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http://hdl.handle.net/2117/127
Mon, 15 Sep 2014 09:47:47 GMT2014-09-15T09:47:47Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoNonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
http://hdl.handle.net/2117/22391
Title: Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
Authors: Cabré Vilagut, Xavier; Sire, Yannick
Abstract: This is the first of two articles dealing with the equation (-)sv = f (v) in Rn, with s ¿ (0,1), where (-)s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized as a local linear degenerate elliptic equation in Rn+1+ together with a nonlinear Neumann boundary condition on ¿Rn+1 + =Rn.
In this ¿rst article, we establish necessary conditions on the nonlinearity f to admit certain type of solutions, with special interest in bounded increasing solutions in all of R. These necessary conditions (which will be proven in a follow-up paper to be also suficient for the existence of a bounded increasing solution) are derived from an equality and an estimate involving a Hamiltonian — in the spirit of a result of Modica for the Laplacian. Our proofs are uniform ass ¿1, establishing in the limit the corresponding known results for the Laplacian.
In addition, we study regularity issues, as well as maximum and Harnack principles associated to the equation.http://hdl.handle.net/2117/22391Cabré Vilagut, Xavier; Sire, YannicknoThis is the first of two articles dealing with the equation (-)sv = f (v) in Rn, with s ¿ (0,1), where (-)s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized as a local linear degenerate elliptic equation in Rn+1+ together with a nonlinear Neumann boundary condition on ¿Rn+1 + =Rn.
In this ¿rst article, we establish necessary conditions on the nonlinearity f to admit certain type of solutions, with special interest in bounded increasing solutions in all of R. These necessary conditions (which will be proven in a follow-up paper to be also suficient for the existence of a bounded increasing solution) are derived from an equality and an estimate involving a Hamiltonian — in the spirit of a result of Modica for the Laplacian. Our proofs are uniform ass ¿1, establishing in the limit the corresponding known results for the Laplacian.
In addition, we study regularity issues, as well as maximum and Harnack principles associated to the equation.Estructuras A-infinito en la opérada de cactus
http://hdl.handle.net/2117/22097
Title: Estructuras A-infinito en la opérada de cactus
Authors: Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew
Abstract: Diversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este pósterhttp://hdl.handle.net/2117/22097Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, AndrewnoDiversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este pósterJ2 effect and elliptic inclined periodic orbits in the collision three-body problem
http://hdl.handle.net/2117/21117
Title: J2 effect and elliptic inclined periodic orbits in the collision three-body problem
Authors: Barrabes, Esther; Cors Iglesias, Josep Maria; Pinyol, Conxita; Soler Villanueva, Jaume
Abstract: The existence of a new class of inclined periodic orbits of the collision restricted
three{body problem is shown. The symmetric periodic solutions found are perturbations of elliptic
kepler orbits and they exist only for special values of the inclination and are related to the motion
of a satellite around an oblate planet.http://hdl.handle.net/2117/21117Barrabes, Esther; Cors Iglesias, Josep Maria; Pinyol, Conxita; Soler Villanueva, Jaumenocollision restricted three-body problem, periodic orbits, symmetric orbits, critical inclination, continuation methodThe existence of a new class of inclined periodic orbits of the collision restricted
three{body problem is shown. The symmetric periodic solutions found are perturbations of elliptic
kepler orbits and they exist only for special values of the inclination and are related to the motion
of a satellite around an oblate planet.The representativeness reliability importance measure
http://hdl.handle.net/2117/24048
Title: The representativeness reliability importance measure
Authors: Freixas Bosch, Josep; Pons Vallès, Montserrat
Abstract: A new reliability importance measure for
components in a system, that we call Representativeness
measure, is introduced. It evaluates to which extent the
performance of a component is representative of the
performance of the whole system. Its relationship with
Birnbaum’s measure is analyzed, and the ranking of
components given by both measures are compared. These
rankings happen to be equal when all components have the
same reliability but different in general. In contrast with
Birnbaum’s, the Representativeness reliability importance
