Search

In this paper, we prove that the trajectories of unreduced $\phi$-simple Chaplygin kinetic systems are reparametrizations of horizontal geodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannian metrics, which are not unique, are obtained explicitly in interesting examples. We also extend these results to $\phi$-simple Chaplygin mechanical systems (not necessarily kinetic).

While the construction of symplectic integrators for Hamiltonian dynamics is well understood, an analogous general theory for Poisson integrators is still lacking. The main challenge lies in overcoming the singular and non-linear geometric behavior of Poisson structures, such as the presence of symplectic leaves with varying dimensions. In this paper, we propose a general approach for the construction of geometric integrators on any Poisson manifold based on independent geometric and dynamic sources of approximation. The novel geometric approximation is obtained by adapting structural results about symplectic realizations of general Poisson manifolds. We also provide an error analysis for the resulting methods and illustrative applications.

The marginal ice zone (MIZ) represents the periphery of the sea ice cover. In this region, the macroscale behavior of the sea ice results from collisions and enduring contact between ice floes. This configuration closely resembles that of dense granular flows, which have been modeled successfully with the $\mu(I)$ rheology. Here, we present a continuum model based on the $\mu(I)$ rheology which treats sea ice as a compressible fluid, with the local sea ice concentration given by a dilatancy function $\Phi(I)$. We infer expressions for $\mu(I)$ and $\Phi(I)$ by nonlinear regression using data produced with a discrete element method (DEM) which considers polygonal-shaped ice floes. We do this by driving the sea ice with a one-dimensional shearing ocean current. The resulting continuum model is a nonlinear system of equations with the sea ice velocity, local concentration, and pressure as unknowns. The rheology is given by the sum of a plastic and a viscous term. In the context of a periodic patch of ocean, which is effectively a one dimensional problem, and under steady conditions, we prove this system to be well-posed, present a numerical algorithm for solving it, and compare its solutions to those of the DEM. These comparisons demonstrate the continuum model's ability to capture most of the DEM's results accurately. The continuum model is particularly accurate for ocean currents faster than 0.25 m/s; however, for low concentrations and slow ocean currents, the continuum model is less effective in capturing the DEM results. In the latter case, the lack of accuracy of the continuum model is found to be accompanied by the breakdown of a balance between the average shear stress and the integrated ocean drag extracted from the DEM.

Methods.We applied distinct selection criteria to attain an SFG sample with minimal AGN contamination. Multiple approaches were used to estimate the intrinsic extinction, SFR and gas-phase metallicity for the SFGs. In conjunction with findings in the literature, we examined the correlation between SFRs and stellar masses ($M_*$), as well as the metallicity evolution depending on $M_*$. Finally, the 3D relationship between $M_*$, SFR and metallicity, is also studied.} Results. From the initial spectroscopic sample of 409 FIR-selected objects from the Lockman--SpReSO catalogue, 69 (17\%) AGNs have been identified and excluded, which is nearly double the percentage found in local studies, leaving a sample of 340 SFGs. The analysis of the $M_*$--SFR relationship revealed that Lockman--SpReSO IR-selected SFGs show signs of evolution at redshifts $z>0.4$, shifting above the main sequence, with a mean value of $\sim0.4$ dex. They are located within the starburst galaxy region since 78\% of the galaxies fall into this category. In addition, no evident flattening was found in the relation to specific SFR with redshift for $\log M_* (M_\odot) \gtrsim 10.5$. In line with the $M_*$--metallicity relation (MZR) outcomes published in previous studies for optically selected SFGs, however, during the analysis of the MZR, it was found that IR-selected SFGs exhibit lower metallicities than those anticipated on the basis of their $M_*$ and redshift. During the investigation of the 3D $M_*$--SFR--metallicity relation (FP), it was established that the research sample is consistent with relations in the existing literature, with an average scatter of $\sim0.2$ dex. However, a re-calibration of the FP when using the SFR obtained from the IR luminosity is required and, in this case, no attenuation in the correlation for $\log M_* (M_\odot) \gtrsim 10.5$ is observed., Comment: 21 pages, 17 figures, accepted in A&A

Polyak's Heavy Ball (PHB; Polyak, 1964), a.k.a. Classical Momentum, and Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well know examples of momentum-descent methods for optimization. While the latter outperforms the former, solely generalizations of PHB-like methods to nonlinear spaces have been described in the literature. We propose here a generalization of NAG-like methods for Lie group optimization based on the variational one-to-one correspondence between classical and accelerated momentum methods (Campos et al., 2023). Numerical experiments are shown., Comment: 24 pages, 2 algorithms, 5 figures

