Stratifying On-Shell Cluster Varieties: the Geometry of Non-Planar On-Shell Diagrams

The correspondence between on-shell diagrams in maximally supersymmetric Yang-Mills theory and cluster varieties in the Grassmannian remains largely unexplored beyond the planar limit. In this article, we describe a systematic program to survey such 'on-shell varieties', and use this to provide a complete classification in the case of $G(3,6)$. In particular, we find exactly 24 top-dimensional varieties and 10 co-dimension one varieties in $G(3,6)$---up to parity and relabeling of the external legs. We use this case to illustrate some of the novelties found for non-planar varieties relative to the case of positroids, and describe some of the features that we expect to hold more generally.Comment: 35 pages, 70 figures, and 1 table; also included is a file with explicit details for our classification. Signs corrected in two residue theorems, and a new interpretation (and formula) given for the las

Regional flow model of west Cape Cod and optimization analysis

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 1997.Includes bibliographical references (leaves 48-51).by Susanna Galloni.M.Eng

A sustainable two-phase procedure for V-catalyzed toluene oxidative bromination with H2O2–KBr

A sustainable V(V) and Mo(VI) catalysed two-phase procedure for bromination of toluene under quite mild conditions is proposed; H2O2 is the primary oxidant and KBr is the bromine source; metal precursors are commercially available salts. The reaction is efficient without any additional solvent. By using PhCH3 as a solvent/substrate good yields, together with interesting selectivity toward the formation of PhCH2Br, are obtained with both metal ions. Recycling of the catalytic phase is also possible. Useful information on the V-peroxido chemistry was obtained

Salophen and salen oxo vanadium complexes as catalysts of sulfides oxidation with H 2O 2: Mechanistic insights

The application of V(V) catalysts in oxidation of sulfides with peroxides offers an efficient procedure, that is compatible with different functional groups, and leads to good yields and selectivities. However, the understanding of the factors affecting the reactivity of different catalysts is still far to be complete. An experimental and theoretical study on a series of V(V) complexes containing variously substituted salen and salophen ligands is reported with the aim to correlate the activity of the catalysts with the electronic character of the vanadium center. The results obtained indicate that steric factors play a major role in determining the outcome of the reaction, often overcoming the electronic effects. Theoretical results suggest the intervention in the catalytic cycle of an hydroperoxo vanadium species

Amplituhedron meets Jeffrey-Kirwan Residue

The tree amplituhedra A^(m)_n,k are mathematical objects generalising the notion of polytopes into the Grassmannian. Proposed for m=4 as a geometric construction encoding tree-level scattering amplitudes in planar N=4 super Yang-Mills theory, they are mathematically interesting for any m. In this paper we strengthen the relation between scattering amplitudes and geometry by linking the amplituhedron to the Jeffrey-Kirwan residue, a powerful concept in symplectic and algebraic geometry. We focus on a particular class of amplituhedra in any dimension, namely cyclic polytopes, and their even-dimensional conjugates. We show how the Jeffrey-Kirwan residue prescription allows to extract the correct amplituhedron volume functions in all these cases. Notably, this also naturally exposes the rich combinatorial and geometric structures of amplituhedra, such as their regular triangulations.Peer reviewedFinal Accepted Versio

Investigation of VO-salophen complexes electronic structure

Vanadyl N,N'-bis(salicylidene)-o-phenylenediamine (salophen) complexes have been extensively investigated by cyclic voltammetry, UV-visible spectroscopy and theoretical calculations in MeCN, THF (tetrahydrofuran) and DMF (N,N-dimethylformamide), in order to elucidate the overall factors that influence the electronic density of the metal and therefore the properties of these complexes in various applications. Different substituents were introduced into the salophen skeleton to change the vanadium electron density. Results obtained and here presented showed that the substituents influence the metal electronic character in a way that cannot be easily predicted by considering only the electronic effect. Similarly, the solvent polarity or coordination ability affects the metal complex properties in an unpredictable way. Therefore, experimental and theoretical data here collected are a powerful tool to a priori design salophen ligands to obtain vanadyl complexes having the specific electronic properties suitable for desired applications