measure of a component does depend on its reliability.Fri, 12 Sep 2014 10:45:20 GMThttp://hdl.handle.net/2117/240482014-09-12T10:45:20ZFreixas Bosch, Josep; Pons Vallès, MontserratnoReliability importance measures, Structural importance measures, Criticality relation, Coherent systems, node criticality relation, Birnbaum RIM, Birnbaum SIMA new reliability importance measure for
components in a system, that we call Representativeness
measure, is introduced. It evaluates to which extent the
performance of a component is representative of the
performance of the whole system. Its relationship with
Birnbaum’s measure is analyzed, and the ranking of
components given by both measures are compared. These
rankings happen to be equal when all components have the
same reliability but different in general. In contrast with
Birnbaum’s, the Representativeness reliability importance
measure of a component does depend on its reliability.Static output-feedback controller design for structural vibration control: a two-step LMI approach
http://hdl.handle.net/2117/24047
Title: Static output-feedback controller design for structural vibration control: a two-step LMI approach
Authors: Palacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid Reza
Abstract: This paper presents a novel controller design strategy, which allows computing static output-feedback controllers by
solving two successive linear matrix inequality (LMI) optimization problems. This strategy is conceptually simple, easy
to implement, computationally efficient, and it can be potentially applied to a wide variety of control problems, in which
effective state-feedback controllers can be synthesized by using standard LMI optimization tools. To illustrate the application
of the new approach in the field of structural vibration control of large structures, a static velocity-feedback H1 controller
for the seismic protection of a five-story building is designed with excellent results.Fri, 12 Sep 2014 10:32:16 GMThttp://hdl.handle.net/2117/240472014-09-12T10:32:16ZPalacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid RezanoThis paper presents a novel controller design strategy, which allows computing static output-feedback controllers by
solving two successive linear matrix inequality (LMI) optimization problems. This strategy is conceptually simple, easy
to implement, computationally efficient, and it can be potentially applied to a wide variety of control problems, in which
effective state-feedback controllers can be synthesized by using standard LMI optimization tools. To illustrate the application
of the new approach in the field of structural vibration control of large structures, a static velocity-feedback H1 controller
for the seismic protection of a five-story building is designed with excellent results.Computing correlation between piecewise-linear functions
http://hdl.handle.net/2117/23696
Title: Computing correlation between piecewise-linear functions
Authors: Agarwal, Pankaj; Aronov, Boris; Van Kreveld, Matias; Löffler, Maarten; Silveira, Rodrigo Ignacio
Abstract: We study the problem of computing correlation between two piecewise-linear bivariate functions defined over a common domain, where the surfaces they define in three dimensions---polyhedral terrains---can be transformed vertically by a linear transformation of the third coordinate (scaling and translation). We present a randomized algorithm that minimizes the maximum vertical distance between the graphs of the two functions, over all linear transformations of one of the terrains, in $O(n^{4/3}\operatorname{polylog}n)$ expected time, where $n$ is the total number of vertices in the graphs of the two functions. We also present approximation algorithms for minimizing the mean distance between the graphs of univariate and bivariate functions. For univariate functions we present a $(1+\varepsilon)$-approximation algorithm that runs in $O(n (1 + \log^2 (1/\varepsilon)))$ expected time for any fixed $\varepsilon >0$. The $(1+\varepsilon)$-approximation algorithm for bivariate functions runs in $O(n/\varepsilon)$ time, for any fixed $\varepsilon >0$, provided the two functions are defined over the same triangulation of their domain.Fri, 29 Aug 2014 10:51:05 GMThttp://hdl.handle.net/2117/236962014-08-29T10:51:05ZAgarwal, Pankaj; Aronov, Boris; Van Kreveld, Matias; Löffler, Maarten; Silveira, Rodrigo Ignacionopiecewise-linear function, polyhedral terrain, similarity, approximation algorithm, correlationWe study the problem of computing correlation between two piecewise-linear bivariate functions defined over a common domain, where the surfaces they define in three dimensions---polyhedral terrains---can be transformed vertically by a linear transformation of the third coordinate (scaling and