The PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimension

The present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order finitedifference-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of efficiency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity offered by the finite-difference scheme and, as expected, is shown to perform substantially more efficiently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the flow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic flow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional flow composed of a counter-rotating pair of nonparallel Batchelor vortices.

A regular perturbation approach to surface tension driven flows

Surface tension induced convection in a liquid bridge held between two parallel, coaxial, solid disks is considered. The surface tension gradient is produced by a small temperature gradient parallel Co the undisturbed surface. The study is performed by using a mathematical regular perturbation approach based on a small parameter, e, which measures the deviation of the imposed temperature field from its mean value. The first order velocity field is given by a Stokes-type problem (viscous terms are dominant) with relatively simple boundary conditions. The first order temperature field is that imposed from the end disks on a liquid bridge immersed in a non-conductive fluid. Radiative effects are supposed to be negligible. The second order temperature field, which accounts for convective effects, is split into three components, one due to the bulk motion, and the other two to the distortion of the free surface. The relative importance of these components in terms of the heat transfer to or from the end disks is assessed

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

Feigenbaum graphs at the onset of chaos

We analyze the properties of networks obtained from the trajectories of unimodal maps at the transi- tion to chaos via the horizontal visibility (HV) algorithm. We find that the network degrees fluctuate at all scales with amplitude that increases as the size of the network grows, and can be described by a spectrum of graph-theoretical generalized Lyapunov exponents. We further define an entropy growth rate that describes the amount of information created along paths in network space, and find that such en- tropy growth rate coincides with the spectrum of generalized graph-theoretical exponents, constituting a set of Pesin-like identities for the network.

Detecting periodicity with horizontal visibility graphs

The horizontal visibility algorithm was recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are in its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.

Reply to Comment on ``Towards a large deviation theory for strongly correlated systems''

The computational study commented by Touchette opens the door to a desirable generalization of standard large deviation theory for special, though ubiquitous, correlations. We focus on three interrelated aspects: (i) numerical results strongly suggest that the standard exponential probability law is asymptotically replaced by a power-law dominant term; (ii) a subdominant term appears to reinforce the thermodynamically extensive entropic nature of q-generalized rate function; (iii) the correlations we discussed, correspond to Q -Gaussian distributions, differing from Lévy?s, except in the case of Cauchy?Lorentz distributions. Touchette has agreeably discussed point (i), but, unfortunately, points (ii) and (iii) escaped to his analysis. Claiming the absence of connection with q-exponentials is unjustified.

El ejercicio físico regular disminuye los niveles de depresión durante el embarazo. Ensayo clínico aleatorizado

El ejercicio físico regular disminuye los niveles de depresión durante el embarazo. Ensayo clínico aleatorizado

Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

Quasiperiodic graphs at the onset of chaos

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers

Numerical and experimental study of the parametric rolling of a fisihing vessel in regular head waves

The dynamic behaviour of a fishing vessel in waves is studied in order to reveal its parametric rolling characteristics. This paper presents experimental and numerical results in longitudinal regular waves. The experimental results are compared against the results of a time-domain non-linear strip theory model of ship motions in six degrees-of-freedom. These results contribute to the validation of the parametric rolling prediction method, so that it can be used as an assessment tool to evaluate both the susceptibility and severity of occurrence of parametric rolling at the early design stage of these types of vessels.

Quasiperiodic Graphs: Structural Design, Scaling and Entropic Properties

A novel class of graphs, here named quasiperiodic, are const ructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Far ey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy

Gromov hyperbolicity of periodic planar graphs

The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.

