Artículos (Matemática Aplicada I)

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

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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; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII); Ministerio de Ciencia e Innovación (MICIN). España; Junta de Andalucía; Universidad de Sevilla. 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; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
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; Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
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.; 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.

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