Artículos (Matemática Aplicada I)

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

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Well-Posedness and Stability Analysis of a Landscape Evolution Model
(Springer anature, 2024) Binard, Julie; Degond, P.; Noble, P.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
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; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
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.
p-Strong Roman Domination in Graphs
(World Scientific and Engineering Academy and Society, 2024) Valenzuela-Tripodoro, J. C.; Mateos-Camacho, M. A.; Cera López, Martín; Moreno Casablanca, Rocío; Álvarez-Ruiz, M. P.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Power concave operators and representation of p-convex and q-concave banach lattices
(Theta Foundation, 2017) Delgado Garrido, Olvido; Sánchez Pérez, Enrique A.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
As a consequence of the analysis of the class of (p, q)-power concave operators, we prove a general representation theorem for p-convex and q-concave Banach lattices as spaces of integrable functions with respect to vector measures. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years.
Optimization of laser scanner positioning networks for architectural surveys through the design of genetic algorithms
(Elsevier, 2021) Cabrera Revuelta. Elena; Chávez de Diego, María José; Barrera Vera, José Antonio; Fernández Rodríguez, Yago; Caballero Sánchez, Manuel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Ingeniería Gráfica
In recent decades, the use of terrestrial laser scanners has become the principal method for metric data collection in architecture. However, there are no systematic procedures in place to plan the data capture process. This means that the obtaining tasks of the clouds of points are based either on operator experience, or on the overlap register that grants a complete acquisition. In both cases, data redundancy represents a significant percentage, which forces subsequent filtration or point removal. This work describes the design and development of an automated methodology, based on genetic algorithms, for the selection of a set of positions from which to execute the data capture process. The algorithm designed herein is applied to a variety of cases, thereby attaining the best station-positioning network for data collection, which maximizes coverage and minimizes overlap between clouds of points.
Gradings on associative triple systems of the second kind
(Elsevier Science, 2024) Daza García, Alberto; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
On this work we study associative triple systems of the second kind. We show that for simple triple systems the automor-phism group scheme is isomorphic to the automorphism group scheme of the 3-graded associative algebra with involution constructed by Loos. This result will allow us to prove our main result which is a complete classification up to isomor-phism of the gradings of structurable algebras.
Further Results on the [k]-Roman Domination in Graphs
(Springer Nature, 2024) Valenzuela-Tripodoro, Juan Carlos; Mateos-Camacho, Maria Antonia; Cera López, Martín; Álvarez-Ruiz, Maria Pilar; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In 2016, Beeler et al. defined the double Roman domination as a variation of Roman domination. Sometime later, in 2021, Ahangar et al. introduced the concept of [k]- Roman domination in graphs and settled some results on the triple Roman domination case. In 2022, Amjadi et al. studied the quadruple version of this Roman-dominationtype problem. Given any labeling of the vertices of a graph, AN(v) stands for the set of neighbors of a vertex v having a positive label. In this paper we continue the study of the [k]-Roman domination functions ([k]-RDF) in graphs which coincides with the previous versions when 2 ≤ k ≤ 4. Namely, f is a [k]-RDF if f (N[v]) ≥ k+|AN(v)| for all v. We prove that the associate decision problem is NP-complete even when restricted to star convex and comb convex bipartite graphs and we also give sharp bounds and exact values for several classes of graphs.
A fuzzy logic approach to preventive conservation of cultural heritage churches in Popayan, Colombia
(Taylor & Francis Inc, 2021) Chávez de Diego, María José; Prieto, Andrés J.; Turbay, Isabel; Ortiz, Rocío; Macías Bernal, Juan Manuel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Construcciones Arquitectónicas II (ETSIE)
From a decision-maker’s perspective, the management of cultural heritage is a challenging task because of different objectives pursued, the public/private nature of heritage constructions studied, the wide variety of associated values (artistic, historical, cultural, economic) and diverse interests of different stakeholders. Careful consideration of environmental, social and economic factors is crucial in order to predict the functional service life of heritage constructions. This study outlines a new fuzzy system approach based on expert knowledge, which focuses on the serviceability of heritage buildings using a Mamdani fuzzy model. The method input considers 10 intrinsic variables directly related to the vulnerability of buildings and 9 external hazards, classified according to static-structural features and environmental hazards, which are considered useful for defining emergency programs in historical centres in South America (Colombia). The automation of inspection programs similar to the one described here may reduce the consumption of natural resources and benefit a more rational management of future maintenance actions. In general terms, this type of fuzzy logic model approach is designed to serve as an indicator for the future evolution of the functionality of buildings. This research contributes to the study of new service life models applied to heritage buildings in South America.
