Articles de revista
http://hdl.handle.net/2117/3918
20171024T09:19:31Z

A finite version of the Kakeya problem
http://hdl.handle.net/2117/108967
A finite version of the Kakeya problem
Ball, Simeon Michael; Blokhuis, Aart; Domenzain, Diego
Let $L$ be a set of lines of an affine space over a field and let $S$ be a set of points with the property that every line of $L$ is incident with at least $N$ points of $S$. Let $D$ be the set of directions of the lines of $L$ considered as points of the projective space at infinity. We give a geometric construction of a set of lines $L$, where $D$ contains an $N^{n1}$ grid and where $S$ has size $2(\frac{1}{2}N)^n$ plus smaller order terms, given a starting configuration in the plane. We provide examples of such starting configurations for the reals and for finite fields. Following Dvir's proof of the finite field Kakeya conjecture and the idea of using multiplicities of Dvir, Kopparty, Saraf and Sudan, we prove a lower bound on the size of $S$ dependent on the ideal generated by the homogeneous polynomials vanishing on $D$. This bound is maximised as $(\frac{1}{2}N)^n$ plus smaller order terms, for $n\geqslant 4$, when $D$ contains the points of a $N^{n1}$ grid.
20171023T11:15:14Z
Ball, Simeon Michael
Blokhuis, Aart
Domenzain, Diego
Let $L$ be a set of lines of an affine space over a field and let $S$ be a set of points with the property that every line of $L$ is incident with at least $N$ points of $S$. Let $D$ be the set of directions of the lines of $L$ considered as points of the projective space at infinity. We give a geometric construction of a set of lines $L$, where $D$ contains an $N^{n1}$ grid and where $S$ has size $2(\frac{1}{2}N)^n$ plus smaller order terms, given a starting configuration in the plane. We provide examples of such starting configurations for the reals and for finite fields. Following Dvir's proof of the finite field Kakeya conjecture and the idea of using multiplicities of Dvir, Kopparty, Saraf and Sudan, we prove a lower bound on the size of $S$ dependent on the ideal generated by the homogeneous polynomials vanishing on $D$. This bound is maximised as $(\frac{1}{2}N)^n$ plus smaller order terms, for $n\geqslant 4$, when $D$ contains the points of a $N^{n1}$ grid.

Bifurcation of 2periodic orbits from nonhyperbolic fixed points
http://hdl.handle.net/2117/108965
Bifurcation of 2periodic orbits from nonhyperbolic fixed points
Cima Mollet, Anna; Gasull Embid, Armengol; Mañosa Fernández, Víctor
We introduce the concept of 2cyclicity for families of onedimensional maps with a nonhyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2periodic orbits that can bifurcate from the fixed point. As an application we study the 2cyclicity of some natural families of polynomial maps.
20171023T10:53:34Z
Cima Mollet, Anna
Gasull Embid, Armengol
Mañosa Fernández, Víctor
We introduce the concept of 2cyclicity for families of onedimensional maps with a nonhyperbolic fixed point by analogy to the cyclicity for families of planar vector fields with a weak focus. This new concept is useful in order to study the number of 2periodic orbits that can bifurcate from the fixed point. As an application we study the 2cyclicity of some natural families of polynomial maps.

Tails and bridges in the parabolic restricted threebody problem
http://hdl.handle.net/2117/108931
Tails and bridges in the parabolic restricted threebody problem
Barrabés Vera, Esther; Cors Iglesias, Josep Maria; Garcia Taberner, Laura; Ollé Torner, Mercè
After a close encounter of two galaxies, bridges and tails can be seen between or around them. A bridge would be a spiral arm between a galaxy and its companion, whereas a tail would correspond to a long and curving set of debris escaping from the galaxy. The goal of this paper is to present a mechanism, applying techniques of dynamical systems theory, that explains the formation of tails and bridges between galaxies in a simple model, the socalled parabolic restricted threebody problem, i.e. we study the motion of a particle under the gravitational influence of two primaries describing parabolic orbits. The equilibrium points and the final evolutions in this problem are recalled,and we showthat the invariant manifolds of the collinear equilibrium points and the ones of the collision manifold explain the formation of bridges and tails. Massive numerical simulations are carried out and their application to recover previous results are also analysed.
This article has been accepted for publication in Monthly notices of the Royal Astronomical Society ©: 2017 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.
20171020T13:49:11Z
Barrabés Vera, Esther
Cors Iglesias, Josep Maria
Garcia Taberner, Laura
Ollé Torner, Mercè
After a close encounter of two galaxies, bridges and tails can be seen between or around them. A bridge would be a spiral arm between a galaxy and its companion, whereas a tail would correspond to a long and curving set of debris escaping from the galaxy. The goal of this paper is to present a mechanism, applying techniques of dynamical systems theory, that explains the formation of tails and bridges between galaxies in a simple model, the socalled parabolic restricted threebody problem, i.e. we study the motion of a particle under the gravitational influence of two primaries describing parabolic orbits. The equilibrium points and the final evolutions in this problem are recalled,and we showthat the invariant manifolds of the collinear equilibrium points and the ones of the collision manifold explain the formation of bridges and tails. Massive numerical simulations are carried out and their application to recover previous results are also analysed.

