene, a series of isostructural aluminosilicates (zeolites) and silicoaluminophosphates (AlPOs and SAPOs) are investigated with and without randomly distributed acidic sites. Distinct variations in diffusion of ethene are observed in terms of temperature, composition, acidity, and topology (AEI, CHA, AFX). In general, diffusion of ethene is an activated process for which free energy barriers for individual rings may be determined. We observe ring-dependent diffusion behavior which cannot be described solely in terms of the composition and topology of the rings. A new descriptor had to be introduced, namely, the accessible window area (AWA), inspired by implicit solvation models of proteins and small molecules. The AWA may be determined throughout the molecular dynamics trajectories and correlates well with the number of ring crossings at the molecular level and the free energy barriers for ring crossings from one cage to the other. The overall observed diffusivity is determined by molecular characteristics of individual rings for which AWA is a proper descriptor. Temperature-induced changes in framework dynamics and diffusivity may be captured by following the new descriptor throughout the simulations.The computational resources and services used were provided by Ghent University (Stevin Supercomputer Infrastructure). Funding was received from the Research Board of Ghent University (BOF), the Foundation of Scientific Research-Flanders (FWO), and BEL-SPO in the frame of IAP/7/05. V.V.S acknowledges funding from the European Research Council under the European Community's Seventh Framework Programme (FP7(2007-2013) ERC Grant Agreement 240483), and from the European Union's Horizon 2020 research and innovation programme (Consolidator ERC Grant Agreement 647755 - DYNPOR (2015-2020)). G.S. thanks the Spanish government for the provision of Severo Ochoa project (SEV 2012-0267) and SGAI-CSIC for computing time.Ghysels, A.; Moors, S.; Hemelsoet, K.; De Wispelaere, K.; Waroquier, M.; Sastre Navarro, GI.; Van Speybroeck, V. (2015). Shape-selective diffusion of olefins in 8-ring solid acid microporous zeolites. Journal of Physical Chemistry C. 119(41):23721-23734. https://doi.org/10.1021/acs.jpcc.5b06010S23721237341194

Common point reguli of different generalized hexagons on Q(6, q)

AbstractIn this paper, we consider any two split Cayley generalized hexagons represented on the parabolic quadric Q(6,q) and determine their common point reguli. As an application of our results we investigate which 1-systems of Q(6,3) that are a derivation of the exceptional spread of H(3), see [A. De Wispelaere, J. Huizinga, H. Van Maldeghem, Ovoids and spreads of the generalized hexagon H(3), Discrete Math. 305 (1–3) (2005) 299–311], are a spread of some hexagon on this quadric

On the Hall-Janko graph with 100 vertices and the near-octagon of order (2,4)

In this paper, we construct the Hall-Janko graph inside the split Cayley hexagon H(4). Using this construction, we then embed the near-octagon of order (2,4) as a subgeometry of the dual of H(4), with J_2:2 as its automorphism group. These constructions are based on a lemma determining the possibilities for the structure of the intersection of two subhexagons of order 2 in H(4)

A distance-2-spread of the generalized hexagon H(3)

In this paper, we construct a distance-2-spread of the known generalized hexagon of order 3 (the split Cayley hexagon H(3)). Furthermore we prove the uniqueness of this distance-2-spread in H(3) and show that its automorphism group is the linear group L2(13). We remark that a distance-2-spread in any split Cayley hexagon H(q) is a line spread of the underlying polar space Q(6;q) and we construct a line spread of Q(6; 2) that is not a distance-2-spread in any H(2) dened on Q(6; 2)

Some new two-character sets in PG(5, q(2)) and a distance-2 ovoid in the generalized hexagon H(4)

AbstractIn this paper, we construct a new infinite class of two-character sets in PG(5,q2) and determine their automorphism groups. From this construction arise new infinite classes of two-weight codes and strongly regular graphs, and a new distance-2 ovoid of the split Cayley hexagon of order 4