DSpace Collection:
http://hdl.handle.net/2117/3918
2014-11-23T03:38:13ZNonlinear 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.J2 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.Signatura de les formes bilineals simètriques
http://hdl.handle.net/2117/24807
Title: Signatura de les formes bilineals simètriques
Authors: Rossell Garriga, Josep Maria; Rubio Díaz, PedroAn extension problem for the CR fractional Laplacian
http://hdl.handle.net/2117/24794
Title: An extension problem for the CR fractional Laplacian
Authors: Frank, Rupert L.; González Nogueras, María del Mar; Monticelli, Dario D.; Tan, Jinggang
Abstract: We show that the conformally invariant fractional powers of the sub-Laplacian
on the Heisenberg group are given in terms of the scattering operator for an extension
problem to the Siegel upper halfspace. Remarkably, this extension problem is di erent
from the one studied, among others, by Ca arelli and Silvestre.2014-11-21T11:27:55ZPreservation of controllability-observability in expanded systems
http://hdl.handle.net/2117/24791
Title: Preservation of controllability-observability in expanded systems
Authors: Bakule, Lubomir; Rodellar Benedé, José; Rossell Garriga, Josep Maria; Rubio Díaz, Pedro
Abstract: The result contributed by the article is that controllability-observability of an original continuous-time LTI dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases, such as aggregations and restrictions, which enable such preservation only in certain special cases. A complete unrestricted transmission of these qualitative properties from the original controllable-observable system to its expansion is a basic requirement on the expansion/contraction process, mainly when controllers/observers are designed in expanded systems to be consequently contracted for implementation in initially given systems. An original system composed of two overlapped subsystems is adopted as a general prototype ease. A numerical example is supplied2014-11-20T16:55:31ZOverlapping reliable control for a cable-stayed bridge benchmark
http://hdl.handle.net/2117/24790
Title: Overlapping reliable control for a cable-stayed bridge benchmark
Authors: Bakule, Lubomir; Paulet-Crainiceanu, Fideliu; Rodellar Benedé, José; Rossell Garriga, Josep Maria
Abstract: The brief presents a reliable 1-out-2 reduced order control design strategy for a cable-stayed bridge benchmark using two overlapping subsystems and the linear quadratic Gaussian (LQG) design. Reliability with regard to controller failures is considered. Local controllers are designed for reduced order subsystems of expanded system. They are implemented and evaluated on the original overall system model. Two different sets of numerical experiments of reliable control design within 1-out-2 controller failure structure have been systematically tested using a SIMULINK scheme and compared to the benchmark sample centralized LQG design. The performance of the reliable control design has been assessed by means of given benchmark evaluation criteria. The dynamics of the closed-loop benchmark model with this multiple controller exhibits an acceptable behavior though slightly worse than in the centralized case. Thereby, the main result is a practical well working 1-out-2 reliable controller designed for a real world large-scale system. The significance of this new strategy lies in its practical systematic approach for reliable control design for large scale systems.2014-11-20T16:48:44ZGeneralized selection of complementary matrices in the inclusion principle
http://hdl.handle.net/2117/24789
Title: Generalized selection of complementary matrices in the inclusion principle
Authors: Bakule, Lubomir; Rodellar Benedé, José; Rossell Garriga, Josep Maria
Abstract: This paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state LQ optimal control of LTI systems, it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices, the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control design2014-11-20T16:12:13ZNonuniform Fuchsian codes for noisy channels
http://hdl.handle.net/2117/24788
Title: Nonuniform Fuchsian codes for noisy channels
Authors: Blanco Chacón, Iván; Remón Adell, Dionís; Hollanti, Camilla; Alsina Aubach, Montserrat
Abstract: We develop a new transmission scheme for additive white Gaussian noisy (AWGN) channels based on Fuchsian groups from rational quaternion algebras. The structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence conventional decoding methods based on linearity and symmetry do not apply. Previously, only brute force decoding methods with complexity that is linear in the code size exist for general nonuniform codes. However, the properly discontinuous character of the action of the Fuchsian groups on the complex upper half-plane translates into decoding complexity that is logarithmic in the code size via a recently introduced point reduction algorithm.2014-11-20T15:52:25ZFixed subgroups in free groups: a survey
http://hdl.handle.net/2117/24787
Title: Fixed subgroups in free groups: a survey
Authors: Ventura Capell, Enric
Abstract: This note is a survey of the main results known about fixed subgroups
of endomorphisms of finitely generated free groups. A historic point
of view is taken, emphasizing the evolution of this line of research, from its
beginning to the present time. The article concludes with a section containing the main open problems and conjectures, with some comments and discussions on them.2014-11-20T13:38:23ZOn automorphism-fixed subgroups of a free group
http://hdl.handle.net/2117/24777
Title: On automorphism-fixed subgroups of a free group
Authors: Martino, Armando; Ventura Capell, Enric
