The Minimum Number of Points Taking Part in k-Sets in Sets of Unaligned Points

En este trabajo se da un ejemplo de un conjunto de n puntos situados en posición general, en el que se alcanza el mínimo número de puntos que pueden formar parte de algún k-set para todo k con 1menor que=kmenor quen/2. Se generaliza también, a puntos en posición no general, el resultado de Erdõs et al., 1973, sobre el mínimo número de puntos que pueden formar parte de algún k-set. The study of k- sets is a very relevant topic in the research area of computational geometry. The study of the maximum and minimum number of k-sets in sets of points of the plane in general position, specifically, has been developed at great length in the literature. With respect to the maximum number of k-sets, lower bounds for this maximum have been provided by Erdõs et al., Edelsbrunner and Welzl, and later by Toth. Dey also stated an upper bound for this maximum number of k-sets. With respect to the minimum number of k-set, this has been stated by Erdos el al. and, independently, by Lovasz et al. In this paper the authors give an example of a set of n points in the plane in general position (no three collinear), in which the minimum number of points that can take part in, at least, a k-set is attained for every k with 1 ≤ k < n/2. The authors also extend Erdos’s result about the minimum number of points in general position which can take part in a k-set to a set of n points not necessarily in general position. That is why this work complements the classic works we have mentioned before.

Ferromanganese nodules and micro-hardgrounds associated with the Cadiz Contourite Channel (NE Atlantic): Palaeoenvironmental records of fluid venting and bottom currents

Ferromanganese nodule fields and hardgrounds have recently been discovered in the Cadiz Contourite Channel in the Gulf of Cadiz (850–1000 m). This channel is part of a large contourite depositional system generated by the Mediterranean Outflow Water. Ferromanganese deposits linked to contourites are interesting tools for palaeoenviromental studies and show an increasing economic interest as potential mineral resources for base and strategic metals. We present a complete characterisation of these deposits based on submarine photographs and geophysical, petrographic, mineralogical and geochemical data. The genesis and growth of ferromanganese deposits, strongly enriched in Fe vs. Mn (av. 39% vs. 6%) in this contourite depositional system result from the combination of hydrogenetic and diagenetic processes. The interaction of the Mediterranean Outflow Water with the continental margin has led to the formation of Late Pleistocene–Holocene ferromanganese mineral deposits, in parallel to the evolution of the contourite depositional system triggered by climatic and tectonic events. The diagenetic growth was fuelled by the anaerobic oxidation of thermogenic hydrocarbons (δ13CPDB=−20 to −37‰) and organic matter within the channel floor sediments, promoting the formation of Fe–Mn carbonate nodules. High 87Sr/86Sr isotopic values (up to 0.70993±0.00025) observed in the inner parts of nodules are related to the influence of radiogenic fluids fuelled by deep-seated fluid venting across the fault systems in the diapirs below the Cadiz Contourite Channel. Erosive action of the Mediterranean Outflow Water undercurrent could have exhumed the Fe–Mn carbonate nodules, especially in the glacial periods, when the lower core of the undercurrent was more active in the study area. The growth rate determined by 230Thexcess/232Th was 113±11 mm/Ma, supporting the hypothesis that the growth of the nodules records palaeoenvironmental changes during the last 70 ka. Ca-rich layers in the nodules could point to the interaction between the Mediterranean Outflow Water and the North Atlantic Deep Water during the Heinrich events. Siderite–rhodochrosite nodules exposed to the oxidising seabottom waters were replaced by Fe–Mn oxyhydroxides. Slow hydrogenetic growth of goethite from the seawaters is observed in the outermost parts of the exhumed nodules and hardgrounds, which show imprints of the Mediterranean Outflow Water with low 87Sr/86Sr isotopic values (down to 0.70693±0.00081). We propose a new genetic and evolutionary model for ferromanganese oxide nodules derived from ferromanganese carbonate nodules formed on continental margins above the carbonate compensation depth and dominated by hydrocarbon seepage structures and strong erosive action of bottom currents. We also compare and discuss the generation of ferromanganese deposits in the Cadiz Contourite Channel with that in other locations and suggest that our model can be applied to ferromanganiferous deposits in other contouritic systems affected by fluid venting.

Quantity of CO2 Emissions in the Life Cycle of a Highway Infrastructure

There is strong evidence to indicate that carbon dioxide and other greenhouse gases are accumulating at unprecedented concentrations in out atmosphere contributing to global climate change. Evidence is equally strong that human activities, mainly the burning of fossil fuels, are driving force in this process (IPCC 2007). While different industries contribute varying amounts to total anthropogenic greenhouse gases, it is incumbent upon each to understand its contribution and search for sensible ways to reduce overall greenhouse gas production. The aim of this paper is the development of a methodology to determine the amount of CO2 emissions of a highway, allowing providing solutions that can improve the energy footprint and reduce its emissions

Quantity of CO2 Emissions in the Life Cycle of a Highway Infrastructure.

