Artículos (Matemática Aplicada I)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10894

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Stability of parametrically driven, damped nonlinear Dirac solitons
(American Institute of Physics, 2025-08-22) Sánchez-Rey, Bernardo; Mellado-Alcedo, David; Quintero, Niurka R.; Física Aplicada I; Matemática Aplicada I; Junta de Andalucía; Ministerio de Ciencia e Innovación (MICIN). España; Universidad de Sevilla; FQM392: Física Interdisciplinar y de no Equilibrio; FQM415: Modelado Físico-Matemático de Sistemas no Lineales
The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the linearization of this equation around the exact solutions. On the one hand, it is proven that one of these solutions is always unstable, which confirms previous analysis based on a variational method. On the other hand, it is shown that sufficiently large dissipation guarantees the stability of the second solution. Specifically, we determine the stability curve that separates stable and unstable regions in the parameter space. The dependence of the stability diagram on the driven frequency is also studied, and it is shown that low-frequency solitons are stable across the entire parameter space. These results have been corroborated with extensive simulations of the parametrically driven and damped nonlinear Dirac equation by employing a novel and recently proposed numerical algorithm that minimizes discretization errors. The nonlinear Dirac equation has attracted a lot of attention in recent years. Far from being restricted to the realm of high-energy particle physics, it also describes nonlinear excitations in other fields, such as nonlinear optics and Bose-Einstein condensates. Since these kinds of systems are susceptible to being controlled and manipulated, they constitute an excellent benchmark to study relativistic solitons. Moreover, dissipative losses, present in all physical systems, cause a decay of the soliton amplitude. Therefore, an interesting question is whether a parametric force can inject energy from outside to compensate for the losses in such a way that the soliton becomes stable. In this paper, this question is answered affirmatively. In fact, we prove that one exact stationary soliton solution of the parametrically driven and damped nonlinear Dirac equation is linearly stable in the majority of the parameter space. Furthermore, it is shown that instability regions tend to disappear for sufficiently low frequencies.
Expected Shot impact Timing (xSIT) and other advanced metrics as indicators of performance in English men’s and women’s professional football
(MDPI, 2025-10-02) Cruz Torres, Blanca de la; Navarro Castro, Miguel; Ruiz de Alarcón Quintero, Anselmo; Fisioterapia; Matemática Aplicada I
Blackground: Football performance analysis has grown rapidly in recent years, with increasing interest in advanced metrics to more accurately evaluate both individual and team performance. The aim of this study was to examine the utility of the Expected Shots Impact Timing (xSIT) metric as an indicator of shooting performance in English professional football, specifically in the men’s Premier League (PL) and the Women’s Super League (WSL). Methods: A total of 9831 shots from the PL (2015/16 season) and 3219 shots from the WSL (2020/21 season) were analyzed. Data were obtained from publicly accessible football databases. The variables examined included goals, Possession Value (PV), Expected Goals (xG), Expected Goals on Target (xGOT), and xSIT. All variables were normalized per match (90 min). Descriptive statistics, correlational analyses, and comparative analyses between leagues. Results: The WSL exhibited a significantly higher PV than the PL (p < 0.001), whereas the remaining metrics showed no significant differences between leagues (p > 0.05). Moreover, in the WSL, all performance indicators displayed very strong correlations with goals, while in the PL, similarly strong associations were observed, except for PV, which showed only a weak relationship. Conclusions: the xSIT metric, as an indicator of shooting performance, may be regarded as an influential factor in determining match outcomes across both leagues.