3-Filiform Leibniz algebras of maximum length, whose naturally graded algebras are Lie algebras
(Taylor and Francis Ltd., 2011-09) Camacho Santana, Luisa María; Cañete, E. M.; Gómez, J. R.; Omirov, B. A.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In this article we present the classification of the 3-filiform Leibniz algebras of maximum length, whose associated naturally graded algebras are Lie algebras. Our main tools are a previous existence result by Cabezas and Pastor [J.M. Cabezas and E. Pastor, Naturally graded p-filiform Lie algebras in arbitrary finite dimension, J. Lie Theory 15 (2005), pp. 379–391] and the construction of appropriate homogeneous bases in the connected gradation considered. This is a continuation of the work done in Ref. [J.M. Cabezas, L.M. Camacho, and I.M. Rodrı´guez, On filiform and 2-filiform Leibniz algebras of maximum length, J. Lie Theory 18 (2008), pp. 335–350].
Determinant of the distance matrix of a tree
(University of Vienna, 2024) Briand, Emmanuel; Esquivias Quintero, Luis; Gutierrez, Alvaro; Lillo, Adrian; Rosas Celis, Mercedes Helena; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Álgebra; MICIU/AEI/10.13039/501100011033; Junta de Andalucía, FEDER, PAIDI2020
We present a combinatorial proof of the Graham–Pollak formula for the determinant of the distance matrix of a tree, via sign-reversing involutions and the Lindström–Gessel–Viennot lemma.
Leveraging the chain on goals model in football: applications for attack and defensive play
(MDPI, 2025-01-20) Cruz Torres, Blanca de la; Navarro Castro, Miguel; Ruiz de Alarcón Quintero, Anselmo; Universidad de Sevilla. Departamento de Fisioterapia; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Introduction: Football analysis has experienced significant growth in recent years as an applied research field. This study aims to contribute to this area by applying the chain on goals model to analyze both the attacking and defensive phases of football matches. Additionally, it introduces four practical concepts to better understand player and team performance in Spain’s professional football leagues. Method: Data for the 2023/24 season were collected from Football Reference, covering both men’s (LaLiga) and women’s (LigaF) leagues. Variables analyzed included team performance, attack and defensive performance, goals saved above average (GSAA), goals and possession value (PV), expected goals (xG), and xG on target (xGOT) for attack and defensive phases. Four practical concepts analyzed were off-ball movement (PV-xG), player’s offensive quality (xG-xGOT), team’s positioning (PVA-xGA), and player’s defensive quality (xGA-xGOTA). Descriptive and comparative statistical analyses were performed to compare all variables between the two leagues using an Independent Student’s test. Additionally, correlation coefficients were calculated to examine the relationships between the four concepts. Results: Significant differences were observed between leagues in defensive performance (p = 0.03) and GSAA (p < 0.001). Practical concepts revealed disparities in off-ball movement and team’s positioning (p < 0.001 in both). No correlations were found between off-ball movement and player’s offensive quality or between team’s positioning and player’s defensive quality. Conclusions: The Spanish women’s league exhibited defensive weaknesses, conceding more goals and showing lower goalkeeper performance. PV was the most influential variable in the women’s league, while xG was critical in the men’s league.
Slopes of hypergeometric systems of codimension one
(EUROPEAN MATHEMATICAL SOC, 2002-04-04) Hartillo Hermoso, Isabel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
We describe the slopes, with respect to the coordinates hyper- planes, of the hypergeometric systems of codimension one, that is when the toric ideal is generated by one element.
