DSpace Community:
http://hdl.handle.net/2117/3227
Wed, 23 Jul 2014 07:54:11 GMT2014-07-23T07:54:11Zwebmaster.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 pósterEl e-portafolio del estudiante en Mahara-Moodle y Google Sites
http://hdl.handle.net/2117/23534
Title: El e-portafolio del estudiante en Mahara-Moodle y Google Sites
Authors: García Planas, María Isabel; Taberna Torres, Judit
Abstract: Es bien conocido el potencial que tiene el uso del e-portfolio del estudiante para hacer visible tanto para el mismo como para los demás, de cómo y hasta que nivel ha logrado sus objetivos.
Para realizar un e-portafolio se pueden utilizar distintas aplicaciones, entre ellas se encuentran Google Sites y Mahara.
Google Sites permite de forma sencilla editando una plantilla previamente preparada por el profesor, crear una página web como muestra de sus trabajos desarrollados a lo largo de sus estudios.
Mahara es un sistema de e-portafolio que puede conectarse a Moodle y el cual puede ser controlado por el estudiante y puede ser visible por el grupo. Debido a la interoperabilidad de Mahara especialmente con Moodle, este permite que desde la plataforma de Atenea se puedan interconectar el profesorado con el e-portafolio del estudiante.
En este trabajo presentamos los resultados obtenidos desde el año 2011 hasta la actualidad en las investigaciones realizadas sobre el e-portafolio en el marco de la Universidad Politècnica de Catalunya.Thu, 17 Jul 2014 07:51:51 GMThttp://hdl.handle.net/2117/235342014-07-17T07:51:51ZGarcía Planas, María Isabel; Taberna Torres, Juditnoe-portafolio, Moodle, Mahara, Google SitesEs bien conocido el potencial que tiene el uso del e-portfolio del estudiante para hacer visible tanto para el mismo como para los demás, de cómo y hasta que nivel ha logrado sus objetivos.
Para realizar un e-portafolio se pueden utilizar distintas aplicaciones, entre ellas se encuentran Google Sites y Mahara.
Google Sites permite de forma sencilla editando una plantilla previamente preparada por el profesor, crear una página web como muestra de sus trabajos desarrollados a lo largo de sus estudios.
Mahara es un sistema de e-portafolio que puede conectarse a Moodle y el cual puede ser controlado por el estudiante y puede ser visible por el grupo. Debido a la interoperabilidad de Mahara especialmente con Moodle, este permite que desde la plataforma de Atenea se puedan interconectar el profesorado con el e-portafolio del estudiante.
En este trabajo presentamos los resultados obtenidos desde el año 2011 hasta la actualidad en las investigaciones realizadas sobre el e-portafolio en el marco de la Universidad Politècnica de Catalunya.Noise and adaptation in multistable perception: noise drives when to switch, adaptation determines percept choice.
http://hdl.handle.net/2117/23524
Title: Noise and adaptation in multistable perception: noise drives when to switch, adaptation determines percept choice.
Authors: Huguet Casades, Gemma; Rinzel, John; Hupé, Jean-Michel
Abstract: We study the dynamics of perceptual switching in ambiguous visual scenes that admit more than two interpretations/percepts to gain insight into the dynamics of perceptual multistability and its underlying neural mechanisms. We focus on visual plaids that are tristable and we present both experimental and computational results. We develop a firing-rate model based on mutual inhibition and adaptation that involves stochastic dynamics of multiple-attractor systems. The model can account for the dynamic properties (transition probabilities, distributions of percept durations, etc.) observed in the experiments. Noise and adaptation have both been shown to play roles in the dynamics of bistable perception. Here, tristable perception allows us to specify the roles of noise and adaptation in our model. Noise is critical in considering the time of a switch. On the other hand, adaptation mechanisms are critical in considering perceptual choice (in tristable perception, each time a percept ends, there is a possible choice between two new percepts).Wed, 16 Jul 2014 07:35:44 GMThttp://hdl.handle.net/2117/235242014-07-16T07:35:44ZHuguet Casades, Gemma; Rinzel, John; Hupé, Jean-MichelnoWe study the dynamics of perceptual switching in ambiguous visual scenes that admit more than two interpretations/percepts to gain insight into the dynamics of perceptual multistability and its underlying neural mechanisms. We focus on visual plaids that are tristable and we present both experimental and computational results. We develop a firing-rate model based on mutual inhibition and adaptation that involves stochastic dynamics of multiple-attractor systems. The model can account for the dynamic properties (transition probabilities, distributions of percept durations, etc.) observed in the experiments. Noise and adaptation have both been shown to play roles in the dynamics of bistable perception. Here, tristable perception allows us to specify the roles of noise and adaptation in our model. Noise is critical in considering the time of a switch. On the other hand, adaptation mechanisms are critical in considering perceptual choice (in tristable perception, each time a percept ends, there is a possible choice between two new percepts).R+aR2 loop quantum cosmology
http://hdl.handle.net/2117/23514
Title: R+aR2 loop quantum cosmology
Authors: Amorós Torrent, Jaume; De Haro, Jaume; Odintsov, Sergei D.