Well-balanced physics-based finite volume schemes for Saint-Venant–Exner-type models of sediment transport
(Elsevier, 2025) Bürguer, Raimund; Fernández Nieto, Enrique Domingo; Garres-Díaz, José; Moya Abuhadba, Jorge Johnny; Matemática Aplicada I; Matemática Aplicada II; Junta de Andalucía; European Union (UE)
The Saint-Venant–Exner (SVE) model is widely used for the description of sediment transport including bedload, erosion, and deposition processes. A modified version of the SVE model, which includes sediment concentration, incorporates exchange of sediment between the fluid and an erodible bed and a non-hydrostatic pressure for the fluid along with non-equilibrium entrainment and deposition velocities, is introduced. Gravitational effects on erosion are described by an effective shear stress formulation. This modified SVE model is derived from a general approach with density variations. It preserves the mass of both the sediment and the fluid, and satisfies a dissipative energy balance. On the other hand, well-balanced finite volume schemes adapted for SVE models are derived since standard well-balanced schemes for the Saint-Venant system with fixed bottom are in general no more well-balanced when applied to the SVE model. The latter property is due to the uncontrolled numerical diffusion associated with the bed evolution equation. Two novel techniques to achieve the well-balanced property for the modified SVE model are proposed. The first is a new polynomial-viscosity-matrix-based (PVM) scheme, denoted “PVM-2I”, that modifies the numerical approximation of the bed evolution equation according to its related characteristic speed. The second is a physically motivated correction of the numerical diffusion term for the Rusanov and Harten–Lax–van Leer (HLL) schemes. The proposed schemes are positivity-preserving for the water height. Numerical solutions are compared with exact solutions with gravitational effects, with a novel exact solution in non-equilibrium conditions, and with experimental data. It is illustrated how the use of standard non-well-balanced schemes leads to a large artificial (unphysical) erosion and completely degraded solutions. This undesirable behaviour is avoided by the proposed well-balanced schemes. Moreover, it is demonstrated that for dam-break flows the inclusion of non-hydrostatic pressure improves the prediction of the water surface and sediment evolution, while for overtopping flow erosion tests, accounting for erosion–deposition exchanges between the bedload and suspended sediment layers leads to better agreement with experimental data.
A Third-Order Finite Volume Semi-Implicit Method for the Shallow Water-Exner Model
(Springer, 2025) Fernández Nieto, Enrique Domingo; Garres-Díaz, José; Macca, Emanuele; Russo, Giovanni; Matemática Aplicada I; Matemática Aplicada II; Junta de Andalucía; European Union; Ministerio de Ciencia e Innovación (MICIN). España
In this work, third-order semi-implicit schemes on staggered meshes for the shallow water and Saint-Venant-Exner systems are presented. They are based on a third-order extension of the technique introduced in Casulli & Cheng [15]. The stability conditions for these schemes depend on the velocity and not on the celerity, allowing us to reduce computational efforts, especially in subcritical flow simulations, which is the regime we are mainly interested in. The main novelty consists in the third-order approximation of the pressure gradient term in the momentum equation through appropriate polynomial reconstructions. Concretely, CWENO conservative reconstruction is considered for the water thickness h and a centered fourth-degree polynomial is adopted interpolating the cell averages of the free surface n. For time discretization, a third-order IMEX scheme is applied. In addition, a novel time-dependent semi-analytical solution for Saint-Venant-Exner system is introduced and compared with the numerical ones. Several tests are performed, including accuracy tests showing third-order accuracy, well-balance tests, and simulations of slow bedload processes for large time.
Analysis of Shots Trajectory and Effectiveness in Women’s and Men’s Football European Championship Matches
(MDPI, 2025-06-12) Cruz Torres, Blanca de la; Navarro Castro, Miguel; Ruiz-de-Alarcón-Quintero, Anselmo; Matemática Aplicada I; Fisioterapia
Shots on target are a crucial factor in football performance, yet the impact of categorizing shots as low or ground-level and high or parabolic has not been fully explored. The objective of this study was to analyze whether there are differences in the frequency and effectiveness (as measured by xGOT) between parabolic and low shots on target in international men’s and women’s football competitions. The results revealed that the most common shot type was the parabolic shot, occurring in 59.86% of shots on goal in the men’s competition (270 shots) and 67.12% in the women’s competition (196 shots). In the overall set of shots, 62.77% were parabolic (466 shots). No significant differences were observed between the competitions (p > 0.05). Regarding the xGOT values, no significant differences were observed for any of the interaction effects analyzed (gender, shot type and shot outcome). The conclusion was that the parabolic shot was the most frequent type of shot on target in both men’s and women’s football.
