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Abstract We considertoric dynamical systems, which are also calledcomplex-balanced mass-action systems. These are remarkably stable polynomial dynamical systems that arise from the analysis of mathematical models of reaction networks when, under the assumption of mass-action kinetics, they can give rise tocomplex-balanced equilibria. Given a reaction network, we study theset of parameter valuesfor which the network gives rise to toric dynamical systems, also calledthe toric locusof the network. The toric locus is an algebraic variety, and we are especially interested in its topological properties. We show that complex-balanced equilibriadepend continuouslyon the parameter values in the toric locus, and, using this result, we prove that the toric locus has a remarkableproduct structure: it is homeomorphic to the product of the set of complex-balanced flux vectors and the affine invariant polyhedron of the network. In particular, it follows that the toric locus is acontractible manifold. Finally, we show that the toric locus is invariant with respect to bijective affine transformations of the generating reaction network.
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Multiscale simulation of plastic transformations: The case of base‐assisted dehydrochlorination of polyvinyl chloride
Abstract Plastic transformations are critical to ongoing recycling and upcycling efforts, but the complexity of the reactions makes it difficult to understand the effect of individual factors on reaction rates and product distributions experimentally. In this work, we report on a multiscale simulation framework for studying polymer transformations that incorporates affordable high‐level coupled cluster calculations combined with benchmarked density functional theory calculations, detailed conformer search, and lattice‐based kinetic Monte Carlo simulations to provide the temporal and spatial evolution of the polymer during transformations. Our framework can match experimentally observed reaction times within an order of magnitudewithoutany parameter estimation in base‐assisted dehydrochlorination of polyvinyl chloride. We determine that the E2 reaction mechanism dominates the reaction and demonstrate that different structural defects can inhibit or promote directional polyene growth as well as affect the structure of the dehydrochlorination product.
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- PAR ID:
- 10641502
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- AIChE Journal
- Volume:
- 70
- Issue:
- 12
- ISSN:
- 0001-1541
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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