Abstract: Working in Einstein frame, we introduce, in order to avoid singularities, holonomy corrections to the f(R)=R+aR2 model. We perform a detailed analytical and numerical study when holonomy corrections are taken into account in both Jordan and Einstein frames, obtaining, in Jordan frame, a dynamics which differs qualitatively, at early times, from the one of the original model. More precisely, when holonomy corrections are taken into account, the Universe is not singular, starting at early times in the contracting phase and bouncing to enter the expanding one where, as in the original model, it inflates. This dynamics is completely different from the one obtained in the original R+aR2 model, where the Universe is singular at early times and never bounces. Moreover, we show that these holonomy corrections may lead to better predictions for the inflationary phase as compared with current observations.Tue, 15 Jul 2014 11:00:50 GMThttp://hdl.handle.net/2117/235142014-07-15T11:00:50ZAmorós Torrent, Jaume; De Haro, Jaume; Odintsov, Sergei D.noWorking in Einstein frame, we introduce, in order to avoid singularities, holonomy corrections to the f(R)=R+aR2 model. We perform a detailed analytical and numerical study when holonomy corrections are taken into account in both Jordan and Einstein frames, obtaining, in Jordan frame, a dynamics which differs qualitatively, at early times, from the one of the original model. More precisely, when holonomy corrections are taken into account, the Universe is not singular, starting at early times in the contracting phase and bouncing to enter the expanding one where, as in the original model, it inflates. This dynamics is completely different from the one obtained in the original R+aR2 model, where the Universe is singular at early times and never bounces. Moreover, we show that these holonomy corrections may lead to better predictions for the inflationary phase as compared with current observations.Auto-Backlund transformations and special integrals for differential-delay Painlevé hierarchies
http://hdl.handle.net/2117/23511
Title: Auto-Backlund transformations and special integrals for differential-delay Painlevé hierarchies
Authors: Fedorov, Yuri; Ruiz Gordoa, Maria Pilar; Pickering, Andrew
Abstract: The six Painleve equations have attracted much interest over the last thirty years or so. More recently many authors have begun to explore properties of higher-order versions of both these equations and their discrete analogues. However, little attention has been paid to differential-delay Painleve equations, i.e., analogues of the Painleve equations involving both shifts in and derivatives with respect to the independent variable, and even less to higher-order analogues of these last. In the current paper we discuss the phenomenon whereby members of one differential-delay Painleve hierarchy define solutions of higher-order members of a second differential-delay Painleve hierarchy. We also give an auto-Backlund transformation for a differential-delay Painleve hierarchy. The key to our approach is the underlying Hamiltonian structure of related completely integrable lattice hierarchies. (C) 2014 Elsevier B.V. All rights reserved.Tue, 15 Jul 2014 10:29:35 GMThttp://hdl.handle.net/2117/235112014-07-15T10:29:35ZFedorov, Yuri; Ruiz Gordoa, Maria Pilar; Pickering, AndrewnoDifferential-delay Painleve hierarchies, MONODROMY PRESERVING DEFORMATION, RATIONAL COEFFICIENTS, EQUATIONSThe six Painleve equations have attracted much interest over the last thirty years or so. More recently many authors have begun to explore properties of higher-order versions of both these equations and their discrete analogues. However, little attention has been paid to differential-delay Painleve equations, i.e., analogues of the Painleve equations involving both shifts in and derivatives with respect to the independent variable, and even less to higher-order analogues of these last. In the current paper we discuss the phenomenon whereby members of one differential-delay Painleve hierarchy define solutions of higher-order members of a second differential-delay Painleve hierarchy. We also give an auto-Backlund transformation for a differential-delay Painleve hierarchy. The key to our approach is the underlying Hamiltonian structure of related completely integrable lattice hierarchies. (C) 2014 Elsevier B.V. All rights reserved.Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies
http://hdl.handle.net/2117/23508
Title: Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies
Authors: Delshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Pere