translation). We present a randomized algorithm that minimizes the maximum vertical distance between the graphs of the two functions, over all linear transformations of one of the terrains, in $O(n^{4/3}\operatorname{polylog}n)$ expected time, where $n$ is the total number of vertices in the graphs of the two functions. We also present approximation algorithms for minimizing the mean distance between the graphs of univariate and bivariate functions. For univariate functions we present a $(1+\varepsilon)$-approximation algorithm that runs in $O(n (1 + \log^2 (1/\varepsilon)))$ expected time for any fixed $\varepsilon >0$. The $(1+\varepsilon)$-approximation algorithm for bivariate functions runs in $O(n/\varepsilon)$ time, for any fixed $\varepsilon >0$, provided the two functions are defined over the same triangulation of their domain.Importance of force decomposition for local stress calculations in biomembrane molecular simulations
http://hdl.handle.net/2117/23686
Title: Importance of force decomposition for local stress calculations in biomembrane molecular simulations
Authors: Vanegas, Juan Manuel; Torres Sánchez, Alejandro; Arroyo Balaguer, Marino
Abstract: Local stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.Thu, 28 Aug 2014 08:29:29 GMThttp://hdl.handle.net/2117/236862014-08-28T08:29:29ZVanegas, Juan Manuel; Torres Sánchez, Alejandro; Arroyo Balaguer, MarinonoCOARSE-GRAINED MODEL, LATERAL PRESSURE PROFILE, DYNAMICS SIMULATIONS, LIPID-BILAYERS, MECHANOSENSITIVE CHANNEL, SURFACE-TENSION, MEMBRANES, CURVATURE, FIELD, WATERLocal stress fields are routinely computed from molecular dynamics trajectories to understand the structure and mechanical properties of lipid bilayers. These calculations can be systematically understood with the Irving-Kirkwood-Noll theory. In identifying the stress tensor, a crucial step is the decomposition of the forces on the particles into pairwise contributions. However, such a decomposition is not unique in general, leading to an ambiguity in the definition of the stress tensor, particularly for multibody potentials. Furthermore, a theoretical treatment of constraints in local stress calculations has been lacking. Here, we present a new implementation of local stress calculations that systematically treats constraints and considers a privileged decomposition, the central force decomposition, that leads to a symmetric stress tensor by construction. We focus on biomembranes, although the methodology presented here is widely applicable. Our results show that some unphysical behavior obtained with previous implementations (e.g. nonconstant normal stress profiles along an isotropic bilayer in equilibrium) is a consequence of an improper treatment of constraints. Furthermore, other valid force decompositions produce significantly different stress profiles, particularly in the presence of dihedral potentials. Our methodology reveals the striking effect of unsaturations on the bilayer mechanics, missed by previous stress calculation implementations.Stochastic optimal sale bid for a wind power producer
http://hdl.handle.net/2117/23684
Title: Stochastic optimal sale bid for a wind power producer
Authors: Sacripante, Simona; Heredia, F.-Javier (Francisco Javier); Corchero Garcia, Cristina
Abstract: Wind power generation has a key role in Spanish electricity system since it is a native source of energy that could help Spain to reduce its dependency on the exterior for the production of electricity. Apart from the great environmental benefits produced, wind energy reduce considerably spot energy price, reaching to cover 16,6 % of peninsular demand. Although, wind farms show high investment costs and need an efficient incentive scheme to be financed. If on one hand, Spain has been a leading country in Europe in developing a successful incentive scheme, nowadays tariff deficit and negative economic conjunctures asks for consistent reductions in the support mechanism and demand wind producers to be able to compete into the market with more mature technologies. The objective of this work is to find an optimal commercial strategy in the production market that would allow wind producer to maximize their daily profit. That can be achieved on one hand, increasing incomes in daily and intraday markets, on the other hand, reducing deviation costs due to error in generation predictions. We will previously analyze market features and common practices in use and then develop our own sale strategy solving a two-stage linear stochastic optimization problem. The first stage variable will be the sale bid in the day–ahead market while second stage variables will be the offers to the six sessions of intraday market. The model is implemented using real data from a wind producer leader in Spain.