Over the past decades, the increase in both frequency and intensity of large-scale wildfires due to climate change has emerged as a significant natural threat. The pressing need to design resilient landscapes capable of withstanding such disasters has become paramount, requiring the development of advanced decision-support tools. Existing methodologies, including Mixed Integer Programming, Stochastic Optimization, and Network Theory, have proven effective but are hindered by computational demands, limiting their applicability. In response to this challenge, we propose using artificial intelligence techniques, specifically Deep Reinforcement Learning, to address the complex problem of firebreak placement in the landscape. We employ value-function based approaches like Deep Q-Learning, Double Deep Q-Learning, and Dueling Double Deep Q-Learning. Utilizing the Cell2Fire fire spread simulator combined with Convolutional Neural Networks, we have successfully implemented a computational agent capable of learning firebreak locations within a forest environment, achieving good results. Furthermore, we incorporate a pre-training loop, initially teaching our agent to mimic a heuristic-based algorithm and observe that it consistently exceeds the performance of these solutions. Our findings underscore the immense potential of Deep Reinforcement Learning for operational research challenges, especially in fire prevention. Our approach demonstrates convergence with highly favorable results in problem instances as large as 40 x 40 cells, marking a significant milestone in applying Reinforcement Learning to this critical issue. To the best of our knowledge, this study represents a pioneering effort in using Reinforcement Learning to address the aforementioned problem, offering promising perspectives in fire prevention and landscape management, Comment: 20 pages, 15 figures

This paper presents a general method to construct Poisson integrators, i.e., integrators that preserve the underlying Poisson geometry. We assume the Poisson manifold is integrable, meaning there is a known local symplectic groupoid for which the Poisson manifold serves as the set of units. Our constructions build upon the correspondence between Poisson diffeomorphisms and Lagrangian bisections, which allows us to reformulate the design of Poisson integrators as solutions to a certain PDE (Hamilton-Jacobi). The main novelty of this work is to understand the Hamilton-Jacobi PDE as an optimization problem, whose solution can be easily approximated using machine learning related techniques. This research direction aligns with the current trend in the PDE and machine learning communities, as initiated by Physics- Informed Neural Networks, advocating for designs that combine both physical modeling (the Hamilton-Jacobi PDE) and data., Comment: 5 pages, 5 figures

In this paper, we revisit the data for the galaxy cluster ZwCl 0024.0+1652 provided by the GLACE survey and study the mass--metallicity function and its relationship with the environment. Here we describe an alternative way to reduce the data from OSIRIS tunable filters. This method gives us better uncertainties in the fluxes of the emission lines and the derived quantities. We present an updated catalogue of cluster galaxies with emission in H$\alpha$ and [N\,{\sc{ii}}] $\lambda\lambda$6548,6583. We also discuss the biases of these new fluxes and describe the way in which we calculated the mass--metallicity relationship and its uncertainties. We generated a new catalogue of 84 emission-line galaxies with reliable fluxes in [N\,{\sc{ii}}] and H$\alpha$ lines from a list of 174 galaxies. We find a relationship between the clustercentric radius and the density of galaxies. We derived the mass--metallicity relationship for ZwCl 0024.0+1652 and compared it with clusters and field galaxies from the literature. We find a difference in the mass--metallicity relationship when compared to more massive clusters, with the latter showing on average higher values of abundance. This could be an effect of the quenching of the star formation, which seems to be more prevalent in low-mass galaxies in more massive clusters. We find little to no difference between ZwCl 0024.0+1652 galaxies and field galaxies located at the same redshift., Comment: 13 pages, 17 figures, accepted for publication in Astronomy and Astrophysics

The effect of the lattice relaxation at vacancy clusters and interstitial-type dislocation loops on the lifetime of positrons in Zn has been studied. Defective relaxed structures have been generated for the lifetime calculations by using a many-body potential for Zn. From the results, it is inferred that the effect of the atomic relaxation is mainly significant for small vacancy clusters. The lifetime associated with interstitial-type loops is very sensitive to the loop structure and its surroundings. Previous experimental results are compared with the theoretical calculations., Comment: 9 pages, 4 figures, 2 tables

Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as well as the discrete momemtum map under the assumption of symmetric preservation for the discretization map. The procedure described here gives a geometrical construction that can be easily adapted to discretize dynamics on more general structures and open the door to reduction processes., Comment: 4 pages