Abstract: Let F be a flnitely generated free group, and let n denote its rank. A subgroup H of F is said to be automorphism-flxed, or auto-flxed for short, if there exists a set S of automorphisms of F such that H is precisely the set of elements flxed by every element of S; similarly, H is 1-auto-flxed if there exists a single automorphism of F whose set of flxed elements is precisely H. We show that each auto-flxed subgroup of F is a free factor of a 1-auto-flxed subgroup of F. We show also that if (and only if) n ‚ 3, then there exist free factors of 1-auto-flxed subgroups of F which are not auto-flxed subgroups of F. A 1-auto-flxed subgroup H of F has rank at most n, by the Bestvina-Handel Theorem, and if H has rank exactly n, then H is said to be a maximum-rank 1-auto-flxed subgroup of F, and similarly for auto-flxed subgroups. Hence a maximum-rank auto-flxed subgroup of F is a (maximum-rank) 1-auto-flxed subgroup of F. We further prove that if H is a maximum-rank 1-auto-flxed subgroup of F, then the group of automorphisms of F which flx every element of H is free abelian of rank at most n ¡ 1. All of our results apply also to endomorphisms.2014-11-19T16:52:21ZTwisted conjugacy in braid groups
http://hdl.handle.net/2117/24771
Title: Twisted conjugacy in braid groups
Authors: Gonzalez Meneses, Juan; Ventura Capell, Enric
Abstract: In this note we solve the twisted conjugacy problem for braid groups, i.e., we propose an algorithm which, given two braids u,v is an element of B-n and an automorphism phi is an element of Aut(B-n), decides whether v = (phi(x))(-1)-ux for some x is an element of B-n. As a corollary, we deduce that each group of the form B-n x H, a semidirect product of the braid group B-n by a torsion-free hyperbolic group H, has solvable conjugacy problem.2014-11-19T15:52:22ZRobust treatment of degenerate elements in interactive corotational FEM simulations
http://hdl.handle.net/2117/24735
Title: Robust treatment of degenerate elements in interactive corotational FEM simulations
Authors: Civit Flores, Oscar; Susín Sánchez, Antonio
Abstract: We address the problem of robust and efficient treatment of element collapse and inversion in corotational FEM simulations of deformable objects in two and three dimensions, and show that existing degeneration treatment methods have previously unreported flaws that seriously threaten robustness and physical plausibility in interactive applications. We propose a new method that avoids such flaws, yields faster and smoother degeneration recovery and extends the range of well-behaved degenerate configurations without adding significant complexity or computational cost to standard explicit and quasi-implicit solvers.2014-11-17T11:06:59ZFunctional output-controllability of time-invariant singular linear systems
http://hdl.handle.net/2117/24676
Title: Functional output-controllability of time-invariant singular linear systems
Authors: García Planas, María Isabel; Tarragona Romero, Sonia
Abstract: In the space of finite-dimensional
singular linear continuous-time-invariant systems described in the form \begin{equation}\label{eq1}\left . \begin{array}{rl} E \dot x(t)&= Ax(t)+Bu(t)\\ y(t)&=Cx(t)\end{array}{\kern-1mm}\right \}\end{equation}
where $E,A\in M=M_{n}(\mathbb{C})$, $B\in M_{n\times m}(\mathbb{C})$, $C\in M_{p\times n}(\mathbb{C})$, functional output-controllability character is considered. A simple test based in
the computation of the rank of a certain constant matrix that can be associated to the system is presented2014-11-11T12:18:07ZOn the local spectra of the subconstituents of a vertex set and completely pseudo-regular codes
http://hdl.handle.net/2117/24667
Title: On the local spectra of the subconstituents of a vertex set and completely pseudo-regular codes
Authors: Cámara Vallejo, Marc; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest
Abstract: In this paper we study the relation between the local spectrum of a vertex set C and the local spectra of its subconstituents. In particular, it is shown that, when C is a completely regular code, such spectra are uniquely determined by the local spectra of C. Moreover, we obtain a new characterization for completely pseudo-regular codes, and consequently for completely regular codes, in terms of the relation between the local spectrum of an extremal set of vertices and the local spectrum of its antipodal set. We also present a new proof of the version of the spectral excess theorem for extremal sets of vertices. (C) 2013 Elsevier B.V. All rights reserved.2014-11-11T09:51:20ZComputational evaluation of the flexoelectric effect in dielectric solids
http://hdl.handle.net/2117/24591
Title: Computational evaluation of the flexoelectric effect in dielectric solids
Authors: Abdollahi Hosnijeh, Amir; Peco Regales, Christian; Millán, Daniel; Arroyo Balaguer, Marino; Arias Vicente, Irene
Abstract: Flexoelectricity is a size-dependent electromechanical mechanism coupling polarization and strain gradient. It exists in a wide variety of materials, and is most noticeable for nanoscale objects, where strain gradients are higher. Simulations are important to understand flexoelectricity because experiments at very small scales are difficult, and analytical solutions are scarce. Here, we computationally evaluate the role of flexoelectricity in the electromechanical response of linear dielectric solids in two-dimensions. We deal with the higher-order coupled partial differential equations using smooth meshfree basis functions in a Galerkin method, which allows us to consider general geometries and boundary conditions. We focus on the most common setups to quantify the flexoelectric response, namely, bending of cantilever beams and compression of truncated pyramids, which are generally interpreted through approximate solutions. While these approximations capture the sizedependent flexoelectric electromechanical coupling, we show that they only provide order-of-magnitude estimates as compared with a solution fully accounting for the multidimensional nature of the problem. We discuss the flexoelectric mechanism behind the enhanced size-dependent elasticity in beam configurations. We show that this mechanism is also responsible for the actuation of beams under purely electrical loading, supporting the idea that a mechanical flexoelectric sensor also behaves as an actuator. The predicted actuation-induced curvature is in a good agreement with experimental results. The truncated pyramid configuration highlights the critical role of geometry and boundary conditions on the effective electromechanical response. Our results suggest that computer simulations can help understanding and quantifying the physical properties of flexoelectric devices. (c) 2014 AIP Publishing LLC.2014-11-07T10:38:00Z