Description: Research ReportWed, 27 Aug 2014 10:46:49 GMThttp://hdl.handle.net/2117/236842014-08-27T10:46:49ZSacripante, Simona; Heredia, F.-Javier (Francisco Javier); Corchero Garcia, Cristinanoelectricity market, wind producer, stochastic programmingWind power generation has a key role in Spanish electricity system since it is a native source of energy that could help Spain to reduce its dependency on the exterior for the production of electricity. Apart from the great environmental benefits produced, wind energy reduce considerably spot energy price, reaching to cover 16,6 % of peninsular demand. Although, wind farms show high investment costs and need an efficient incentive scheme to be financed. If on one hand, Spain has been a leading country in Europe in developing a successful incentive scheme, nowadays tariff deficit and negative economic conjunctures asks for consistent reductions in the support mechanism and demand wind producers to be able to compete into the market with more mature technologies. The objective of this work is to find an optimal commercial strategy in the production market that would allow wind producer to maximize their daily profit. That can be achieved on one hand, increasing incomes in daily and intraday markets, on the other hand, reducing deviation costs due to error in generation predictions. We will previously analyze market features and common practices in use and then develop our own sale strategy solving a two-stage linear stochastic optimization problem. The first stage variable will be the sale bid in the day–ahead market while second stage variables will be the offers to the six sessions of intraday market. The model is implemented using real data from a wind producer leader in Spain.Impacts on effluent contaminants from mine sites : risk assessment, fate, and distribution of pollution at basin scale
http://hdl.handle.net/2117/23669
Title: Impacts on effluent contaminants from mine sites : risk assessment, fate, and distribution of pollution at basin scale
Authors: Yacoub López, Cristina; Pérez Foguet, Agustí; Valderrama Angel, César Alberto; Miralles Esteban, Núria
Abstract: The environmental implications of mining activities are of worldwide concern. An environmental evaluation at the basin level was conducted because of widespread mining in Cajamarca in Northern Peru. A sediment monitoring program was developed at the Jequetepeque basin, located in Cajamarca. A total of 16 sites were monitored at three different times between June 2009 and July 2010, and a total of 42 samples were collected. All samples were analyzed by microwave digestion and by a sequential extraction scheme following the three-stage European Community Bureau of Reference (three-stage BCR) protocol. Trace element mobilization from the sediments to the water column was assessed by the risk assessment code (RAC). Spatial and temporal distribution of trace elements was evaluated by principal component analysis and hierarchical cluster analysis. Cd, Zn, As, and Pb showed the highest concentrations independent of season. Notably, Cu concentration and mobility increased during the wet season for all samples. Additionally, Hg concentration and mobility increased during the wet season near the mine sites. According to the enrichment factor, the highest enrichments of Cd, Zn, Pb, and As were related to mine runoff. The effect of trace elements near the mine sites at the Jequetepeque basin was considered a significant threat to the environment due to Cd, Zn, Pb, and As, and the concentrations of Cu and Hg were also considered a concern. This work establishes a baseline for the environmental quality status of the Jequetepeque basin that may support water quality management in Peru.
Description: Electronic supplementary material The online Electronic supplementary material: the on-line version of this article
(doi:10.1007/s11356-014-2559-7) contains supplementary material, which is available to authorized users.Fri, 01 Aug 2014 11:18:55 GMThttp://hdl.handle.net/2117/236692014-08-01T11:18:55ZYacoub López, Cristina; Pérez Foguet, Agustí; Valderrama Angel, César Alberto; Miralles Esteban, NúrianoEnrichment factor, Environmental pollution, Risk assessment, Sequential extraction, Spatio-temporal distribution, Trace elementThe environmental implications of mining activities are of worldwide concern. An environmental evaluation at the basin level was conducted because of widespread mining in Cajamarca in Northern Peru. A sediment monitoring program was developed at the Jequetepeque basin, located in Cajamarca. A total of 16 sites were monitored at three different times between June 2009 and July 2010, and a total of 42 samples were collected. All samples were analyzed by microwave digestion and by a sequential extraction scheme following the three-stage European Community Bureau of Reference (three-stage BCR) protocol. Trace element mobilization from the sediments to the water column was assessed by the risk assessment code (RAC). Spatial and temporal distribution of trace elements was evaluated by principal component analysis and hierarchical cluster analysis. Cd, Zn, As, and Pb showed the highest concentrations independent of season. Notably, Cu concentration and mobility increased during the wet season for all samples. Additionally, Hg concentration and mobility increased during the wet season near the mine sites. According to the enrichment factor, the highest enrichments of Cd, Zn, Pb, and As were related to mine runoff. The effect of trace elements near the mine sites at the Jequetepeque basin was considered a significant threat to the environment due to Cd, Zn, Pb, and As, and the concentrations of Cu and Hg were also considered a concern. This work establishes a baseline for the environmental quality status of the Jequetepeque basin that may support water quality management in Peru.Central cohomology operations and K-theory