Irregular hypergeometric systems associated with a singular monomial curve
(AMER MATHEMATICAL SOC, 2005) Hartillo Hermoso, Isabel; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In this paper we study irregular hypergeometric systems defined by one row. Specifically, we calculate slopes of such systems. In the case of reduced semigroups, we generalize the case studied by Castro and Takayama. In all the cases we find that there always exists a slope with respect to a hyperplane of this system. Only in the case of an irregular system defined by a 1 × 2 integer matrix we might need a change of coordinates to study slopes at infinity. In the other cases slopes are always at the origin, defined with respect to a hyperplane. We also compute all the L-characteristic varieties of the system, so we have a section of the Gr¨obner fan of the module defined by the hypergeometric system.
Mathematical modeling of heat treatment for a steering rack including mechanical effects
(Walter de Gruyter GmbH, 2012) Díaz, J. M.; García, C.; González Montesinos, María Teresa; Ortegón, F.; Viglialoro, G.; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Heat treatment is the controlled heating and cooling of metals used to alter their physical and mechanical properties. This is a very enabling process that can facilitate machining, formability and restore ductility, after a cold working operation, improving the product’s performances by increasing its strength or other desirable characteristics. This paper summarizes a mathematical model for the induction–conduction hardening of a specific s teel workpiece: the steering rack of an automobile. The whole formulation takes into account both electromagnetic effects that lead to heating the workpiece and the corresponding thermomechanical effects that cause the hardening, Joule’s heating being the main responsible of the coupling between them. Some numerical simulations are presented; these numerical results have been computed using the freefem++ software.
Explicit models for perverse sheaves, II
(Springer, 2008) Gudiel Rodríguez, Félix; Narváez Macarro, Luis; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Álgebra
In this paper we show that any p-perverse sheaf on an arbitrary stratified topological space ( p is a perversity function) is functorially determined by a system of usual sheaves on the open sets Ur (r ≥ 0) and certain gluing data, where Ur is the union of strata of perversity ≤ r.
Unconditionally stable operator splitting algorithms for the incompressible magnetohydrodynamics system discretized by a stabilized finite element formulation based on projections
(Wiley, 2013) Badia, Santiago; Planas, Ramon; Gutiérrez Santacreu, Juan Vicente; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In this article, we propose different splitting procedures for the transient incompressible magnetohydrodynamics (MHD) system that are unconditionally stable. We consider two levels of splitting, on one side we perform the segregation of the fluid pressure and magnetic pseudo-pressure from the vectorial fields computation. At the second level, the fluid velocity and induction fields are also decoupled. This way, we transform a fully coupled indefinite multi-physics system into a set of smaller definite ones, clearly reducing the CPU cost. With regard to the finite element approximation, we stick to an unconditionally convergent stabilized finite element formulation because it introduces convection stabilization, allows to cir-cumvent inf-sup conditions (clearly simplifying implementation issues), and is able to capture nonsmooth solutions of the magnetic subproblem. However, residual-based finite element formulations are not suitable for segregation, because they lose the skew-symmetry of the off-diagonal blocks. Therefore, in this work, we have proposed a novel term-by-term stabilization of the MHD system based on projections that is still unconditionally convergent.
Stability and convergence for a complete model of mass diffusion
(Elsevier, 2011) Cabrales, R. C.; Guillén González, Francisco Manuel; Gutiérrez Santacreu, Juan Vicente; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
We propose a fully discrete scheme for approximating a three-dimensional, strongly nonlinear model of mass diffusion, also called the complete Kazhikhov–Smagulov model. The scheme uses a C0 finite-element approximation for all unknowns (density, velocity and pressure), even though the density limit, solution of the continuous problem, belongs to H2. A first-order time discretization is used such that, at each time step, one only needs to solve two decoupled linear problems for the discrete density and the velocity–pressure, separately. We extend to the complete model, some stability and convergence results already obtained by the last two authors for a simplified model where λ2-terms are not considered, λ being the mass diffusion coefficient. Now, different arguments must be introduced, based mainly on an induction process with respect to the time step, obtaining at the same time the three main properties of the scheme: an approximate discrete maximum principle for the density, weak estimates for the velocity and strong ones for the density. Furthermore, the convergence towards a weak solution of the density-dependent Navier–Stokes problem is also obtained as λ→0 (jointly with the space and time parameters). Finally, some numerical computations prove the practical usefulness of the scheme.
