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  A NEW CORRESPONDENCE BETWEEN TASEPAND BURGERS’ EQUATION; ; Grotto, Francesco  E-print/Working paper (2020) We introduce a new particle model, which we dub Active Bi-Directional Flow, conjugated to the Totally Asymmetric Exclusion Processin discrete time. We then associate to our model intrinsically stochastic ... [more ▼] We introduce a new particle model, which we dub Active Bi-Directional Flow, conjugated to the Totally Asymmetric Exclusion Processin discrete time. We then associate to our model intrinsically stochastic, non-entropic weak solutions of Burgers’ equation onR, thus linking the latter tothe KPZ universality class. [less ▲] Detailed reference viewed: 36 (2 UL)Burst of Point Vortices and Non-Uniqueness of 2D Euler EquationsGrotto, Francesco ; in arXiv (2020) We give a rigorous construction of solutions to the Euler point vortices system in which three vortices burst out of a single one in a configuration of many vortices, or equivalently that there exist ... [more ▼] We give a rigorous construction of solutions to the Euler point vortices system in which three vortices burst out of a single one in a configuration of many vortices, or equivalently that there exist configurations of arbitrarily many vortices in which three of them collapse in finite time. As an intermediate step, we show that well-known self-similar bursts and collapses of three isolated vortices in the plane persist under a sufficiently regular external perturbation. We also discuss how our results produce examples of non-unique weak solutions to 2-dimensional Euler's equations -- in the sense introduced by Schochet -- in which energy is dissipated. [less ▲] Detailed reference viewed: 64 (4 UL)Rubik's Snakes on a planeGrotto, Francesco ; Perucca, Antonella ; E-print/Working paper (n.d.) Detailed reference viewed: 124 (36 UL) |
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