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Gaset J, Gràcia X, Muñoz-Lecanda Mc, Rivas X, Román-Roy NAuthor

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March 14, 2024
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A K-contact Lagrangian formulation for nonconservative field theories

Publicated to: Reports On Mathematical Physics. 87 (3): 347-368 - 2021-01-01 87(3), DOI: 10.1016/S0034-4877(21)00041-0

Authors:

Gaset J; Gràcia X; Muñoz-Lecanda MC; Rivas X; Román-Roy N
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Affiliations

Department of Mathematics, Universitat Politècnica de Catalunya, Campus Nord edifici C3, C/ Jordi Girona 1, Barcelona, Catalonia 08034, Spain - Author
Department of Physics, Universitat Autònoma de Barcelona, Campus UAB, Facultat Ciències Nord, Bellaterra, Catalonia 08193, Spain - Author

Abstract

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 where we introduced the notion of k-contact structure, and obtained a modified version of the De Donder–Weyl equations of covariant Hamiltonian field theory. In this paper we continue this study by presenting a k-contact Lagrangian formulation for nonconservative field theories. The Lagrangian density is defined on the product of the space of k-velocities times a k-dimensional Euclidean space with coordinates sα, which are responsible for the dissipation. We analyze the regularity of such Lagrangians; only in the regular case we obtain a k-contact Hamiltonian system. We study several types of symmetries for k-contact Lagrangian systems, and relate them with dissipation laws, which are analogous to conservation laws of conservative systems. Several examples are discussed: we find contact Lagrangians for some kinds of second-order linear partial differential equations, with the damped membrane as a particular example, and we also study a vibrating string with a magnetic-like term. © 2021 Polish Scientific Publishers
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Keywords

Contact structureDissipationField theoryK-contact structureK-symplectic structureLagrangian system

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Reports On Mathematical Physics, and although the journal is classified in the quartile Q4 (Agencia WoS (JCR)), its regional focus and specialization in Physics, Mathematical, give it significant recognition in a specific niche of scientific knowledge at an international level.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations from Scopus Elsevier, it yields a value for the Field-Weighted Citation Impact from the Scopus agency: 1.96, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 13, 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-12-20, the following number of citations:

  • Scopus: 19
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Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-12-20:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 10.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 10 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 1.
  • The number of mentions on the social network X (formerly Twitter): 3 (Altmetric).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
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Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (GASET RIFA, JORDI) .

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