17 research outputs found
Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs
We construct, for any given the
second-order \textit{nonlinear} partial differential equations (PDEs) which are
invariant under the transformations generated by the centrally extended
conformal Galilei algebras. The generators are obtained by a coset construction
and the PDEs are constructed by standard Lie symmetry technique. It is observed
that the invariant PDEs have significant difference for Comment: 22pages, 3figure
On dynamical realizations of l-conformal Galilei and Newton-Hooke algebras
In two recent papers [N. Aizawa, Y. Kimura, J. Segar, J. Phys. A 46 (2013)
405204] and [N. Aizawa, Z. Kuznetsova, F. Toppan, J. Math. Phys. 56 (2015)
031701], representation theory of the centrally extended l-conformal Galilei
algebra with half-integer l has been applied so as to construct second order
differential equations exhibiting the corresponding group as kinematical
symmetry. It was suggested to treat them as the Schrodinger equations which
involve Hamiltonians describing dynamical systems without higher derivatives.
The Hamiltonians possess two unusual features, however. First, they involve the
standard kinetic term only for one degree of freedom, while the remaining
variables provide contributions linear in momenta. This is typical for
Ostrogradsky's canonical approach to the description of higher derivative
systems. Second, the Hamiltonian in the second paper is not Hermitian in the
conventional sense. In this work, we study the classical limit of the quantum
Hamiltonians and demonstrate that the first of them is equivalent to the
Hamiltonian describing free higher derivative nonrelativistic particles, while
the second can be linked to the Pais-Uhlenbeck oscillator whose frequencies
form the arithmetic sequence omega_k=(2k-1), k=1,...,n. We also confront the
higher derivative models with a genuine second order system constructed in our
recent work [A. Galajinsky, I. Masterov, Nucl. Phys. B 866 (2013) 212] which is
discussed in detail for l=3/2.Comment: V2:12 pages,clarifying remarks included into the Introduction and
Conclusion, the version to appear in NP
On dynamical realizations of l-conformal Galilei and Newton-Hooke algebras
In two recent papers [N. Aizawa, Y. Kimura, J. Segar, J. Phys. A 46 (2013)
405204] and [N. Aizawa, Z. Kuznetsova, F. Toppan, J. Math. Phys. 56 (2015)
031701], representation theory of the centrally extended l-conformal Galilei
algebra with half-integer l has been applied so as to construct second order
differential equations exhibiting the corresponding group as kinematical
symmetry. It was suggested to treat them as the Schrodinger equations which
involve Hamiltonians describing dynamical systems without higher derivatives.
The Hamiltonians possess two unusual features, however. First, they involve the
standard kinetic term only for one degree of freedom, while the remaining
variables provide contributions linear in momenta. This is typical for
Ostrogradsky's canonical approach to the description of higher derivative
systems. Second, the Hamiltonian in the second paper is not Hermitian in the
conventional sense. In this work, we study the classical limit of the quantum
Hamiltonians and demonstrate that the first of them is equivalent to the
Hamiltonian describing free higher derivative nonrelativistic particles, while
the second can be linked to the Pais-Uhlenbeck oscillator whose frequencies
form the arithmetic sequence omega_k=(2k-1), k=1,...,n. We also confront the
higher derivative models with a genuine second order system constructed in our
recent work [A. Galajinsky, I. Masterov, Nucl. Phys. B 866 (2013) 212] which is
discussed in detail for l=3/2.Comment: V2:12 pages,clarifying remarks included into the Introduction and
Conclusion, the version to appear in NP
New Directions for Contact Integrators
Contact integrators are a family of geometric numerical schemes which
guarantee the conservation of the contact structure. In this work we review the
construction of both the variational and Hamiltonian versions of these methods.
We illustrate some of the advantages of geometric integration in the
dissipative setting by focusing on models inspired by recent studies in
celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282
The Fifteenth Marcel Grossmann Meeting
The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity
The Fifteenth Marcel Grossmann Meeting
The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity
A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium
When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available