Now showing items 1-15 of 15

    • A contact geometry framework for field theories with dissipation 

      Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso (2020-03-01)
      Article
      Open Access
      We develop a new geometric framework suitable for dealing with Hamiltonian field theories with dissipation. To this end we define the notions of k-contact structure and k-contact Hamiltonian system. This is a generalization ...
    • A K-contact Lagrangian formulation for nonconservative field theories 

      Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso (2021-06-01)
      Article
      Open Access
      Dynamical systems with dissipative behaviour can be described in terms of contact manifolds and a modified version of Hamilton's equations. Dissipation terms can also be added to field equations, as showed in a recent paper ...
    • Griffiths variational multisymplectic formulation for Lovelock gravity 

      Capriotti, Santiago; Gaset Rifà, Jordi; Román Roy, Narciso; Salomone, Leandro (2020-08-24)
      Article
      Open Access
      This work is mainly devoted to constructing a multisymplectic description of Lovelock’s gravity, which is an extension of General Relativity. We establish the Griffiths variational problem for the Lovelock Lagrangian, ...
    • Higher-order contact mechanics 

      De León, Manuel; Gaset Rifà, Jordi; Lainz Valcázar, Manuel; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso (Elsevier, 2021-02-01)
      Article
      Open Access
      We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent ...
    • Multicontact formulation for non-conservative field theories 

      de León Rodríguez, Manuel; Gaset Rifà, Jordi; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso (Institute of Physics (IOP), 2023-01-13)
      Article
      Restricted access - publisher's policy
      A new geometric structure inspired by multisymplectic and contact geometries, which we call multicontact structure, is developed to describe non-conservative classical field theories. Using the differential forms that ...
    • A multisymplectic approach to gravitational theories 

      Gaset Rifà, Jordi (Universitat Politècnica de Catalunya, 2018-07-25)
      Doctoral thesis
      Open Access
      The theories of gravity are one of the most important topics in theoretical physics and mathematical physics nowadays. The classical formulation of gravity uses the Hilbert-Einstein Lagrangian, which is a singular ...
    • Multisymplectic formalism for cubic horndeski theories 

      Doniz Hernández, Mauricio; Gaset Rifà, Jordi (2023-07-10)
      Article
      Restricted access - publisher's policy
      We present the covariant multisymplectic formalism for the so-called cubic Horndeski theories and discuss the geometrical and physical interpretation of the constraints that arise in the uni¿ed Lagrangian-Hamiltonian ...
    • Multisymplectic unified formalism for Einstein-Hilbert gravity 

      Gaset Rifà, Jordi; Román Roy, Narciso (2018-03-01)
      Article
      Open Access
      We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of ...
    • New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries 

      Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier; Román Roy, Narciso (2020-06-01)
      Article
      Open Access
      We provide new insights into the contact Hamiltonian and Lagrangian formulations of dissipative mechanical systems. In particular, we state a new form of the contact dynamical equations, and we review two recently presented ...
    • New multisymplectic approach to the Metric-Affine (Einstein-Palatini) action for gravity 

      Gaset Rifà, Jordi; Román Roy, Narciso (American Institute of Mathematical Sciences, 2019-09-01)
      Article
      Open Access
      We present a covariant multisymplectic formulation for the Einstein-Palatini (or Metric-Affine) model of General Relativity (without energy-matter sources). As it is described by a first-order affine Lagrangian (in the ...
    • Order reduction, projectability and constrainsts of second-order field theories and higuer-order mechanics 

      Gaset Rifà, Jordi; Román Roy, Narciso (2016-12-01)
      Article
      Open Access
      The consequences of the projectability of Poincar\'e-Cartan forms in a third-order jet bundle $J^3\pi$ to a lower-order jet bundle are analyzed using the constraint algorithm for the Euler-Lagrange equations in $J^3\pi$. ...
    • The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model 

      Adame Carrillo, David; Gaset Rifà, Jordi; Román Roy, Narciso (springer-Verlag, 2022-01-01)
      Article
      Open Access
      In general, the system of 2nd-order partial differential equations made of the Euler–Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. ...
    • Time-dependent contact mechanics 

      de León Rodríguez, Manuel; Gaset Rifà, Jordi; Gràcia Sabaté, Francesc Xavier; Muñoz Lecanda, Miguel Carlos; Rivas Guijarro, Xavier (2022-09-16)
      Article
      Open Access
      Contact geometry allows us to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this ...
    • Unified Lagrangian-Hamiltonian formalism for contact systems 

      De León, Manuel; Gaset Rifà, Jordi; Lainz Valcázar, Manuel; Rivas Guijarro, Xavier; Román Roy, Narciso (2020-06-23)
      Article
      Open Access
      We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of contact autonomous mechanical systems, which is based on the approach of the pioneering work of R. Skinner and R. ...
    • Variational principles and symmetries on fibered multisymplectic manifolds 

      Gaset Rifà, Jordi; Prieto Martínez, Pedro Daniel; Román Roy, Narciso (2016-12-01)
      Article
      Open Access
      The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multi-symplectic structure. Then, for the corresponding variational equations, conserved quantities ...