Abstract: We study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a frequency vector omega = (1, Omega), where Omega is a quadratic irrational number, or a 3-dimensional torus with a frequency vector w = (1, Omega, Omega(2)), where Omega is a cubic irrational number. Applying the Poincare-Melnikov method, we find exponentially small asymptotic estimates for the maximal splitting distance between the stable and unstable manifolds associated to the invariant torus, and we show that such estimates depend strongly on the arithmetic properties of the frequencies. In the quadratic case, we use the continued fractions theory to establish a certain arithmetic property, fulfilled in 24 cases, which allows us to provide asymptotic estimates in a simple way. In the cubic case, we focus our attention to the case in which Q is the so-called cubic golden number (the real root of x(3) x - 1= 0), obtaining also asymptotic estimates. We point out the similitudes and differences between the results obtained for both the quadratic and cubic cases.Tue, 15 Jul 2014 08:21:36 GMThttp://hdl.handle.net/2117/235082014-07-15T08:21:36ZDelshams Valdés, Amadeu; Gonchenko, Marina; Gutiérrez Serrés, Perenosplitting of separatrices, Melnikov integrals, quadratic and cubic frequencies, INTEGRABLE HAMILTONIAN-SYSTEMS, ADIABATIC INVARIANTS, CONTINUED FRACTIONS, MELNIKOV METHOD, MCMILLAN MAP, UPPER-BOUNDS, RENORMALIZATION, APPROXIMATION, PERTURBATION, PENDULUMWe study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with a frequency vector omega = (1, Omega), where Omega is a quadratic irrational number, or a 3-dimensional torus with a frequency vector w = (1, Omega, Omega(2)), where Omega is a cubic irrational number. Applying the Poincare-Melnikov method, we find exponentially small asymptotic estimates for the maximal splitting distance between the stable and unstable manifolds associated to the invariant torus, and we show that such estimates depend strongly on the arithmetic properties of the frequencies. In the quadratic case, we use the continued fractions theory to establish a certain arithmetic property, fulfilled in 24 cases, which allows us to provide asymptotic estimates in a simple way. In the cubic case, we focus our attention to the case in which Q is the so-called cubic golden number (the real root of x(3) x - 1= 0), obtaining also asymptotic estimates. We point out the similitudes and differences between the results obtained for both the quadratic and cubic cases.Station-keeping of real Earth-Moon libration point orbits using discrete-time sliding mode control
http://hdl.handle.net/2117/23453
Title: Station-keeping of real Earth-Moon libration point orbits using discrete-time sliding mode control
Authors: Lian, Yijun; Gómez Muntané, Gerard; Masdemont Soler, Josep; Tang, Guojian
Abstract: In this work, station-keeping of real Earth–Moon libration point orbits is studied using discrete-time sliding mode control (DSMC). For comparison, a discrete linear quadratic regulator (DLQR) controller is also considered. The libration orbits are termed “real” in the sense that they are obtained in a complete Solar System model, taking into account all the gravitational forces of the planets, the Moon, and the Sun. This is a key point for any station-keeping study, that the use of far from real orbits as nominal ones increases unnecessarily the station-keeping cost. The resulting controlled system, linearised with respect to some nominal orbit, takes a discrete-time form suitable for applying impulsive maneuvers. The DSMC controller is designed by the reaching law with the parameters chosen in an adaptive way. A method for designing the sliding surface is proposed. In order to assess and compare the performance of the two controllers, simulations are done for six libration point orbits around the L2L2 point (three halo orbits and three Lissajous ones) during a time span of 10 years. Several practical constraints are also considered in the simulations. Extensive Monte Carlo results show that the proposed DSMC approach is able to maintain the spacecraft within a close vicinity of the nominal orbits with a maneuver cost less than 2 m/s per year, and it outperforms the DLQR approach in terms of the position controllability. Some comparison with previous results obtained by other authors with different procedures is also given.Wed, 09 Jul 2014 11:19:18 GMThttp://hdl.handle.net/2117/234532014-07-09T11:19:18ZLian, Yijun; Gómez Muntané, Gerard; Masdemont Soler, Josep; Tang, GuojiannoStation-keeping, Libration point orbit, Siding mode control, LQR, Discrete-time, Earth-Moon system, CONTROL-SYSTEMS, HALO ORBITIn this work, station-keeping of real Earth–Moon libration point orbits is studied using discrete-time sliding mode control (DSMC). For comparison, a discrete linear quadratic regulator (DLQR) controller is also considered. The