Mapping Dynamics into Graphs. The Visibility Algorithm

Si no tenemos en cuenta posibles procesos subyacentes con significado físico, químico, económico, etc., podemos considerar una serie temporal como un mero conjunto ordenado de valores y jugar con él algún inocente juego matemático como transformar dicho conjunto en otro objeto con la ayuda de una operación matemática para ver qué sucede: qué propiedades del conjunto original se conservan, cuáles se transforman y cómo, qué podemos decir de alguna de las dos representaciones matemáticas del objeto con sólo atender a la otra... Este ejercicio sería de cierto interés matemático por sí solo. Ocurre, además, que las series temporales son un método universal de extraer información de sistemas dinámicos en cualquier campo de la ciencia. Esto hace ganar un inesperado interés práctico al juego matemático anteriormente descrito, ya que abre la posibilidad de analizar las series temporales (vistas ahora como evolución temporal de procesos dinámicos) desde una nueva perspectiva. Hemos para esto de asumir la hipótesis de que la información codificada en la serie original se conserva de algún modo en la transformación (al menos una parte de ella). El interés resulta completo cuando la nueva representación del objeto pertencece a un campo de la matemáticas relativamente maduro, en el cual la información codificada en dicha representación puede ser descodificada y procesada de manera efectiva. ABSTRACT Disregarding any underlying process (and therefore any physical, chemical, economical or whichever meaning of its mere numeric values), we can consider a time series just as an ordered set of values and play the naive mathematical game of turning this set into a different mathematical object with the aids of an abstract mapping, and see what happens: which properties of the original set are conserved, which are transformed and how, what can we say about one of the mathematical representations just by looking at the other... This exercise is of mathematical interest by itself. In addition, it turns out that time series or signals is a universal method of extracting information from dynamical systems in any field of science. Therefore, the preceding mathematical game gains some unexpected practical interest as it opens the possibility of analyzing a time series (i.e. the outcome of a dynamical process) from an alternative angle. Of course, the information stored in the original time series should be somehow conserved in the mapping. The motivation is completed when the new representation belongs to a relatively mature mathematical field, where information encoded in such a representation can be effectively disentangled and processed. This is, in a nutshell, a first motivation to map time series into networks.

La identificaciónde de los daños estructurales, herramienta de la nueva atribución de responsabilidades : análisis crítico de la transición del art. 1591 cc al art. 17 LOE

