DSpace Collection:
http://hdl.handle.net/2117/3918
2014-09-15T04:21:35ZNonlinear 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.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.2014-08-29T10:51:05ZImportance 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.2014-08-28T08:29:29ZImpacts 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.2014-08-01T11:18:55ZCentral 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.2014-07-29T08:35:40ZSimulation 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 del2014-07-25T10:56:15ZThree-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.2014-07-17T08:57:13ZOptimal design of complex passive-damping systems for vibration control of large structures: an energy-to-peak approach
http://hdl.handle.net/2117/23527
Title: Optimal design of complex passive-damping systems for vibration control of large structures: an energy-to-peak approach
Authors: Palacios Quiñonero, Francisco; Rubió Massegú, Josep; Rossell Garriga, Josep Maria; Karimi, Hamid Reza
Abstract: We present a new design strategy that makes it possible to synthesize decentralized output-feedback controllers by solving two successive optimization problems with linear matrix inequality (LMI) constraints. In the initial LMI optimization problem, two auxiliary elements are computed: a standard state-feedback controller, which can be taken as a reference in the performance assessment, and a matrix that facilitates a proper definition of the main LMI optimization problem. Next, by solving the second optimization problem, the output-feedback controller is obtained. The proposed strategy extends recent results in static output-feedback control and can be applied to design complex passive-damping systems for vibrational control of large structures. More precisely, by taking advantages of the existing link between fully decentralized velocity-feedback controllers and passive linear dampers, advanced active feedback control strategies can be used to design complex passive-damping systems, which combine the simplicity and robustness of passive control systems with the efficiency of active feedback control. To demonstrate the effectiveness of the proposed approach, a passive-damping system for the seismic protection of a five-story building is designed with excellent results.2014-07-16T09:47:48ZNoise 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.2014-07-15T08:21:36ZExcessively duplicating patterns represent non-regular languages
http://hdl.handle.net/2117/23504
Title: Excessively duplicating patterns represent non-regular languages
Authors: Creus López, Carles; Godoy Balil, Guillem; Ramos Garrido, Lander
Abstract: A constrained term pattern s:¿ represents the language of all instances of the term s satisfying the constraint ¿. For each variable in s, this constraint specifies the language of its allowed substitutions. Regularity of languages represented by sets of patterns has been studied for a long time. This problem is known to be co-NP-complete when the constraints allow each variable to be replaced by any term over a fixed signature, and EXPTIME-complete when the constraints restrict each variable to a regular set. In both cases, duplication of variables in the terms of the patterns is a necessary condition for non-regularity. This is because duplications force the recognizer to test equality between subterms. Hence, for the specific classes of constraints mentioned above, if all patterns are linear, then the represented language is necessarily regular. In this paper we focus on the opposite case, that is when there are patterns with2014-07-14T12:29:43ZThe extremal solution for the fractional Laplacian
http://hdl.handle.net/2117/23499
Title: The extremal solution for the fractional Laplacian
Authors: Ros Oton, Xavier; Serra Montolí, Joaquim
Abstract: We study the extremal solution for the problem (-¿)su=¿f(u) in O , u=0 in Rn\O , where ¿>0 is a parameter and s¿(0,1) . We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded in dimensions n<4s . We also show that, for exponential and power-like nonlinearities, the extremal solution is bounded whenever n<10s . In the limit s¿1 , n<10 is optimal. In addition, we show that the extremal solution is Hs(Rn) in any dimension whenever the domain is convex. To obtain some of these results we need Lq estimates for solutions to the linear Dirichlet problem for the fractional Laplacian with Lp data. We prove optimal Lq and Cß estimates, depending on the value of p . These estimates follow from classical embedding results for the Riesz potential in Rn . Finally, to prove the Hs regularity of the extremal solution we need an L8 estimate near the boundary of convex domains, which we obtain via the moving planes method. For it, we use a maximum principle in small domains for integro-differential operators with decreasing kernels.2014-07-14T11:48:18Z