http://hdl.handle.net/2117/23645
Title: Central cohomology operations and K-theory
Authors: Gálvez Carrillo, Maria Immaculada; Whitehouse, Sarah
Abstract: For stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP<n> for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.Tue, 29 Jul 2014 08:35:40 GMThttp://hdl.handle.net/2117/236452014-07-29T08:35:40ZGálvez Carrillo, Maria Immaculada; Whitehouse, SarahnoK-theory, Operations, CobordismFor stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP<n> for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.Observation of the internal states of a PEMFC anode gas channel
http://hdl.handle.net/2117/23623
Title: Observation of the internal states of a PEMFC anode gas channel
Authors: Luna Pacho, Julio Alberto; Batlle Arnau, Carles; Kunusch, Cristian; Riera Colomer, Jordi; Sarmiento Carnevali, María Laura; Serra, Maria
Abstract: In this work a non-linear, model-based state observer is developed. Dynamics of the system described by a distributed parameter, partial differential equations model. Forward and backward discretization of the model to take advantage of the boundary conditions. Simulation results are presented to show the performance of the observer. Comparison between the linear and nonlinear approaches of the observers.Fri, 25 Jul 2014 11:46:12 GMThttp://hdl.handle.net/2117/236232014-07-25T11:46:12ZLuna Pacho, Julio Alberto; Batlle Arnau, Carles; Kunusch, Cristian; Riera Colomer, Jordi; Sarmiento Carnevali, María Laura; Serra, Marianocontrol nonlinearities, observability
PEMFC, distrubuted model, nonlinear observers, super-twisting, sliding modeIn this work a non-linear, model-based state observer is developed. Dynamics of the system described by a distributed parameter, partial differential equations model. Forward and backward discretization of the model to take advantage of the boundary conditions. Simulation results are presented to show the performance of the observer. Comparison between the linear and nonlinear approaches of the observers.Simulation of cable dynamics for moored ocean platforms: modeling aids design of large, underwater power cable
http://hdl.handle.net/2117/23616
Title: Simulation of cable dynamics for moored ocean platforms: modeling aids design of large, underwater power cable
Authors: Prat Farran, Joana d'Arc; Zaragoza Monroig, M. Luisa; Río Fernandez, Joaquín delFri, 25 Jul 2014 10:56:15 GMThttp://hdl.handle.net/2117/236162014-07-25T10:56:15ZPrat Farran, Joana d'Arc; Zaragoza Monroig, M. Luisa; Río Fernandez, Joaquín delnoDiscrete-time static output-feedback H-infinity controller design for vehicle suspensions
http://hdl.handle.net/2117/23579
Title: Discrete-time static output-feedback H-infinity controller design for vehicle suspensions
Authors: Palacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid Reza
Abstract: This paper provides a direct and practical presentation of a novel methodology for static output feedback controller design. The proposed design strategy has been successfully applied in the fields of control systems for seismic protection of large
buildings and multi-building structures, control of offshore wind
turbines, and active control of vehicle suspensions. The positive
results obtained in these initial applications clearly indicate that
this approach could be an effective tool in a large variety of
control problems, for which an LMI formulation of the statefeedback
version of the problem is available. The main objective
of the paper is to facilitate a brief and friendly presentation of the
main ideas involved in the new design methodology. To this end,
a discrete-time static output-feedback H1 controller is designed
for a simplified quarter-car suspension system. Numerical simulations
indicate that the proposed controller exhibits a remarkably
good behavior when compared with the corresponding statefeedback
H1 controller.Mon, 21 Jul 2014 11:46:38 GMThttp://hdl.handle.net/2117/235792014-07-21T11:46:38ZPalacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid RezanoThis paper provides a direct and practical presentation of a novel methodology for static output feedback controller design. The proposed design strategy has been successfully applied in the fields of control systems for seismic protection of large
buildings and multi-building structures, control of offshore wind
turbines, and active control of vehicle suspensions. The positive
results obtained in these initial applications clearly indicate that
this approach could be an effective tool in a large variety of
control problems, for which an LMI formulation of the statefeedback
version of the problem is available. The main objective