libration orbits are termed “real” in the sense that they are obtained in a complete Solar System model, taking into account all the gravitational forces of the planets, the Moon, and the Sun. This is a key point for any station-keeping study, that the use of far from real orbits as nominal ones increases unnecessarily the station-keeping cost. The resulting controlled system, linearised with respect to some nominal orbit, takes a discrete-time form suitable for applying impulsive maneuvers. The DSMC controller is designed by the reaching law with the parameters chosen in an adaptive way. A method for designing the sliding surface is proposed. In order to assess and compare the performance of the two controllers, simulations are done for six libration point orbits around the L2L2 point (three halo orbits and three Lissajous ones) during a time span of 10 years. Several practical constraints are also considered in the simulations. Extensive Monte Carlo results show that the proposed DSMC approach is able to maintain the spacecraft within a close vicinity of the nominal orbits with a maneuver cost less than 2 m/s per year, and it outperforms the DLQR approach in terms of the position controllability. Some comparison with previous results obtained by other authors with different procedures is also given.Códigos de convolución desde el punto de vista de teoría de control. Análisis de la observabilidad
http://hdl.handle.net/2117/23450
Title: Códigos de convolución desde el punto de vista de teoría de control. Análisis de la observabilidad
Authors: García Planas, María Isabel; Tarragona Romero, Sonia; Um, Laurence Emilie
Abstract: En este trabajo se realiza un estudio detallado
de la estructura algebraica de los códigos de convolución
empleando técnicas de la teoría de sistemas lineales. La
conexión entre estos conceptos ayuda a comprender mejor
las propiedades de los códigos convolucionales. Más
explícitamente, esta conexión es debida a que los
conceptos de controlabilidad y observabilidad, de los
sistemas lineales, pueden ser expresados, en el marco de
los códigos convolucionales, como el carácter no
catastrófico de los códigos. En particular, en este trabajo
se examina la propiedad de “output-observabilidad” y
damos condiciones que aseguran el cumplimiento de esta
propiedad.Wed, 09 Jul 2014 10:49:12 GMThttp://hdl.handle.net/2117/234502014-07-09T10:49:12ZGarcía Planas, María Isabel; Tarragona Romero, Sonia; Um, Laurence EmilienoCódigos, sistemas lineales, output-observabilidad.En este trabajo se realiza un estudio detallado
de la estructura algebraica de los códigos de convolución
empleando técnicas de la teoría de sistemas lineales. La
conexión entre estos conceptos ayuda a comprender mejor
las propiedades de los códigos convolucionales. Más
explícitamente, esta conexión es debida a que los
conceptos de controlabilidad y observabilidad, de los
sistemas lineales, pueden ser expresados, en el marco de
los códigos convolucionales, como el carácter no
catastrófico de los códigos. En particular, en este trabajo
se examina la propiedad de “output-observabilidad” y
damos condiciones que aseguran el cumplimiento de esta
propiedad.The Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
http://hdl.handle.net/2117/23448
Title: The Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
Authors: Fedorov, Yuri; Pantazi, Chara
Abstract: We consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third kind, as functions of some parameters of the curves. The systems can be regarded as extensions of the well-studied Picard-Fuchs equations for periods of complete integrals of first and second kind on odd hyperelliptic curves. The periods we consider are linear combinations of the action variables of several integrable systems, in particular the generalized Neumann system with polynomial separable potentials. Thus the solutions of the extended Picard-Fuchs equations can be used to study various properties of the actions. (C) 2014 AIP Publishing LLC.Wed, 09 Jul 2014 10:41:57 GMThttp://hdl.handle.net/2117/234482014-07-09T10:41:57ZFedorov, Yuri; Pantazi, CharanoSEPARABLE SYSTEMSWe consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third kind, as functions of some parameters of the curves. The systems can be regarded as extensions of the well-studied Picard-Fuchs equations for periods of complete integrals of first and second kind on odd hyperelliptic curves. The periods we consider are linear combinations of the action variables of several integrable systems, in particular the generalized Neumann system with polynomial separable potentials. Thus the solutions of the extended Picard-Fuchs equations can be used to study various properties of the actions. (C) 2014 AIP Publishing LLC.Reflexivity in precompact groups and extensions
