http://www.recercat.cat:80/handle/2072/199862 Wed, 19 Jun 2013 22:30:35 GMT 2013-06-19T22:30:35Z http://www.recercat.cat:80/handle/2072/205476 Statistical similarity between the compression of a porous material and earthquakes Baró, Jordi; Corral, Álvaro; Illa Vila, Xavier; Planes Vila, Antoni; Salje, Ekhard K. H.; Schranz, Wilfried; Soto-Parra, Daniel; Vives i Santa-Eulàlia, Eduard It has been long stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallelisms between these so separate phenomena. We study the Acoustic Emission events produced during the compression of Vycor (SiO&sub&2&/sub&). The Gutenberg-Richter law, the modified Omori's law, and the law of aftershock productivity hold for a minimum of 5 decades, are independent of the compression rate, and keep stationary for all the duration of the experiments. The waiting-time distribution fulfills a unified scaling law with a power-law exponent close to 2.45 for long times, which is explained in terms of the temporal variations of the activity rate. Thu, 01 Nov 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/205476 2012-11-01T00:00:00Z http://www.recercat.cat:80/handle/2072/206096 Equidistribution estimates for Fekete points on complex manifolds Lev, Nir; Ortega Cerdà, Joaquim We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich-Wasserstein distance of the Fekete points to its limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles. Thu, 01 Nov 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/206096 2012-11-01T00:00:00Z http://www.recercat.cat:80/handle/2072/206095 Kuranishi type Moduli Spaces for proper CR submersions fibering over the circle Meersseman, Laurent Kuranishi's fundamental result (1962) associates to any compact complex manifold X&sub&0&/sub& a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to X&sub&0&/sub&. In this paper, we give an analogous statement for Levi-flat CR manifolds fibering properly over the circle by describing explicitely an infinite-dimensional Kuranishi type local moduli space of Levi-flat CR structures. We interpret this result in terms of Kodaira-Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples. Mon, 01 Oct 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/206095 2012-10-01T00:00:00Z http://www.recercat.cat:80/handle/2072/206094 Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians Bounemoura, Abed This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori. Sat, 01 Dec 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/206094 2012-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/206093 Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians Bounemoura, Abed In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians. Sat, 01 Dec 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/206093 2012-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/206092 Holomorphic maps between moduli spaces Aramayona, Javier; Souto, Juan A. We prove that every non-constant holomorphic map&em&M&/em&&sub&g,p&/sub&→ &em&M&/em&&sub& g',p'&/sub& between moduli spaces of Riemann surfaces is a forgetful map, provided that g ≥ 6 and g' ≤ 2g-2. Sat, 01 Dec 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/206092 2012-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/206091 Rigidity phenomena in the mapping class group Aramayona, Javier; Souto, Juan A Sat, 01 Dec 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/206091 2012-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/206090 Variétés CR polarisées et G-polarisées, partie I Meersseman, Laurent Polarized and G-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation &em&F&/em& (given by the action of a Lie group G in the G-polarized case) and a transverse CR distribution. Polarized means that (E,J) is roughly speaking invariant by&em&F&/em&. Both structures are therefore linked up. The interplay between them gives to polarized CR-manifolds a very rich geometry. In this paper, we study the properties of polarized and G-polarized manifolds, putting special emphasis on their deformations. Sat, 01 Dec 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/206090 2012-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/205953 Modelling the cardiovascular system for automatic interpretation of the blood pressure curve Myers, Timothy; Sáez de Tejada, Anna; McGuinness, Mark J.; Mitchell, Sarah L.; Ribas Ripoll, Vicent Jordi A four compartment model of the cardiovascular system is developed. To allow for easy interpretation and to minimise the number of parameters, an effort was made to keep the model as simple as possible. A sensitivity analysis is first carried out to determine which are the most important model parameters to characterise the blood pressure signal. A four stage process is then described which accurately determines all parameter values. This process is applied to data from three patients and good agreement is shown in all cases. Sat, 01 Dec 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/205953 2012-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/205485 On concentrators and related approximation constants Bondarenko, Andriy; Prymak, A; Radchenko, Danylo Pippenger [Pi77] showed the existence of (6m,4m,3m,6)-concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of (6m,4m,3m,5.05)-concentrator (which is no longer regular, but has fewer edges). We apply this result to improve the constant of approximation of almost additive set functions by additive set functions from 44.5 (established by Kalton and Roberts in [KaRo83] to 39. We show a more direct connection of the latter problem to the Whitney type estimate for approximation of continuous functions on a cube in &b&R&/b&&sup&d&/sup& by linear functions, and improve the estimate of this Whitney constant from 802 (proved by Brudnyi and Kalton in [BrKa00] to 73. Sat, 01 Dec 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/205485 2012-12-01T00:00:00Z http://www.recercat.cat:80/handle/2072/205484 One-dimensional solidification of supercooled melts Font Martínez, Francesc; Myers, T. G.; Mittchell, Sara L. In this paper a one-phase supercooled Stefan problem, with a nonlinear relation between the phase change temperature and front velocity, is analysed. The model with the standard linear approximation, valid for small supercooling, is first examined asymptotically. The nonlinear case is more difficult to analyse and only two simple asymptotic results are found. Then, we apply an accurate heat balance integral method to make further progress. Finally, we compare the results found against numerical solutions. The results show that for large supercooling the linear model may be highly inaccurate and even qualitatively incorrect. Similarly as the Stefan number β → 1&sup&+&/sup& the classic Neumann solution which exists down to β =1 is far from the linear and nonlinear supercooled solutions and can significantly overpredict the solidification rate. Tue, 04 Dec 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/205484 2012-12-04T00:00:00Z http://www.recercat.cat:80/handle/2072/205482 Feuilletages par variétés complexes et problèmes d'uniformisation Meersseman, Laurent Ce texte est une introduction aux feuilletages par variétés complexes et aux problèmes d'uniformisation de tels feuilletages. Nous donnons en introduction une liste fondamentale de questions naturelles sur ces objets ainsi qu'un aperçcu des résultats connus. Thu, 01 Nov 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/205482 2012-11-01T00:00:00Z http://www.recercat.cat:80/handle/2072/205479 Tenseness of Riemannian flows Nozawa, Hiraku; Royo Prieto, José Ignacio We show that any transversally complete Riemannian foliation &em&F&/em& of dimension one on any possibly non-compact manifold M is tense; namely, (M,&em&F&/em&) admits a Riemannian metric such that the mean curvature form of &em&F&/em& is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize some well known results including Masa's characterization of tautness. Thu, 01 Nov 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/205479 2012-11-01T00:00:00Z http://www.recercat.cat:80/handle/2072/204756 Folner sequences and finite operators Yakubovich, Dmitry V.; Lledó, Fernando,1967- This article analyzes Folner sequences of projections for bounded linear operators and their relationship to the class of finite operators introduced by Williams in the 70ies. We prove that each essentially hyponormal operator has a proper Folner sequence (i.e. a Folner sequence of projections strongly converging to 1). In particular, any quasinormal, any subnormal, any hyponormal and any essentially normal operator has a proper Folner sequence. Moreover, we show that an operator is finite if and only if it has a proper Folner sequence or if it has a non-trivial finite dimensional reducing subspace. We also analyze the structure of operators which have no Folner sequence and give examples of them. For this analysis we introduce the notion of strongly non-Folner operators, which are far from finite block reducible operators, in some uniform sense, and show that this class coincides with the class of non-finite operators. Mon, 01 Oct 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/204756 2012-10-01T00:00:00Z http://www.recercat.cat:80/handle/2072/204699 Stability of cascade networks via fluid models Delgado de la Torre, Rosario; Morozov, Evsey Vegeu el resum a l'inici del document de l'arxiu adjunt Mon, 01 Oct 2012 00:00:00 GMT http://www.recercat.cat:80/handle/2072/204699 2012-10-01T00:00:00Z http://www.recercat.cat:80/handle/2072/204379 Schwarz methods for a preconditioned WOPSIP method for elliptic problems Antonietti, Paola F.; Ayuso, B.; Brenner, Susanne C.; Sung, Li-Yeng We construct and analyze non-overlapping Schwarz methods for a preconditioned weakly over-penalized symmetric interior penalty (WOPSIP) method for elliptic problems. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/204379 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203824 Parametrization of spectral surfaces of a class of periodic 5-diagonal matrices Moale, Ionela; Yuditskii, Peter The main result of this work is a parametric description of the spectral surfaces of a class of periodic 5-diagonal matrices, related to the strong moment problem. This class is a self-adjoint twin of the class of CMV matrices. Jointly they form the simplest possible classes of 5-diagonal matrices. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203824 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203823 Sobolev orthogonal polynomials on a simplex Aktas, Rabía; Yu, Yuan Vegeu el resum a l'inici del document de l'arxiu adjunt Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203823 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203582 MIinimal N-point diameters and f-best-packing constants in Rd[superindex] Bondarenko, Andriy; Saff, E. B.; Hardin, D.P. Vegeu el resum a l'inici del document de l'arxiu adjunt Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203582 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203581 Bernstein's problem on weighted polynomial approximation Poltoratski, Alexei We formulate a necessary and sufficient condition for polynomials to be dense in a space of continuous functions on the real line, with respect to Bernstein's weighted uniform norm. Equivalently, for a positive finite measure [lletra "mu" minúscula de l'alfabet grec] on the real line we give a criterion for density of polynomials in Lp[lletra "mu" minúscula de l'alfabet grec entre parèntesis]. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203581 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203580 Operator algebras: an informal overview Lledó, Fernando, 1967- This article is an informal introduction to some classical results of the theory of operator algebras. It aims to illustrate the richness and diversity of possible applications of this topic. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203580 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203579 On spectral approximation, Folner sequences and crossed products Lledó, Fernando, 1967- In this article we review first some of the possibilities in which the notions of Fo lner sequences and quasidiagonality have been applied to spectral approximation problems. We construct then a canonical Fo lner sequence for the crossed product of a concrete C* -algebra and a discrete amenable group. We apply our results to the rotation algebra (which contains interesting operators like almost Mathieu operators or periodic magnetic Schrödinger operators on graphs) and the C* -algebra generated by bounded Jacobi operators. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203579 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203578 Gap probabilities for the cardinal sine Antezana, Jorge; Buckley, Jeremiah; Marzo Sánchez, Jordi; Olsen, Jan-Fredrik We study the zero set of random analytic functions generated by a sum of the cardinal sine functions which form an orthogonal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero in a bounded interval decays exponentially as a function of the length. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203578 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203577 A block solver for the exponentally fitted IIPG-0 method Ayuso, B.; Lombardi, Ariel; Pietra, Paola; Zikatanov, Ludmil We consider an exponentially fitted discontinuous Galerkin method for advection dominated problems and propose a block solver for the resulting linear systems. In the case of strong advection the solver is robust with respect to the advection direction and the number of unknowns. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203577 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203576 Mutigrid preconditioner for nonconforming discretization of elliptic problems with jump coefficients Ayuso, B.; Holst, M.; Zhu, Y.; Zikatanov, Ludmil In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coe fficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coe fficient and near-optimality with respect to the number of degrees of freedom. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203576 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/203575 L2−estimates for the DG IIPG-0 scheme Ayuso, B.; Brezzi, Franco; Havle, Oto; Marini, L. Donatella We discuss the optimality in L2 of a variant of the Incomplete Discontinuous Galerkin Interior Penalty method (IIPG) for second order linear elliptic problems. We prove optimal estimate, in two and three dimensions, for the lowest order case under suitable regularity assumptions on the data and on the mesh. We also provide numerical evidence, in one dimension, of the necessity of the regularity assumptions. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/203575 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/200244 Reconstruction of a superscheme from its derived category Dubey, Umesh V.; Mallick, Vivek M. The aim of this paper is to construct a "super" version of a tensor triangulated category, and to show that super-schemes can be reconstructed from its category of perfect complexes in a way similar to Balmer [Bal05] provided we consider this extra structure. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/200244 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/200243 Analogs of Cuntz algebras on Lp-spaces Phillips, N. Christopher Vegeu el resum a l'inici del document del fitxer adjunt. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/200243 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/200242 KAM theory for conformally symplectic systems Calleja, Renato C.; Celletti, A. (Alessandra); Llave, Rafael de la We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/200242 2011-01-01T00:00:00Z http://www.recercat.cat:80/handle/2072/200241 Universal complex structures in written language Corral, Álvaro; Ferrer Cancho, Ramon; Díaz Guilera, Albert; Boleda Torrent, Gemma Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf’s law of word frequencies. Zipf’s law appears to be universal, and may not even be unique to human language. However, there is ongoing controversy over whether Zipf’s law is a good indicator of complexity. Here we present an alternative approach that puts Zipf’s law in the context of critical phenomena (the cornerstone of complexity in physics) and establishes the presence of a large-scale “attraction” between successive repetitions of words. Moreover, this phenomenon is scale-invariant and universal – the pattern is independent of word frequency and is observed in texts by different authors and written in different languages. There is evidence, however, that the shape of the scaling relation changes for words that play a key role in the text, implying the existence of different “universality classes” in the repetition of words. These behaviours exhibit striking parallels with complex catastrophic phenomena. Sat, 01 Jan 2011 00:00:00 GMT http://www.recercat.cat:80/handle/2072/200241 2011-01-01T00:00:00Z