Latin bitrades derived from quasigroup autoparatopisms
(Springer, 2025) Cavenagh, Nicholas J.; Falcón Ganfornina, Raúl Manuel; Matemática Aplicada I; Universidad de Sevilla
In 2008, Cavenagh, Drápal and Hämäläinen described a method of constructing Latin trades using groups. The Latin trades that arise from this construction are entry-transitive (that is, there always exists an autoparatopism of the Latin trade mapping any ordered triple to any other ordered triple). Moreover, useful properties of the Latin trade can be established using properties of the group. However, the construction does not give a direct embedding of the Latin trade into any particular Latin square. In this paper , we propose a similar approach to the above to construct Latin trades embedded in a Latin square L, via the autoparatopism group of the quasigroup with Cayley table L. We apply this theory to identify non-trivial entry-transitive trades in some group operation tables as well as in Latin squares that arise from quadratic orthomorphisms. Explore related subjects
Physics-based stabilized finite element approximations of the Poisson–Nernst–Planck equations
(Elsevier Science, 2025) Bonilla, Jesús; Gutiérrez Santacreu, Juan Vicente; Matemática Aplicada I; Ministerio de Ciencia e Innovación (MICIN). España; Consejería de Economía, Conocimiento, Empresas y Universidad
We present and analyze two stabilized finite element methods for solving numerically the Poisson–Nernst–Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for the ion equations, whereas the discrete equation for the electric potential need not be stabilized. Discrete solutions stemmed from the first algorithm preserve both maximum and minimum discrete principles. For the second algorithm, its discrete solutions are conceived so that they hold discrete principles and obey an entropy law provided that an acuteness condition is imposed for meshes. Remarkably the latter is found to be unconditionally stable. We validate our methodology through transient numerical experiments that show convergence toward steady-state solutions.
Partial functions induced by morphisms between of persistence modules
(Universitat Jaume I, 2023) González Díaz, Rocío; Soriano Trigueros, Manuel; Torras Casas, Álvaro; Matemática Aplicada I; Agencia Estatal de Investigación. España; Agencia Andaluza del Conocimiento
Persistence modules are fundamental algebraic structures in topological data analysis. One often needs to understand morphisms between a pair of persistence modules as these appear very naturally in practical situations. Even though one might express such morphisms as the direct sum of indecomposable modules, in most cases the decomposition is out of our reach. We define an easy-to-compute partial function relating the interval decomposition of the domain and codomain of such morphisms. This approach gives information about the inner structure of the morphism in a computable way, allowing their use in topological data analysis.
Well-balanced POD-based reduced-order models for finite volume approximation of hyperbolic balance laws
(Elsevier Science , 2025-05-04) Gómez Bueno, Irene; Fernández Nieto, Enrique Domingo; Rubino, Samuele; Matemática Aplicada I; Ministerio de Ciencia e Innovación (MICIN). España
This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval Decomposition (PID). Applied to systems such as the transport equation with source term, non-homogeneous Burgers equation, and shallow water equations with non-flat bathymetry and Manning friction, this method achieves significant improvements in computational efficiency and accuracy compared to previous time averaging techniques. A theoretical result justifying the use of well-balanced FullOrder Models (FOMs) is presented. Numerical experiments validate the approach, demonstrating its accuracy and efficiency. Furthermore, the question of prediction of solutions for systems that depend on some physical parameters is also addressed, and a sensitivity analysis on POD parameters confirms the model’s robustness and efficiency in this case.