http://hdl.handle.net/2117/23167
Title: Reflexivity in precompact groups and extensions
Authors: Galindo Pastor, Jorge; Tkachenko, Mikhail; Bruguera Padró, Mª Montserrat; Hernandez, Constancio
Abstract: We establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that:; (1) A precompact Abelian group G of bounded order is reflexive if the dual group G<^> has no infinite compact subsets and every compact subset of G is contained in a compact subgroup of G.; (2) Any extension of a reflexive P-group by another reflexive P-group is again reflexive.; We show on the other hand that an extension of a compact group by a reflexive omega-bounded group (even dual to a reflexive P-group) can fail to be reflexive.; We also show that the P-modification of a reflexive sigma-compact group can be non-reflexive (even if, as proved in [20], the P-modification of a locally compact Abelian group is always reflexive). (C) 2013 Elsevier B.V. All rights reserved.Thu, 05 Jun 2014 15:04:55 GMThttp://hdl.handle.net/2117/231672014-06-05T15:04:55ZGalindo Pastor, Jorge; Tkachenko, Mikhail; Bruguera Padró, Mª Montserrat; Hernandez, ConstancionoPrecompact, Pseudocompact, omega-Bounded, Reflexive, P-group, Extension, ABELIAN TOPOLOGICAL-GROUPS, PONTRYAGIN DUALITY, SPACEWe establish some general principles and find some counter-examples concerning the Pontryagin reflexivity of precompact groups and P-groups. We prove in particular that:; (1) A precompact Abelian group G of bounded order is reflexive if the dual group G<^> has no infinite compact subsets and every compact subset of G is contained in a compact subgroup of G.; (2) Any extension of a reflexive P-group by another reflexive P-group is again reflexive.; We show on the other hand that an extension of a compact group by a reflexive omega-bounded group (even dual to a reflexive P-group) can fail to be reflexive.; We also show that the P-modification of a reflexive sigma-compact group can be non-reflexive (even if, as proved in [20], the P-modification of a locally compact Abelian group is always reflexive). (C) 2013 Elsevier B.V. All rights reserved.Decomposition spaces, incidence algebras and Möbius inversion
http://hdl.handle.net/2117/23130
Title: Decomposition spaces, incidence algebras and Möbius inversion
Authors: Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, AndrewTue, 03 Jun 2014 08:45:51 GMThttp://hdl.handle.net/2117/231302014-06-03T08:45:51ZGálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, AndrewnoAlgebraic topology, CombinatoricsThe influence of fractional diffusion in Fisher-KPP equations
http://hdl.handle.net/2117/23044
Title: The influence of fractional diffusion in Fisher-KPP equations
Authors: Cabré Vilagut, Xavier; Roquejoffre, Jean-Michel
Abstract: We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the standard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable Lévy process, the front position is exponential in time. Our results provide a mathematically rigorous justification of numerous heuristics about this model.Mon, 26 May 2014 08:26:15 GMThttp://hdl.handle.net/2117/230442014-05-26T08:26:15ZCabré Vilagut, Xavier; Roquejoffre, Jean-MichelnoWe study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the standard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable Lévy process, the front position is exponential in time. Our results provide a mathematically rigorous justification of numerous heuristics about this model.Degree and algebraic properties of lattice and matrix ideals
http://hdl.handle.net/2117/23006
Title: Degree and algebraic properties of lattice and matrix ideals
Authors: O'Carroll, Liam; Planas Vilanova, Francesc d'Assís; Villarreal Rodríguez, Rafael Heraclio
Abstract: We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Z(s) and in terms of relative volumes of lattice polytopes. We also study primary decompositions of lattice ideals over an arbitrary field using the Eisenbud-Sturmfels theory of binomial ideals over algebraically closed fields. We then use these results to study certain families of integer matrices (positive critical binomial (PCB), generalized positive critical binomial (GPCB), critical binomial (CB), and generalized critical binomial (GCB) matrices) and the algebra of their corresponding matrix ideals. In particular, the family of GPCB matrices is shown to be closed under transposition, and previous results for PCB ideals are extended to GPCB ideals. Then, more particularly, we give some applications to the theory of 1-dimensional binomial ideals. If G is a connected graph, we show as a further application that the order of its sandpile group is the degree of the Laplacian ideal and the degree of the toppling ideal. We also use our