DSpace Collection:
http://hdl.handle.net/2117/3228
2014-07-29T05:23:33ZNonlinear 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.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).2014-07-16T07:35:44ZR+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.2014-07-15T11:00:50ZAuto-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.2014-07-15T10:29:35ZExponentially 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.2014-07-15T08:21:36ZStation-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.2014-07-09T11:19:18ZCódigos 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.2014-07-09T10:49:12ZThe 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.2014-07-09T10:41:57ZReflexivity 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.2014-06-05T15:04:55ZThe 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.2014-05-26T08:26:15ZDegree 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.2014-05-16T08:09:45ZStability 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 results2014-05-07T10:12:54ZCapturing small asteroids into a Sun-Earth Lagrangian point
http://hdl.handle.net/2117/22768
Title: Capturing small asteroids into a Sun-Earth Lagrangian point
Authors: Lladó, Neus; Ren, Yuan; Masdemont Soler, Josep; Gómez Muntané, Gerard
Abstract: In this paper we address the feasibility of capturing small Near-Earth Asteroids (NEAs) into the vicinity of the Sun-Earth L-2 libration point using a continuous-thrust propulsion system assumed to be attached to the asteroid. The vicinity of this libration point is a gateway to the Earth-Moon neighborhood and using it for capture, or for transit, small NEAs could be interesting for mining or science purposes.; Due to limited maneuver capabilities and security concerns, only NEAs with very small mass, and not representing a potential hazard, are analyzed. First, the NEAs are pruned from JPL NEAs (Jet Propulsion Laboratory, 2012) [1] database and their diameter and mass are estimated using two different methods based on physical properties. Then, fuel-optimal continuous-thrust transfer orbits from the original positions of the NEAs to the Sun-Earth L-2 libration point are computed. For this trajectory optimization, the initial seeds are generated by means of a global optimization procedure based on a differential evolution algorithm. Next, these initial seeds are refined with a fourth order Runge-Kutta shooting method, and finally we list the candidate NEAs to be captured using a continuous-thrust propulsion system including the key parameters defining their transfer trajectory. (C) 2013 IAA. Published by Elsevier Ltd. All rights reserved.2014-04-30T08:14:03ZDetecting invariant manifolds using hyperbolic Lagrangian coherent structures
http://hdl.handle.net/2117/22688
Title: Detecting invariant manifolds using hyperbolic Lagrangian coherent structures
Authors: Pérez, Daniel; Gómez Muntané, Gerard; Masdemont Soler, Josep
Abstract: Using as reference test model the Planar Circular Restricted Three Body Prob-
lem, this paper explores its Lagrangian Coherent Structures, as well as its Hy-
perbolic Lagrangian Coherent Structures. The purpose is to identify stable and
unstable manifolds acting as separatrices between orbits with different qualitative
behaviour and, therefore, relevant to the dynamics of the problem. Particular at-
tention is given to the manifolds associated to the collinear libration points and to
the practical stability regions around the triangular equilibrium points2014-04-24T10:00:06ZThe scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
http://hdl.handle.net/2117/22671
Title: The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
Authors: Granados Corsellas, Albert; Hogan, Stephen John; Martínez-Seara Alonso, M. Teresa
Abstract: We consider a non-autonomous dynamical system formed by coupling two piecewise-smooth systems in R-2 through a non-autonomous periodic perturbation. We study the dynamics around one of the heteroclinic orbits of one of the piecewise-smooth systems. In the unperturbed case, the system possesses two C-0 normally hyperbolic invariant manifolds of dimension two with a couple of three dimensional heteroclinic manifolds between them. These heteroclinic manifolds are foliated by heteroclinic connections between C-0 tori located at the same energy levels. By means of the impact map we prove the persistence of these objects under perturbation. In addition, we provide sufficient conditions of the existence of transversal heteroclinic intersections through the existence of simple zeros of Melnikov-like functions. The heteroclinic manifolds allow us to define the scattering map, which links asymptotic dynamics in the invariant manifolds through heteroclinic connections. First order properties of this map provide sufficient conditions for the asymptotic dynamics to be located in different energy levels in the perturbed invariant manifolds. Hence we have an essential tool for the construction of a heteroclinic skeleton which, when followed, can lead to the existence of Arnold diffusion: trajectories that, on large time scales, destabilize the system by further accumulating energy. We validate all the theoretical results with detailed numerical computations of a mechanical system with impacts, formed by the linkage of two rocking blocks with a spring. (C) 2013 Elsevier B.V. All rights reserved.2014-04-23T12:58:06Z