Urban-scale building assessment and energy vulnerability mapping through an interactive geo-referenced web tool: demonstration applicability to southern Spain
(Springer, 2025-06-27) Calama-González, Carmen María; Escandón Ramírez, Rocío; Suárez, Rafael; Abajo Casado, María Encarnación; Diánez Martínez, Ana Rosa; Estructuras de Edificación e Ingeniería del Terreno; Construcciones Arquitectónicas I; Matemática Aplicada I; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Junta de Andalucía; TEP999: HABITAE: Habitabilidad, Acondicionamiento y Energía en Arquitectura; FQM240: Invariantes en Teoría de Grafos y Optimización
Building decarbonization through energy renovation is a key challenge across the European Union, particularly in social housing sectors marked by high vulnerability. To support this goal, this study introduces a GIS-based open-access web tool for evaluating the energy performance and social vulnerability of the existing residential stock at the urban scale. The tool integrates data from public and open-source databases into a georeferenced environment, enabling systematic characterization of geometric, constructional, energy and social parameters at the urban-level, and supporting bottom-up and top-down approaches. This allows for performance evaluations, simulation model construction and the identification of high-priority buildings through energy and socioeconomic vulnerability indicators. Results from the city of Seville, used as a case study involving 2,888 dwellings) reveal that over 90% of buildings present severe winter energy vulnerability, while summer vulnerability is generally low. Socioeconomic analysis shows that more than a third of buildings house users living in severe poverty conditions. The combined vulnerability index highlights specific neighbourhoods, such as Polígono Sur, with particularly acute vulnerability levels. The tool’s scalability was demonstrated by extending it to 41 municipalities in southern Spain. This study concludes that this approach enables detailed diagnosis of structural and energy-related inequalities, integrating and analysing existing open data to perform thorough building performance assessment at urban level, and offers a rapid and reliable method for acquiring key building data and ensuring long-term adaptability through continuous updates.
Automorphism group schemes of special simple Jordan pairs of types I and IV
(Elsevier, 2025-10-01) Aranda Orna, Diego; Daza García, Alberto; Matemática Aplicada I
In this work, the automorphism group schemes of finite-dimensional simple Jordan pairs of types I and IV, and of some Jordan triple systems related to them, are determined. We assume char F=2 for the base field F.
On the Total Version of Triple Roman Domination in Graphs
(MDPI, 2025) Valenzuela-Tripodoro, Juan Carlos; Mateos-Camacho, Maria Antonia; Cera López, Martín; Álvarez-Ruiz, María Pilar; Matemática Aplicada I
In this paper, we describe the study of total triple Roman domination. Total triple Roman domination is an assignment of labels from {0, 1, 2, 3, 4} to the vertices of a graph such that every vertex is protected by at least three units either on itself or its neighbors while ensuring that none of its neighbors remains unprotected. Formally, a total triple Roman dominating function is a function f : V(G) → {0, 1, 2, 3, 4} such that f (N[v]) ≥ |AN(v)| + 3, where AN(v) denotes the set of active neighbors of vertex v, i.e., those assigned a positive label. We investigate the algorithmic complexity of the associated decision problem, establish sharp bounds regarding graph structural parameters, and obtain the exact values for several graph families.
An expected goals on target (xGOT) model: accounting for goalkeeper performance in football
(MDPI, 2025-03-10) Cruz Torres, Blanca de la; Navarro Castro, Miguel; Ruiz de Alarcón Quintero, Anselmo; Fisioterapia; Matemática Aplicada I
A key challenge in utilizing the expected goals on target (xGOT) metric is the limited public access to detailed football event and positional data, alongside other advanced metrics. This study aims to develop an xGOT model to evaluate goalkeeper (GK) performance based on the probability of successful actions, considering not only the outcomes (saves or goals conceded) but also the difficulty of each shot faced. Formal definitions were established for the following: (i) the initial distance between the ball and the GK at the moment of the shot, (ii) the distance between the ball and the GK over time post-shot, and (iii) the distance between the GK’s initial position and the goal, with respect to the y-coordinate. An xGOT model incorporating geometric parameters was designed to optimize performance based on the ball position, trajectory, and GK positioning. The model was tested using shots on target from the 2022 FIFA World Cup. Statistical evaluation using k-fold cross-validation yielded an AUC-ROC score of 0.67 and an 85% accuracy, confirming the model’s ability to differentiate successful GK performances. This approach enables a more precise evaluation of GK decision-making by analyzing a representative dataset of shots to estimate the probability of success.