RESUMEN Su objetivo esencial: Regular el proceso de la edificación, está basado en 3 grandes pilares: 1.- Completar la configuración legal de los agentes que intervienen en el mismo, fijando sus obligaciones para así establecer las responsabilidades. 2.- Fomentar la calidad de los edificios. 3.- Fijar las garantías a los usuarios frente a los posibles daños. Estos tres fundamentos están intensamente relacionados, ya que, las obligaciones y responsabilidades de los agentes son la base de la constitución de las garantías a los usuarios, definidas mediante los requisitos básicos que deben satisfacer los edificios. Partiendo del análisis cualitativo y cuantitativo del grado de cumplimiento del objetivo de la nueva Ley, elaborado a través del estudio de sus tres pilares fundamentales, proponemos medidas tendentes a la plena entrada en vigor de la misma. Para ello se deberá desarrollar el Real Decreto previsto en la Disposición Adicional 2ª, una vez conseguido el grado de madurez de los sectores de la edificación y del seguro. En todo este proceso de estudio hemos podido apreciar que la objetiva identificación de los daños y en especial los que afectan la estabilidad del edificio, constituye una herramienta fundamental para la correcta atribución de responsabilidades a los agentes, basada en la aplicación de los tres grados de responsabilidad “ex lege” por daños materiales y sus plazos de prescripción surgidos del nuevo régimen impuesto por el art. 17 LOE Para avalar esta propuesta hemos analizado: 1.- El entorno económico, general y pormenorizado al sector de la edificación, en Europa y España durante el período comprendido entre los años 1990 y 2013, años previos y posteriores a la entrada en vigor de la Ley, dada la influencia de los ciclos de actividad producidos en la regulación del sector, las responsabilidades atribuidas a los agentes, el fomento de la calidad y las garantías ofrecidas a los adquirentes. 2.- Las diversas legislaciones sobre responsabilidades y garantías de los agentes de la edificación en los países de nuestro entorno económico. 3.- La gestación de la LOE, incidiendo en la evolución de los últimos borradores y su tramitación parlamentaria. 4.- El desarrollo doctrinal de la Transición desde el régimen de responsabilidades, fijado por el art. 1591 de Código Civil, y su Jurisprudencia, hacia el nuevo régimen de responsabilidades establecido por el art. 17 LOE. En esta tarea además de apreciar la asimilación, por parte de los Jueces y Magistrados, de los principios doctrinales de la LOE, hemos observado la labor de los peritos, de cuya experta identificación de las causas de los daños depende la justa y eficaz atribución de responsabilidades. 5 -. El grado de eficacia de la LOE a la vista de la estadística siniestral, de la que ya hay datos consolidados, tras la cancelación de casi 15.000 expedientes de reclamación a Arquitectos. 6 -. También hemos estudiado el grado de cumplimiento con el usuario y propietario de las garantías previstas en el art. 19 de la Ley y en la D.A. 1ª, los efectos reales alcanzados y las tareas pendientes por delante. Analizando la atribución de responsabilidades a los agentes de la edificación, dentro del primer pilar fundamental de la LOE, hemos estudiado las actuaciones de los peritos expertos y su incidencia en este objetivo, previa selección de casos de gran interés y dificultad. Fruto de ello se han formulado propuestas tendentes a la especialización de este colectivo, evitando conductas “irregulares” que tanto daño provocan a los agentes reclamados como a los propietarios afectados. Este daño es evidente pudiendo ocasionar condenas injustas, enriquecimientos ilícitos o bien falsas expectativas de satisfacción de daños mal dictaminados y costosas e ineficaces reparaciones. De cara a la consecución del pilar de la calidad de la edificación, mediante los requisitos básicos planteados por la LOE y desarrollados por el Código Técnico de la Edificación (Real Decreto 314/2006, de 17 de marzo), hemos procesado datos de expedientes de reclamaciones por daños que afectan a edificios ejecutados bajo el nuevo régimen LOE. Con esta base se han analizado las causas generadoras de las diversas lesiones y su frecuencia para que de este análisis puedan establecerse pautas de actuación para su prevención. Finalmente, tras demostrar que las garantías obligatorias impuestas por la LOE sólo abarcan un pequeño porcentaje de los posibles daños a la edificación, insistimos en la necesidad de la plena eficacia de la Ley mediante la aprobación de todas las garantías previstas y para todo tipo de edificaciones. En suma, se ha diseñado la tesis como una matriz abierta en la que podremos continuar incorporando datos de la evolución de la doctrina, la jurisprudencia y la estadística de los daños en la edificación. ABSTRACT The approval of Law 38/1999 on November 5, 1999, (Official Gazette BOE 266/1999 of 11.6.1999, p. 38925), was the culmination of a long period of over 20 years of gestation for which deep agreements were needed between all stakeholders affected. Although several parliamentary groups denounced its incomplete approval, regarding mandatory guarantees to the purchaser, its enactment caused general satisfaction among most of the the building agents. This assessment remains after fourteen years since its partial enactment. Its essential purpose, “to regulate the building process”, is based on 3 pillars: 1.- To complete the legal configuration of the agents involved in it, setting their obligations in order to establish their responsibilities. 2.- To promote the buildings quality. 3.- To specify users´guarantees against possible buildings damage. These three issues are strongly related, since the obligations and responsibilities of the actors are the basis of the users’guarantees constitution, defined by the basic performance required by buildings. Based on the qualitative and quantitative analysis of the fulfillment of the new law’s objectives, made by monitoring the three pillars, we propose measures to the full enactment of this Directive, by the development of the Royal Decree, provided in its Second Additional Provision, once maturity in the sectors of the building and insurance is achieved. Throughout this process of study we have seen that the skill identification of damage, particularly those affecting the stability of the building, is an essential tool for the proper allocation of responsibilities of the new regime installed by the art. 17 LOE, based on the application of the three degrees of responsibility "ex lege" for property damage and limitation periods. To support this proposal, we have analyzed: 1.- The evolution of the building sector in Europe and Spain during the years before and after the enactment of the Law, due to the influence of cycles of activity produced in industry regulation, the responsibilities attributed to agents, promotion of the quality and the assurances given to acquirers. 2.- The scope of various laws on liability and building agents warranties in the countries of our economic environment. 3.- The long period of LOE generation, focusing on the developments in recent drafts and parliamentary procedure. 4.- The doctrinal development in the Transition from the regime of responsibilities, set by art. 1591 of the Civil Code, and its Jurisprudence, to the new liability regime established by art. 17 LOE. In this task, while we have noted assimilation by the Judges and Magistrates of the doctrinal principles of the LOE, we have also analyzed the work of experts, whose skilled identification of the damage causes helps the fair and efficient allocation of responsibilities. 5 - The effectiveness of the LOE based on knowledge of the siniestral statistics, which are already consolidated data, after the cancellation of nearly 15,000 claims to Architects. 6.- We have also studied the degree of compliance with the user and owner guarantees, established in art. 19 and the D.A. 1th of the LOE, exposing the real effects achieved and the pending tasks ahead. Analyzing the allocation of the building agents´ responsibilities, within the first cornerstone of the LOE, we have studied the expert witnesses actions and their impact on this duty, selecting cases of great interest and difficulty in this aim. The result of this enterprise has been to propose the specialization of this group, avoiding "irregular" behaviors that create as much damage as the agents claimed to affected owners. This damage is evident and can cause wrong convictions, illicit enrichment, false expectations and inefficient and costly damage repairs. In order to achieve the pillar of building quality through the basic requirements set by the LOE and developed by the Technical Building Code (Royal Decree 314/ 2006 of 17 March), we have analyzed records of damage claims involving buildings executed under the new regime LOE. On this basis we have analyzed the root causes of various damages and their frequency, from these data it will be easy to propose lines of action for prevention. Finally, after demonstrating that mandatory warranties imposed by LOE cover only a small percentage of the potential building damage, we emphasize the need for the full effectiveness of the Law by the obligation all the guarantees provided in the art. 19 LOE, and for all types of buildings. In conclusion, this thesis is designed as an open matrix in which we will continue including data on the evolution of the doctrine, jurisprudence and the statistics of the damage to the building.