earlier results to give a structure theorem for graded lattice ideals of dimension 1 in 3 variables and for homogeneous lattices in Z(3) in terms of CB ideals and CB matrices, respectively, thus complementing a well-known theorem of Herzog on the toric ideal of a monomial space curve.Fri, 16 May 2014 08:09:45 GMThttp://hdl.handle.net/2117/230062014-05-16T08:09:45ZO'Carroll, Liam; Planas Vilanova, Francesc d'Assís; Villarreal Rodríguez, Rafael Heraclionolattice ideal, graded binomial ideal, degree, primary decomposition, PCB ideal, BINOMIAL IDEALS, GRAPHSWe study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Z(s) and in terms of relative volumes of lattice polytopes. We also study primary decompositions of lattice ideals over an arbitrary field using the Eisenbud-Sturmfels theory of binomial ideals over algebraically closed fields. We then use these results to study certain families of integer matrices (positive critical binomial (PCB), generalized positive critical binomial (GPCB), critical binomial (CB), and generalized critical binomial (GCB) matrices) and the algebra of their corresponding matrix ideals. In particular, the family of GPCB matrices is shown to be closed under transposition, and previous results for PCB ideals are extended to GPCB ideals. Then, more particularly, we give some applications to the theory of 1-dimensional binomial ideals. If G is a connected graph, we show as a further application that the order of its sandpile group is the degree of the Laplacian ideal and the degree of the toppling ideal. We also use our earlier results to give a structure theorem for graded lattice ideals of dimension 1 in 3 variables and for homogeneous lattices in Z(3) in terms of CB ideals and CB matrices, respectively, thus complementing a well-known theorem of Herzog on the toric ideal of a monomial space curve.Stability analysis of a clamped-pinned pipeline conveying fluid
http://hdl.handle.net/2117/22879
Title: Stability analysis of a clamped-pinned pipeline conveying fluid
Authors: García Planas, María Isabel; Mediano Valiente, Begoña
Abstract: Increasing advances in materials engineering and cost reduction in their testing have lead to the study of
the stability of vibration of pipes conveying fluid an important problem to deal with. Currently, such analysis is
done either by means of simulation with costly specialized software or by making laboratory tests of the selected
material. One of the main issues with the last process is that if appears any trouble on the material selection, it is
necessary to restart all the process, and it is happening each time there is a mistake on the material selection. In
order to avoid such costly tests, a general mathematical description of the dynamic behavior of a clamped-pinned
pipeline conveying fluid is presented. The system stability has been studied by means of the eigenvalues of a
Hamiltonian linear system associated. From this analysis, characteristic expressions dependent on material constants
have been developed as inequalities, which ensure the stability of the material if it matches all expressions.
Finally, some specific materials are introduced as study cases to compare the mathematical description proposed
with the results obtained from specialized software as ANSYS, in order to validate the resultsWed, 07 May 2014 10:12:54 GMThttp://hdl.handle.net/2117/228792014-05-07T10:12:54ZGarcía Planas, María Isabel; Mediano Valiente, BegoñanoStability, eigenvalues analysis, pipe conveying fluid, material selectionIncreasing advances in materials engineering and cost reduction in their testing have lead to the study of
the stability of vibration of pipes conveying fluid an important problem to deal with. Currently, such analysis is
done either by means of simulation with costly specialized software or by making laboratory tests of the selected
material. One of the main issues with the last process is that if appears any trouble on the material selection, it is
necessary to restart all the process, and it is happening each time there is a mistake on the material selection. In
order to avoid such costly tests, a general mathematical description of the dynamic behavior of a clamped-pinned
pipeline conveying fluid is presented. The system stability has been studied by means of the eigenvalues of a
Hamiltonian linear system associated. From this analysis, characteristic expressions dependent on material constants
have been developed as inequalities, which ensure the stability of the material if it matches all expressions.
Finally, some specific materials are introduced as study cases to compare the mathematical description proposed
with the results obtained from specialized software as ANSYS, in order to validate the results