xavi

Xavier Rivas

Escuela Superior en Ingeniería y Tecnología, Universidad Internacional de La Rioja

e-mail
xavier.rivas(at)unir.net
xavier.rivas(at)upc.edu
web page
xavirivas.com
ORCID code
ResearcherID
GQI-1759-2022
MR Author ID
1375865
Scopus ID
57215094927
Other links
Google Scholar
ResearchGate
arxiv.org
Zotero

■ Research

I develop my research in differential geometry and its applications to mathematical physics, mechanics and field theory. I am part of the GEOMVAP group. We collaborate with other groups, in particular with those in the Geometry, Mechanics and Control Network.

My PhD advisors were Narciso Román-Roy and Xavier Gràcia Sabaté. You can find my thesis here.

List of publications:
  1. L. Colombo, J. de Lucas, X. Rivas and B. M. Zawora, "An energy-momentum method for ordinary differential equations with an underlying k-polysymplectic manifold". Preprint. arxiv: 2311.15035
  2. J. de Lucas, X. Rivas and M. Zając, "Hamiltonian stochastic Lie systems and applications". Preprint. arxiv: 2307.06232
  3. X. Gràcia, J. de Lucas, X. Rivas and N. Román-Roy, "On Darboux theorems for geometric structures induced by closed forms". Preprint. arxiv: 2306.08556
  4. X. Rivas, M. Salgado and S. Souto, "Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws". Preprint. arxiv: 2304.00833
  5. J. de Lucas, X. Rivas, S. Vilariño and B. M. Zawora, "On k-polycosymplectic Marsden–Weinstein reductions". J. Geom. Phys. 191:104899, 2023. arxiv: 2302.09037 doi: 10.1016/j.geomphys.2023.104899
  6. J. Gaset, A. López-Gordón and X. Rivas, "Symmetries, conservation and dissipation in time-dependent contact systems". Fortschr. Phys. 71(8-9):2300048, 2023. arxiv: 2212.14848 doi: 10.1002/prop.202300048
  7. J. Gaset, M. Lainz, A. Mas and X. Rivas, "The Herglotz variational principle for dissipative field theories". Preprint. arxiv: 2211.17058
  8. X. Rivas, "Nonautonomous k-contact field theories". J. Math. Phys. 64(3):033507, 2023. arxiv: 2210.09166 doi: 10.1063/5.0131110
  9. M. de León, J. Gaset, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy, "Multicontact formulation for non-conservative field theories". J. Phys. A: Math. Theor. 56(2):025201, 2023. arxiv: 2209.08918 doi: 10.1088/1751-8121/acb575
  10. M. de León, M. Lainz, A. López-Gordón and X. Rivas, "Hamilton–Jacobi theory and integrability for autonomous and non-autonomous contact systems". J. Geom. Phys. 187:104787, 2023. arxiv: 2208.07436 doi: 10.1016/j.geomphys.2023.104787
  11. J. de Lucas and X. Rivas, "Contact Lie systems: theory and applications". J. Phys. A: Math. Theor. 56(33):335203, 2023. arxiv: 2207.04038 doi: 10.1088/1751-8121/ace0e7
  12. X. Rivas and D. Torres, "Lagrangian–Hamiltonian formalism for cocontact systems". J. Geom. Mech. 15(1):1-26, 2023. arxiv: 2205.14757 doi: 10.3934/jgm.2023001
  13. M. de León, J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda and X. Rivas, "Time-dependent contact mechanics". Monatsh. Math. 201:1149-1183, 2023. arxiv: 2205.09454 doi: 10.1007/s00605-022-01767-1
  14. J. de Lucas, X. Gràcia, X. Rivas, N. Román-Roy and S. Vilariño, "Reduction and reconstruction of multisymplectic Lie systems". J. Phys. A: Math. Theor. 55(29):295204, 2022. arxiv: 2202.13748 doi: 10.1088/1751-8121/ac78ab
  15. X. Gràcia, X. Rivas and N. Román-Roy, "Skinner–Rusk formalism for k-contact systems". J. Geom. Phys. 172:104429, 2022. arxiv: 2109.07257 doi: 10.1016/j.geomphys.2021.104429
  16. M. de León, J. Gaset, M. Lainz-Valcázar, X. Rivas and N. Román-Roy, "Unified Lagrangian-Hamiltonian formalism for contact systems". Fortschr. Phys. 68 (8):2000045, 2020. arxiv: 2003.13037 doi: 10.1002/prop.202000045
  17. J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy, "A k-contact Lagrangian formulation for nonconservative field theories". Rep. Math. Phys., 87 (3):347-368, 2021. arxiv: 2002.10458 doi: 10.1016/S0034-4877(21)00041-0
  18. J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy, "New contributions to the Hamiltonian and Lagrangian contact formalisms for dissipative mechanical systems and their symmetries". Int. J. Geom. Methods Mod. Phys., 17 (6):2050090, 2020. arxiv: 1907.02947, doi: 10.1142/S0219887820500905
  19. J. Gaset, X. Gràcia, M. C. Muñoz-Lecanda, X. Rivas and N. Román-Roy, "A contact geometry framework for field theories with dissipation". Ann. Phys., 414:168090, 2020. arxiv: 1905.07354, doi: 10.1016/j.aop.2020.168092
  20. X. Gràcia, X. Rivas and N. Román-Roy, "Constraint algorithm for singular field theories in the k-cosymplectic framework". J. Geom. Mech., 12 (1):1-23, 2020. arxiv: 1812.08487, doi: 10.3934/jgm.2020002
Collaborators:

Some of the colleagues I have collaborated with are:

■ Teaching

Grado en Matemática Computacional

Universidad Internacional de La Rioja. UNIR.

Grado en Matemática Computacional

Universidad Internacional de La Rioja. UNIR.

Grado en Física

Universidad Internacional de La Rioja. UNIR.

Grado en Física

Universidad Internacional de La Rioja. UNIR.

Grado en Economia

Universidad Internacional de La Rioja. UNIR.

Old courses