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• W4315797755 abstract "In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a $b$-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in $b$-cotangent bundles featuring two models: the canonical (or non-twisted) model and the twisted one. The first one models systems on manifolds with boundary and the twisted model represents Hamiltonian systems where the singularity of the system is in the fiber of the bundle. The twisted cotangent model includes (for linear potentials) the case of fluids with dissipation. We relate the complexity of the fluids in terms of the Reynolds number and the (non)-existence of cotangent lift dynamics. We also discuss more general physical interpretations of the twisted and non-twisted $b$-symplectic models. These models offer a Hamiltonian formulation for systems which are dissipative, extending the horizons of Hamiltonian dynamics and opening a new approach to study non-conservative systems." @default.
• W4315797755 created "2023-01-13" @default.
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• W4315797755 date "2023-04-01" @default.
• W4315797755 modified "2023-10-18" @default.
• W4315797755 title "Singular cotangent models in fluids with dissipation" @default.
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• W4315797755 doi "https://doi.org/10.1016/j.physd.2023.133655" @default.
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