A multilayer shallow water model for tsunamis and coastal forest interaction
(EDP Sciences, Société de Mathématiques Appliquées et Industrielles, 2025) Bürger, Raimund; Fernández Nieto, Enrique Domingo; Moya Abuhadba, Jorge Johnny; Matemática Aplicada I; Gobierno de España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
Models and numerical methods of the impact of tsunamis on coastal forests are of vital importance for exploring the potential of coastal vegetation as a means of mitigation. Such a model is formulated as a multilayer shallow water system based on a free-surface formulation of the Euler equations for an ideal fluid. Specifically, the Euler equations are approximated by a layer averaged non-hydrostatic (LDNH) approach involving linear pressures and piecewise constant velocities. Furthermore, based on [Iimura and Tanaka, Ocean Eng. 54 (2012) 223–232] drag forces, inertia forces, and porosity are added to model the interaction with the forest. These ingredients are specified in a layer-wise manner. Thus, the vertical features of the forest are described with higher accuracy than within a single-layer approach. Projection methods for the non-hydrostatic pressure in conjunction with polynomial viscosity matrix finite volume methods [Castro and Fernández-Nieto, SIAM J. Sci. Comput. 34 (2012) A2173–A2196] are employed for the numerical solution of the multilayer model, that is for the propagation of tsunamis and coastal flooding. Experimental observations and field data are used to validate the model. In general good agreement is obtained.
A series of two-phase models for grain–fluid flows with dilatancy
(2025-04-04) Bouchut, François; Drach, Elias; Fernández Nieto, Enrique Domingo; Mangeney, Anne; Narbona Reina, Gladys; Matemática Aplicada I; Ministerio de Ciencia e Innovación (MICIN). España; Junta de Andalucía; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
Debris flows are a growing natural hazard as a result of climate change and population density. To effectively assess this hazard, simulating field-scale debris flows at a reasonable computational cost is crucial. We enhance existing debris flow models by rigorously deriving a series of depth-averaged shallow models with varying complexities describing the behaviour of grain–fluid flows, considering granular mass dilatancy and pore fluid pressure feedback. The most complete model includes a mixture layer with an upper fluid layer, and solves for solid and fluid velocity in the mixture and for the upper fluid velocity. Simpler models are obtained by assuming velocity equality in the mixture or single-layer descriptions with a virtual thickness. Simulations in a uniform configuration mimicking submarine landslides and debris flows reveal that these models are extremely sensitive to the rheology, the permeability (grain diameter) and initial volume fraction, parameters that are hard to measure in the field. Notably, velocity equality assumptions in the mixture hold true only for low permeability (corresponding to grain diameter d=10−3 m). The one-layer models’ results can strongly differ from those of the complete model, for example, the mass can stop much earlier. One-layer models, however, provide a rough estimate of two-layer models when permeability is low, initial volume fraction is far from critical and the upper fluid layer is very thin. Our work with uniform settings highlights the need of developing two-layer models accounting for dilatancy and for an upper layer made either of fluid or grains.
Optimal secret share distribution in degree splitting communication networks
(AMER INST MATHEMATICAL SCIENCES-AIMS, 2023-10-13) Falcón Ganfornina, Raúl Manuel; Aparna, Venkitachalam; Mohanapriya, Nagaraj; Matemática Aplicada I
Dynamic coloring has recently emerged as a valuable tool to optimize cryptographic protocols based on secret sharing, which enforce data security in communication networks and have significant importance in both online storage and cloud computing. This type of graph labeling enables the dealer to distribute secret shares among the nodes of a communication network so that everybody can recover the secret after a minimum number of rounds of communication. This paper delves into this topic by dealing with the dynamic coloring problem for degree splitting graphs. The topological structure of the latter enables the dealer to avoid dishonesty by adding control nodes that supervise all those participants with a similar influence in the network. More precisely, we solve the dynamic coloring problem for degree splitting graphs of any regular graph. The irregular case is partially solved by establishing a lower bound for the corresponding dynamic chromatic number. As illustrative examples, we solve the dynamic coloring problem for the degree splitting graphs of cycles, cocktail, book, comb, fan, jellyfish, windmill and barbell graphs.