In this paper we will study some interesting properties of modifications of the Euler-Poincar\'e equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism. The metriplectic representation of the dynamics allows us to describe the conservation of energy, as well as to guarantee entropy production. Moreover, we describe the use of discrete gradient systems to numerically simulate the evolution of the continuous metriplectic equations preserving their main properties: preservation of energy and correct entropy production rate., Comment: 14 pages, 5 figures

Methods. We performed measurements of the \MgII, \MgI, \FeIIa, \FeIIb, and \FeIIc\ spectral lines present in the spectra of the selected sample to determine the EW and velocity of the flows observed in the star-forming galaxies. Subsequently, we conducted $10^7$ bootstrap simulations using Spearman's rank correlation coefficient ($\rho_s$) to explore correlations with galaxy properties. Furthermore, we calculated the covering factor, gas density, and optical depth for the measured \ion{Fe}{II} doublets. Results. Our analysis revealed strong correlations between the EW of \ion{Mg}{II} lines and both $M_{*}$ ($\rho_s=0.43$, 4.5$\sigma$) and SFR ($\rho_s=0.42$, 4.4$\sigma$). For the \ion{Fe}{II} lines, we observed strong correlations between the EW and SFR ($\rho_s\sim0.65$, $>3.9\sigma$), with a weaker correlation for $M_{*}$ ($\rho_s\sim0.35$, $>1.9\sigma$). No notable correlations were found between velocity measurements of \ion{Mg}{II} line and $M_{*}$, SFR, or sSFR of the objects ($\rho_s\sim0.1)$. However, a negative strong correlation was found between the velocity of the \ion{Fe}{II} lines and the SFR of the galaxies ($\rho_s\sim-0.45$, $\sim3\sigma$). Our results align with previous studies but studying FIR-selected objects. Finally, we detected a candidate \textit{loitering outflow}, a recently discovered subtype of FeLoBAL quasar, at redshift of $z=1.4399$, exhibiting emission in \ion{C}{III}] and low line velocities ($|v|\lesssim$ 200 km/s)., Comment: 25 pages, 31 figures

Since its mission, Fermi Collaboration reported the highest flux observed during July - September 2012 for the BL Lac Markarian 421 (Mrk 421). The integrated flux was eight times greater than the average flux reported in the second Fermi catalog. During April 2013, Mrk 421 exhibited the highest TeV $\gamma$-ray and optical fluxes recorded. The Telescope Array (TA) collaboration reported the arrival of 72 ultra-high-energy cosmic rays (UHECRs), two in temporal and positional coincidence with the flaring activity observed in 2012 and one with the flaring activity in 2013. The IceCube collaboration has reported around 100 neutrino events in the High-Energy Starting Events (HESE) catalog. Although no neutrino track-like event has been associated with this source, a neutrino shower-like event (IC31) is in temporal and positional coincidence with the flare in 2012. Describing the broadband spectral energy distribution during the flaring activities exhibited in 2012 and 2013 with one- and two-zone lepto-hadronic scenarios and one-zone SSC model, we study a possible correlation between the neutrino event IC31 and the three UHECRs. We estimate the number of neutrino and UHECR events generated from the proposed models, and show that while the neutrino events are low to associate the event IC31 with Mrk 421, the number of UHECRs are similar to those reported by TA collaboration., Comment: 20 pages, 5 figures, 7 Tables

We present some examples that refute two recent results in the literature concerning the equality of the domination and matching numbers for power and generalized power hypergraphs. In this note we pinpoint the flaws in the proofs and suggest how they may be mended., Comment: 7 pages, 1 figure, XIII Encuentro Andaluz de Matem\'atica Discreta, (C\'adiz) Spain, july, 2023

We extend known constructions of almost-Poisson brackets and their gauge transformations to nonholonomic systems whose Lagrangian is not mechanical but possesses a gyroscopic term linear in the velocities. The new feature introduced by such a term is that the Legendre transformation is an affine, instead of linear, bundle isomorphism between the tangent and cotangent bundles of the configuration space and some care is needed in the development of the geometric formalism. At the end of the day, the affine nature of the Legendre transform is reflected in the affine dependence of the brackets that we construct on the momentum variables. Our study is motivated by a wide class of nonholonomic systems involving rigid bodies with internal rotors which are of interest in control. Our construction provides a natural geometric framework for the (known) Hamiltonisations of the Suslov and Chaplygin sphere problems with a gyrostat., Comment: 39 pages