Surface fitting in geomorphology - examples for regular-shaped volcanic landforms

In nature, several types of landforms have simple shapes: as they evolve they tend to take on an ideal, simple geometric form such as a cone, an ellipsoid or a paraboloid. Volcanic landforms are possibly the best examples of this ?ideal? geometry, since they develop as regular surface features due to the point-like (circular) or fissure-like (linear) manifestation of volcanic activity. In this paper, we present a geomorphometric method of fitting the ?ideal? surface onto the real surface of regular-shaped volcanoes through a number of case studies (Mt. Mayon, Mt. Somma, Mt. Semeru, and Mt. Cameroon). Volcanoes with circular, as well as elliptical, symmetry are addressed. For the best surface fit, we use the minimization library MINUIT which is made freely available by the CERN (European Organization for Nuclear Research). This library enables us to handle all the available surface data (every point of the digital elevation model) in a one-step, half-automated way regardless of the size of the dataset, and to consider simultaneously all the relevant parameters of the selected problem, such as the position of the center of the edifice, apex height, and cone slope, thanks to the highly performing adopted procedure. Fitting the geometric surface, along with calculating the related error, demonstrates the twofold advantage of the method. Firstly, we can determine quantitatively to what extent a given volcanic landform is regular, i.e. how much it follows an expected regular shape. Deviations from the ideal shape due to degradation (e.g. sector collapse and normal erosion) can be used in erosion rate calculations. Secondly, if we have a degraded volcanic landform, whose geometry is not clear, this method of surface fitting reconstructs the original shape with the maximum precision. Obviously, in addition to volcanic landforms, this method is also capable of constraining the shapes of other regular surface features such as aeolian, glacial or periglacial landforms.