A rockslide-generated tsunami in a Greenland fjord rang Earth for 9 days
(AMER ASSOC ADVANCEMENT SCIENCE, 2024-09-12) Svennevig, Kristian; Hicks, Stephen P.; Forbriger, Thomas; Lecocq, Thomas; Widmer-Schnidrig, Rudolf; Mangeney, Anne; Fernández Nieto, Enrique Domingo; Wirtz, Bastien; Matemática Aplicada I
Climate change is increasingly predisposing polar regions to large landslides. Tsunamigenic landslides have occurred recently in Greenland (Kalaallit Nunaat), but none have been reported from the eastern fjords. In September 2023, we detected the start of a 9-day-long, global 10.88-millihertz (92-second) monochromatic very-long-period (VLP) seismic signal, originating from East Greenland. In this study, we demonstrate how this event started with a glacial thinning–induced rock-ice avalanche of 25 × 106 cubic meters plunging into Dickson Fjord, triggering a 200-meter-high tsunami. Simulations show that the tsunami stabilized into a 7-meter-high long-duration seiche with a frequency (11.45 millihertz) and slow amplitude decay that were nearly identical to the seismic signal. An oscillating, fjord-transverse single force with a maximum amplitude of 5 × 1011 newtons reproduced the seismic amplitudes and their radiation pattern relative to the fjord, demonstrating how a seiche directly caused the 9-day-long seismic signal. Our findings highlight how climate change is causing cascading, hazardous feedbacks between the cryosphere, hydrosphere, and lithosphere.
A dynamic geometry system approach to analyse distance geometry problems based on partial Latin squares
(Taylor & Francis Inc, 2020) Falcón Ganfornina, Raúl Manuel
Partial Latin squares constitute an interesting approach to improve the teaching of different subjects in the mathematics classroom. This paper delves into this topic by introducing the use of a Dynamic Geometry System to deal with these combinatorial structures as a source of loci of points in the Euclidean plane. It is assumed to this end that the distance matrix among all these points contains a zerodiagonal symmetric partial Latin square with at least one non-zero filled cell per row.
Well-Posedness and Stability Analysis of a Landscape Evolution Model
(Springer anature, 2024) Binard, Julie; Degond, P.; Noble, P.; Matemática Aplicada I
In this paper, we study a system of partial differential equations modeling the evolution of a landscape in order to describe the mechanisms of pattern formations. A ground surface is eroded by the flow of water over it, by either sedimentation or dilution. We consider a model, composed of three evolution equations: one on the elevation of the ground surface, one on the fluid height and one on the concentration of sediments in the fluid layer. We first establish the well-posedness of the system in short time and under the assumption that the initial fluid height does not vanish. Then, we focus on pattern formation in the case of a film flow over an inclined erodible plane. For that purpose, we carry out a spectral stability analysis of constant state solutions in order to determine instability conditions and identify a mechanism for pattern formations. These patterns, which are rills and gullies, are the starting point of the formation of rivers and valleys in landscapes. Finally, we carry out some numerical simulations of the full system in order to validate the spectral instability scenario, and determine the resulting patterns.
Solvable Lie and Leibniz superalgebras with a given nilradical
(Walter de Gruyter GmbH, 2020) Camacho Santana, Luisa María; Fernández Barroso, José Manuel; Navarro, Rosa María; Matemática Aplicada I
Throughout this paper we show that under certain conditions the method for describing solvable Leibniz (resp. Lie) algebras with given nilradical by means of non-nilpotent outer derivations of the nilradical is also applicable to the case Leibniz (resp. Lie) superalgebras. Moreover, after having established the general method for Lie and Leibniz superalgebras, we classify all the solvable superalgebras on a very important class of each of them, that is, those with nilradical of maximal nilindex. Note that for (n+m)-dimensional superalgebras this maximal nilindex is n+m−1 in the Lie case and n+m in Leibniz.

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