Time decay in dualphaselag thermoelasticity: critical case
http://hdl.handle.net/2117/108915
Time decay in dualphaselag thermoelasticity: critical case
Liu, Zhuangyi; Quintanilla de Latorre, Ramón
This note is devoted to the study of the time decay of the onedimensional dualphaselag thermoelasticity. In this theory two delay parameters tq and t¿ are proposed. It is known that the system is exponentially stable if tq < 2t¿ [22]. We here make two new contributions to this problem. First, we prove the polynomial stability in the case that tq = 2t¿ as well the optimality of this decay rate. Second, we prove that the exponential stability remains true even if the inequality only holds in a proper subinterval of the spatial domain, when t¿ is spatially dependent.
20171020T11:43:29Z
Liu, Zhuangyi
Quintanilla de Latorre, Ramón
This note is devoted to the study of the time decay of the onedimensional dualphaselag thermoelasticity. In this theory two delay parameters tq and t¿ are proposed. It is known that the system is exponentially stable if tq < 2t¿ [22]. We here make two new contributions to this problem. First, we prove the polynomial stability in the case that tq = 2t¿ as well the optimality of this decay rate. Second, we prove that the exponential stability remains true even if the inequality only holds in a proper subinterval of the spatial domain, when t¿ is spatially dependent.

On the spatial behavior in twotemperature generalized thermoelastic theories
http://hdl.handle.net/2117/108910
On the spatial behavior in twotemperature generalized thermoelastic theories
Miranville, Alain; Quintanilla de Latorre, Ramón
This paper investigates the spatial behavior of the solutions of two generalized thermoelastic theories with two temperatures. To be more precise, we focus on the Green–Lindsay theory with two temperatures and the Lord–Shulman theory with two temperatures. We prove that a Phragmén–Lindelöf alternative of exponential type can be obtained in both cases. We also describe how to obtain a bound on the amplitude term by means of the boundary conditions for the Green–Lindsay theory with two temperatures.
The final publication is available at link.springer.com via https://doi.org/10.1007/s000330170857x
20171020T11:21:30Z
Miranville, Alain
Quintanilla de Latorre, Ramón
This paper investigates the spatial behavior of the solutions of two generalized thermoelastic theories with two temperatures. To be more precise, we focus on the Green–Lindsay theory with two temperatures and the Lord–Shulman theory with two temperatures. We prove that a Phragmén–Lindelöf alternative of exponential type can be obtained in both cases. We also describe how to obtain a bound on the amplitude term by means of the boundary conditions for the Green–Lindsay theory with two temperatures.

AARbased decomposition method for lower bound limit analysis
http://hdl.handle.net/2117/108908
AARbased decomposition method for lower bound limit analysis
Muñoz Romero, José; Rabiei, Nima
Despite the recent progress in optimisation techniques, finiteelement stability analysis of realistic threedimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive deremeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but nonlinear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other wellknown decomposition algorithms.
20171020T10:53:50Z
Muñoz Romero, José
Rabiei, Nima
Despite the recent progress in optimisation techniques, finiteelement stability analysis of realistic threedimensional problems is still hampered by the size of the resulting optimisation problem. Current solvers may take a prohibitive computational time, if they give a solution at all. The possible remedies to this are the design of adaptive deremeshing techniques, decomposition of the system of equations or of the optimisation problem. This paper concentrates on the last approach, and presents an algorithm especially suited for limit analysis. Optimisation problems in limit analysis are in general convex but nonlinear. This fact renders the design of decomposition techniques specially challenging. The efficiency of general approaches such as Benders or Dantzig–Wolfe is not always satisfactory, and strongly depends on the structure of the optimisation problem. This work presents a new method that is based on rewriting the feasibility region of the global optimisation problem as the intersection of two subsets. By resorting to the averaged alternating reflections (AAR) method in order to find the distance between the sets, the optimisation problem is successfully solved in a decomposed manner. Some representative examples illustrate the application of the method and its efficiency with respect to other wellknown decomposition algorithms.

