Published in Lecture Notes in Computer Science, Springer, 2024
We present a framework for generalizing tropical homotopy continuation for computing stable intersections of tropical hypersurfaces, tropical linear spaces, and tropical inverted linear spaces. We also report on beginning implementations in OSCAR.
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Published in SIGMA 20 (2024), 2024
We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated to the cominuscule representation of \(E_6\). The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the \(E_n\) Dynkin diagrams for \(n\leq 6\). We conjecture the existence of a further finite type LPA, associated to the Freudenthal variety of type \(E_7\).
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Published in APS-DFD 2020, Chicago, 2020
We present a numerical solver based on the opensource finite volume library OpenFOAM that solves the filtered two-fluid equations for fluidized gas-particle flows using a wide range of diverse models developed in recent literature. We illustrate the phase coupling algorithm and discuss the implementation of the model of Sarkar et al. (2016). Finally, we compare the predictions from different constitutive models against experimental results using very coarse grids.
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