Bound-preserving finite element approximations of the Keller-Segel equations
(World Scientific Public., 2023) Badia, Santiago; Bonilla, Jesús; Gutiérrez Santacreu, Juan Vicente; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
This paper aims to develop numerical approximations of the Keller{Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a non-negative variable. We propose two algorithms, which combine a stabilized nite element method and a semi-implicit time integration. The stabilization consists of a nonlinear arti cial di usion that employs a graph-Laplacian operator and a shock detector that localizes local extrema. As a result, both algorithms turn out to be nonlinear and can generate cell and chemoattractant numerical densities ful lling lower bounds. However, the rst algorithm requires a suitable constraint between the space and time discrete parameters, whereas the second one does not. We design the latter to attain a discrete energy law on acute meshes.
Free boundary CMC annuli in spherical and hyperbolic balls
(Springer, 2025-01-06) Cerezo Cid, Alberto; Fernández Delgado, Isabel; Mira Carrillo, Pablo; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Universidad de Sevilla. FQM-325 Problemas Variacionales en Geometría
We construct, for any H ∈ R, infinitely many free boundary annuli in geodesic balls of S3 with constant mean curvature H and a discrete, non-rotational, symmetry group. Some of these free boundary CMC annuli are actually embedded if H ≥ 1/ √3. We also construct embedded, non-rotational, free boundary CMC annuli in geodesic balls of H3, for all values H > 1 of the mean curvature H.
Two-phase magma flow with phase exchange. Part I. Physical modeling of a volcanic conduit
(Wiley, 2024) Narbona Reina, Gladys; Bresch, Didier; Burgisser, Alain; Collombet, Marielle; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
In a review paper in this same volume, we present the state of the art on modeling of compressible viscous flows ranging from single-phase to two-phase systems. It focuses on mathematical properties related to weak stability because they are important for numerical resolution and on the homogenization process that leads from a microscopic description of two separate phases to an averaged two-phase model. This review serves as the foundation for Parts I and II, which present averaged two-phase models with phase exchange applicable to magma flow during volcanic eruptions. Here, in Part I, after introducing the physical processes occurring in a volcanic conduit, we detail the steps needed at both microscopic and macroscopic scales to obtain a two-phase transient conduit flow model ensuring: 1) mass and volatile species conservation, 2) disequilibrium degassing considering both viscous relaxation and volatile diffusion, and 3) dissipation of total energy. The resulting compressible/incompressible system has 8 transport equations on 8 unknowns (gas volume fraction and density, dissolved water content, liquid pressure, and the velocity and temperature of both phases) as well as algebraic closures for gas pressure and bubble radius. We establish valid sets of boundary conditions such as imposing pressures and stress-free conditions at the conduit outlet and either velocity or pressure at the inlet. This model is then used to obtain a drift-flux system that isolates the effects of relative velocities, pressures, and temperatures. The dimensional analysis of this drift-flux system suggests that relative velocities can be captured with a Darcy equation and that gas–liquid pressure differences partly control magma acceleration. Unlike the vanishing small gas–liquid temperature differences, bulk magma temperature is expected to vary because of gas expansion. Mass exchange being a major control of flow dynamics, we propose a limit case of mass exchange by establishing a relaxed system at chemical equilibrium. This singlevelocity, single-temperature system is a generalization of an existing volcanic conduit flow model. Finally, we compare our full compressible/incompressible system to another existing volcanic conduit flow model where both phases are compressible. This comparison illustrates that different two-phase systems may be obtained depending on the governing unknowns chosen. Part II presents a 1.5D version of the model established herein that is solved numerically. The numerical outputs are compared to those of another steady-state, equilibrium degassing, isothermal model under conditions typical of an effusive eruption at an andesitic volcano.

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