On the viscoelastic mixtures of solids
http://hdl.handle.net/2117/108907
On the viscoelastic mixtures of solids
Fernández, Jose R.; Magaña Nieto, Antonio; Masid, Maria; Quintanilla de Latorre, Ramón
In this paper we analyze an homogeneous and isotropic mixture of viscoelastic solids. We propose conditions to guarantee the coercivity of the internal energy and also of the dissipation, first in dimension two and later in dimension three. We obtain an uniqueness result for the solutions when the dissipation is positive and without any hypothesis over the internal energy. When the internal energy and the dissipation are both positive, we prove the existence of solutions as well as their analyticity. Exponential stability and impossibility of localization of the solutions are immediate consequences.
The final publication is available at link.springer.com via https://doi.org/10.1007/s0024501794398
20171020T10:49:05Z
Fernández, Jose R.
Magaña Nieto, Antonio
Masid, Maria
Quintanilla de Latorre, Ramón
In this paper we analyze an homogeneous and isotropic mixture of viscoelastic solids. We propose conditions to guarantee the coercivity of the internal energy and also of the dissipation, first in dimension two and later in dimension three. We obtain an uniqueness result for the solutions when the dissipation is positive and without any hypothesis over the internal energy. When the internal energy and the dissipation are both positive, we prove the existence of solutions as well as their analyticity. Exponential stability and impossibility of localization of the solutions are immediate consequences.

Hysteresis based vibration control of baseisolated structures
http://hdl.handle.net/2117/108880
Hysteresis based vibration control of baseisolated structures
Rodellar Benedé, José; García, Guillem; Vidal Seguí, Yolanda; Acho Zuppa, Leonardo; Pozo Montero, Francesc
An active control strategy for baseisolated structures is proposed in this work. The key idea comes from the observation that
passive base isolation systems are hysteretic. Thus, an hysteresis based vibration control is designed in a way that the control force
is smooth and limited by a prescribed bound. A model of a threestory building is used to study and compare the efficacy of a
passive pure friction damper alone, with the addition of the proposed active control. We introduce a rate limiter to the actuator
to simulate its limited speed capacity, present in every physical actuator. Simulations demonstrate that our active control strategy
significantly reduces base displacements and shears without an increase in drift or accelerations.
20171020T07:20:21Z
Rodellar Benedé, José
García, Guillem
Vidal Seguí, Yolanda
Acho Zuppa, Leonardo
Pozo Montero, Francesc
An active control strategy for baseisolated structures is proposed in this work. The key idea comes from the observation that
passive base isolation systems are hysteretic. Thus, an hysteresis based vibration control is designed in a way that the control force
is smooth and limited by a prescribed bound. A model of a threestory building is used to study and compare the efficacy of a
passive pure friction damper alone, with the addition of the proposed active control. We introduce a rate limiter to the actuator
to simulate its limited speed capacity, present in every physical actuator. Simulations demonstrate that our active control strategy
significantly reduces base displacements and shears without an increase in drift or accelerations.

Constraints on the automorphism group of a curve
http://hdl.handle.net/2117/108769
Constraints on the automorphism group of a curve
González Rovira, Josep
For a curve of genus > 1 defined over a finite field, we present a sufficient criterion for the nonexistence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the automorphism group of some modular curves of high genus.
20171017T15:07:55Z
González Rovira, Josep
For a curve of genus > 1 defined over a finite field, we present a sufficient criterion for the nonexistence of automorphisms of order a power of a rational prime. We show how this criterion can be used to determine the automorphism group of some modular curves of high genus.

Wildness of the problems of classifying twodimensional spaces of commuting linear operators and certain Lie algebras
http://hdl.handle.net/2117/108725
Wildness of the problems of classifying twodimensional spaces of commuting linear operators and certain Lie algebras
Futorny, Vyacheslav; Klymchuk, Tetiana; Petravchukc, Anatolii P.; Sergeichuk, Vladimir V.
For each twodimensional vector space V of commuting n×n matrices over a field F with at least 3 elements, we denote by V˜ the vector space of all (n+1)×(n+1) matrices of the form [A¿00] with A¿V. We prove the wildness of the problem of classifying Lie algebras V˜ with the bracket operation [u,v]:=uvvu. We also prove the wildness of the problem of classifying twodimensional vector spaces consisting of commuting linear operators on a vector space over a field.
20171016T14:24:24Z
Futorny, Vyacheslav
Klymchuk, Tetiana
Petravchukc, Anatolii P.
Sergeichuk, Vladimir V.
For each twodimensional vector space V of commuting n×n matrices over a field F with at least 3 elements, we denote by V˜ the vector space of all (n+1)×(n+1) matrices of the form [A¿00] with A¿V. We prove the wildness of the problem of classifying Lie algebras V˜ with the bracket operation [u,v]:=uvvu. We also prove the wildness of the problem of classifying twodimensional vector spaces consisting of commuting linear operators on a vector space over a field.