of the paper is to facilitate a brief and friendly presentation of the
main ideas involved in the new design methodology. To this end,
a discrete-time static output-feedback H1 controller is designed
for a simplified quarter-car suspension system. Numerical simulations
indicate that the proposed controller exhibits a remarkably
good behavior when compared with the corresponding statefeedback
H1 controller.Generalizing the Steiner-Lehmus theorem using the Gröbner cover
http://hdl.handle.net/2117/23574
Title: Generalizing the Steiner-Lehmus theorem using the Gröbner cover
Authors: Montes Lozano, Antonio; Recio Muñiz, Tomás
Abstract: In this note we present an application of a new tool (the Gröbner cover method, to discuss parametric polynomial systems of equations) in the realm of automatic discovery of theorems in elementary geometry. Namely, we describe, through a relevant example, how the Gröbner cover algorithm is particularly well suited to obtain the missing hypotheses for a given geometric statement to hold true. We deal with the following problem: to describe the triangles that have at least two bisectors of equal length. The case of two inner bisectors is the well known, XIX century old, Steiner-Lehmus theorem, but the general case of inner and outer bisectors has been only recently addressed. We show how the Gröbner cover method automatically provides, while yielding more insight than through any other method, the conditions for a triangle to have two equal bisectors of whatever kind.Mon, 21 Jul 2014 08:52:22 GMThttp://hdl.handle.net/2117/235742014-07-21T08:52:22ZMontes Lozano, Antonio; Recio Muñiz, TomásnoAutomatic deduction, Automatic discovery, Comprehensive Gröbner system, Elementarygeometry, Gröbner coverIn this note we present an application of a new tool (the Gröbner cover method, to discuss parametric polynomial systems of equations) in the realm of automatic discovery of theorems in elementary geometry. Namely, we describe, through a relevant example, how the Gröbner cover algorithm is particularly well suited to obtain the missing hypotheses for a given geometric statement to hold true. We deal with the following problem: to describe the triangles that have at least two bisectors of equal length. The case of two inner bisectors is the well known, XIX century old, Steiner-Lehmus theorem, but the general case of inner and outer bisectors has been only recently addressed. We show how the Gröbner cover method automatically provides, while yielding more insight than through any other method, the conditions for a triangle to have two equal bisectors of whatever kind.Three-dimensional simulation of crack propagation in ferroelectric polycrystals: Effect of combined toughening mechanisms
http://hdl.handle.net/2117/23536
Title: Three-dimensional simulation of crack propagation in ferroelectric polycrystals: Effect of combined toughening mechanisms
Authors: Abdollahi Hosnijeh, Amir; Arias Vicente, Irene
Abstract: We simulate the fracture processes of ferroelectric polycrystals in three dimensions using a phase-field model. In this model, the grain boundaries, cracks and ferroelectric domain walls are represented in a diffuse way by three phase-fields. We thereby avoid the difficulty of tracking the interfaces in three dimensions. The resulting model can capture complex interactions between the crack and the polycrystalline and ferroelectric domain microstructures. The simulation results show the effect of the microstructures on the fracture response of the material. Crack deflection, crack bridging, crack branching and ferroelastic domain switching are observed to act as the main fracture toughening mechanisms in ferroelectric polycrystals. Our fully 3-D simulations illustrate how the combination of these mechanisms enhances the fracture toughness of the material, and pave the way for further systematic studies, including fracture homogenization.Thu, 17 Jul 2014 08:57:13 GMThttp://hdl.handle.net/2117/235362014-07-17T08:57:13ZAbdollahi Hosnijeh, Amir; Arias Vicente, IrenenoPolycrystals, Ferroelectricity, Fracture, Phase-field models, Finite element analysis, PHASE-FIELD SIMULATION, ENERGY-RELEASE RATE, R-CURVE BEHAVIOR, ELECTRIC-FIELDS, ELECTROMECHANICAL FRACTURE, BRITTLE-FRACTURE, COMPUTER-SIMULATION, COMPUTATIONAL MODEL, BOUNDARY-CONDITIONS, DOMAIN EVOLUTIONWe simulate the fracture processes of ferroelectric polycrystals in three dimensions using a phase-field model. In this model, the grain boundaries, cracks and ferroelectric domain walls are represented in a diffuse way by three phase-fields. We thereby avoid the difficulty of tracking the interfaces in three dimensions. The resulting model can capture complex interactions between the crack and the polycrystalline and ferroelectric domain microstructures. The simulation results show the effect of the microstructures on the fracture response of the material. Crack deflection, crack bridging, crack branching and ferroelastic domain switching are observed to act as the main fracture toughening mechanisms in ferroelectric polycrystals. Our fully 3-D simulations illustrate how the combination of these mechanisms enhances the fracture toughness of the material, and pave the way for further systematic studies, including fracture homogenization.