Now showing items 1-14 of 14

    • Computability and Beltrami fields in Euclidean space 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta-Salas, Daniel (2022-11-12)
      Article
      Open Access
      In this article, we pursue our investigation of the connections between the theory of computation and hydrodynamics. We prove the existence of stationary solutions of the Euler equations in Euclidean space, of Beltrami ...
    • Constructing Turing complete Euler flows in dimension 3 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta-Salas, Daniel; Presas, Francisco (2021-05-11)
      Article
      Open Access
      Can every physical system simulate any Turing machine? This is a classical problem which is intimately connected with the undecidability of certain physical phenomena. Concerning fluid flows, Moore asked in [15] if ...
    • Euler flows and singular geometric structures 

      Miranda Galcerán, Eva; Cardona Aguilar, Robert; Peralta-Salas, Daniel (Royal Society, 2019)
      Article
      Open Access
      Tichler proved in [24] that a manifold admitting a smooth non vanishing and closed one-form bers over a circle. More generally a manifold admitting k independent closed one-forms bers over a torus Tk. In this article we ...
    • Integrable Systems in singular symplectic manifolds 

      Cardona Aguilar, Robert (Universitat Politècnica de Catalunya, 2018-07)
      Master thesis
      Open Access
      En aquest treball es presenten les nocions de geometria simplèctica, de Poisson i b-simplèctica. En cada cas està demostrat un teorema de Arnold-Liouville per a sistemes integrables. Desprès de demostrar una part d'aquests ...
    • Integrable systems on singular symplectic manifolds: from local to global 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva (2021-09-22)
      Article
      Open Access
      In this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes ...
    • Integrable systems on singular symplectic manifolds: from local to global 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva (2020-09)
      Research report
      Open Access
      In this article we consider integrable systems on manifolds endowed with singular sym-plectic structures of order one. By singular symplectic structures of order one we mean structureswhich are symplectic away from an ...
    • Looking at Euler flows through a contact mirror: universality and undecidability 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta-Salas, Daniel (European Mathematical Society (EMS), 2021)
      Conference report
      Open Access
      The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. In recent papers by Cardona, Miranda, and Peralta- Salas, several unknown facets of the Euler flows ...
    • On the volume elements of a manifold with transverse zeroes 

      Miranda Galcerán, Eva; Cardona Aguilar, Robert (Springer, 2019)
      Article
      Open Access
      Moser proved in 1965 in his seminal paper [15] that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if their associated cohomology classes in ...
    • Reeb embeddings and universality of Euler flows 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta Salas, Daniel; Presas, Francisco (Springer, 2021)
      Part of book or chapter of book
      Open Access
      We use a new geometrical approach to the universality of Euler flows. By proving flexibility results on embeddings for Reeb flows in contact topology, we deduce some new universal properties for Euler flows. As a byproduct, ...
    • Symplectic toric manifolds, Delzant theorem and integrable sytems 

      Cardona Aguilar, Robert (Universitat Politècnica de Catalunya, 2017-07)
      Bachelor thesis
      Open Access
      En aquesta tesi estudiarem la relació entre les varietats simplèctiques tòriques i els sistemes integrables. Per això, presentem en primer lloc tots els preliminars necessaris de geometria simplèctica. Després presentem ...
    • The geometry and topology of steady Euler flows, integrability and singular geometric structures 

      Cardona Aguilar, Robert (Universitat Politècnica de Catalunya, 2021-05-26)
      Doctoral thesis
      Open Access
      In this thesis, we make a deep investigation of the geometry and dynamics of several objects (singular or not) appearing in nature. The main goal is to study rigidity versus flexibility dynamical behavior of the objects ...
    • Turing universality of the incompressible Euler equations and a conjecture of Moore 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta-Salas, Daniel (2021-08-24)
      Article
      Open Access
      In this article, we construct a compact Riemannian manifold of high dimension on which the time-dependent Euler equations are Turing complete. More precisely, the halting of any Turing machine with a given input is equivalent ...
    • Universality of Euler flows and flexibility of Reeb embeddings 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta-Salas, Daniel; Presas, Francisco (2019-11-05)
      Research report
      Open Access
      The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier ...
    • Universality of Euler flows and flexibility of Reeb embeddings 

      Cardona Aguilar, Robert; Miranda Galcerán, Eva; Peralta Salas, Daniel; Presas, Francisco (Elsevier, 2023-09-01)
      Article
      Open Access
      The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao [38], [39] launched a programme to address the global existence problem for the Euler and ...