This work presents a general geometric framework for simulating and learning the dynamics of Hamiltonian systems that are invariant under a Lie group of transformations. This means that a group of symmetries is known to act on the system respecting its dynamics and, as a consequence, Noether's Theorem, conserved quantities are observed. We propose to simulate and learn the mappings of interest through the construction of $G$-invariant Lagrangian submanifolds, which are pivotal objects in symplectic geometry. A notable property of our constructions is that the simulated/learned dynamics also preserves the same conserved quantities as the original system, resulting in a more faithful surrogate of the original dynamics than non-symmetry aware methods, and in a more accurate predictor of non-observed trajectories. Furthermore, our setting is able to simulate/learn not only Hamiltonian flows, but any Lie group-equivariant symplectic transformation. Our designs leverage pivotal techniques and concepts in symplectic geometry and geometric mechanics: reduction theory, Noether's Theorem, Lagrangian submanifolds, momentum mappings, and coisotropic reduction among others. We also present methods to learn Poisson transformations while preserving the underlying geometry and how to endow non-geometric integrators with geometric properties. Thus, this work presents a novel attempt to harness the power of symplectic and Poisson geometry towards simulating and learning problems., Comment: 32 pages, 19 figures

Besides the neutrino source detected by IceCube, NGC 1068, the association of the IceCube-170922A neutrino with the blazar in a flaring state among several wavelengths (from radio up to high-energy (HE) gamma-rays), the site and mechanisms of production of HE neutrino remains in discussion. Extragalactic sources such as Quasars, Blazars, Radio galaxies, and Gamma-ray bursts have been proposed as progenitors of HE neutrinos. In this work, we study the Blazars reported by Fermi-LAT in the 4LAC catalog, which are embedded inside the 90\% error of the best-fit position from the neutrinos reported by IceCube. We propose a one-zone lepto-hadronic scenario to describe the broadband Spectral Energy Distribution and then estimate the number of neutrinos to compare with those in the direction of each source. A brief discussion is provided of the results., Comment: 7 pages

We generalise the dynamic Laplacian introduced in (Froyland, 2015) to a dynamic $p$-Laplacian, in analogy to the generalisation of the standard $2$-Laplacian to the standard $p$-Laplacian for $p>1$. Spectral properties of the dynamic Laplacian are connected to the geometric problem of finding "coherent" sets with persistently small boundaries under dynamical evolution, and we show that the dynamic $p$-Laplacian shares similar geometric connections. In particular, we prove that the first eigenvalue of the dynamic $p$-Laplacian with Dirichlet boundary conditions exists and converges to a dynamic version of the Cheeger constant introduced in (Froyland, 2015) as $p\rightarrow 1$. We develop a numerical scheme to estimate the leading eigenfunctions of the (nonlinear) dynamic $p$-Laplacian, and through a series of examples we investigate the behaviour of the level sets of these eigenfunctions. These level sets define the boundaries of sets in the domain of the dynamics that remain coherent under the dynamical evolution.

We study the dynamics of contact mechanical systems on Lie groups that are invariant under a Lie group action. Analogously to standard mechanical systems on Lie groups, existing symmetries allow for reducing the number of equations. Thus, we obtain Euler-Poincar\'e-Herglotz equations on the extended reduced phase space $\mathfrak{g}\times \R$ associated with the extended phase space $TG\times \R$, where the configuration manifold $G$ is a Lie group and $\mathfrak{g}$ its Lie algebra. Furthermore, we obtain the Hamiltonian counterpart of these equations by studying the underlying Jacobi structure. Finally, we extend the reduction process to the case of symmetry-breaking systems which are invariant under a Lie subgroup of symmetries., Comment: 38 pages

A new procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the discretization rule rather than viceversa. As a result, the constraint submanifold is exactly preserved by the discrete flow and the extension of the methods to the case of non-linear configuration spaces is straightforward.

Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to a higher-order tangent bundle to construct geometric integrators for the higher-order Euler-Lagrange equations. Given a cost function, an optimal control problem for fully actuated mechanical systems can be understood as a higher-order variational problem. In this paper we introduce the notion of a higher-order discretization map associated with a retraction map to construct geometric integrators for the optimal control of mechanical systems. In particular, we study applications to path planning for obstacle avoidance of a planar rigid body., Comment: 8 pages

In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods., Comment: 8 pages, conference paper