The complexity of climate change and its evolution during the last few years has a positive impact on new developments and approaches to reduce the emissions of CO2. Looking for a methodology to evaluate the sustainability of a roadway, a tool has been developed. Life Cycle Assessment (LCA) is being accepted by the road industry to measure and evaluate the environmental impacts of an infrastructure, as the energy consumption and carbon footprint. This paper describes the methodology to calculate the CO2 emissions associated with the energy embodied on a roadway along its life cycle, including construction, operations and demolition. It will assist to find solutions to improve the energy footprint and reduce the amount of CO2 emissions. Details are provided of both, the methodology and the data acquisition. This paper is an application of the methodology to the Spanish highways, using a local database. Two case studies and a practical example are studied to show the model as a decision support for sustainable construction in the road industry.

Numerical issues in Lagrangian tracking and topological evolution of fluid particles in wallbounded turbulent flows

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.

Minimum volume of long liquid bridges between noncoaxial, nonequal diameter circular disks under lateral acceleration

The stability limit of minimum volume and the breaking dynamics of liquid bridges between nonequal, noncoaxial, circular supporting disks subject to a lateral acceleration were experimentally analyzed by working with liquid bridges of very small dimensions. Experimental results are compared with asymptotic theoretical predictions, with the agreement between experimental results and asymptotic ones being satisfactory

Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

The influence of diet on the effectiveness of garlic oil and cinnamaldehyde to manipulate in vitro ruminal fermentation and methane production.

The objective of this study was to evaluate the effects of increasing doses [0 (control: CON), 20, 60, 180 and 540 mg/L incubation medium] of garlic oil (GO) and cinnamaldehyde (CIN) on in vitro ruminal fermentation of two diets. Batch cultures of mixed ruminal microorganisms were inoculated with ruminal fluid from four sheep fed a medium-concentrate diet (MC; 50 : 50 alfalfa hay : concentrate) or four sheep fed a high-concentrate diet (HC; 15 : 85 barley straw : concentrate). Diets MC and HC were representative of those fed to dairy and fattening ruminants, respectively. Samples of each diet were used as incubation substrates for the corresponding inoculum, and the incubation was repeated on 4 different days (four replicates per experimental treatment). There were GO × diet-type and CIN × diet-type interactions (P < 0.001–0.05) for many of the parameters determined, indicating different effects of both oils depending on the diet type. In general, effects of GO were more pronounced for MC compared with HC diet. Supplementation of GO did not affect (P > 0.05) total volatile fatty acid (VFA) production at any dose. For MC diet, GO at 60, 180 and 540 mg/L decreased (P < 0.05) molar proportion of acetate (608, 569 and 547 mmol/mol total VFA, respectively), and increased (P < 0.05) propionate proportion (233, 256 and 268 mmol/mol total VFA, respectively), compared with CON values (629 and 215 mmol/mol total VFA for acetate and propionate, respectively). A minimum dose of 180 mg of GO/L was required to produce similar modifications in acetate and propionate proportions with HC diet, but no effects (P > 0.05) on butyrate proportion were detected. Methane/VFA ratio was reduced (P < 0.05) by GO at 60, 180 and 540 mg/L for MC diet (0.23, 0.16 and 0.10 mol/mol, respectively), and by GO at 20, 60, 180 and 540 mg/L for HC diet (0.19, 0.19, 0.16 and 0.08 mol/mol, respectively), compared with CON (0.26 and 0.21 mol/mol for MC and HC diets, respectively). No effects (P = 0.16–0.85) of GO on final pH and concentrations of NH3-N and lactate were detected. For both diet types, the highest CIN dose decreased (P < 0.05) production of total VFA, gas and methane, which would indicate an inhibition of fermentation. Compared with CON, CIN at 180 mg/L increased (P < 0.05) acetate proportion for the MC (629 and 644 mmol/mol total VFA for CON and CIN, respectively) and HC (525 and 540 mmol/mol total VFA, respectively) diets, without affecting the proportions of any other VFA or total VFA production. Whereas for MC diet CIN at 60 and 180 mg/L decreased (P < 0.05) NH3-N concentrations compared with CON, only a trend (P < 0.10) was observed for CIN at 180 mg/L with the HC diet. Supplementation of CIN up to 180 mg/L did not affect (P = 0.18–0.99) lactate concentrations and production of gas and methane for any diet. The results show that effectiveness of GO and CIN to modify ruminal fermentation may depend on diet type, which would have practical implications if they are confirmed in vivo.

Multi-fluid Eulerian model of an electrospray in a host gas.

An Eulerian multifluid model is used to describe the evolution of an electrospray plume and the flow induced in the surrounding gas by the drag of the electrically charged spray droplets in the space between an injection electrode containing the electrospray source and a collector electrode. The spray is driven by the voltage applied between the two electrodes. Numerical computations and order-of-magnitude estimates for a quiescent gas show that the droplets begin to fly back toward the injection electrode at a certain critical value of the flux of droplets in the spray, which depends very much on the electrical conditions at the injection electrode. As the flux is increased toward its critical value, the electric field induced by the charge of the droplets partially balances the field due to the applied voltage in the vicinity of the injection electrode, leading to a spray that rapidly broadens at a distance from its origin of the order of the stopping distance at which the droplets lose their initial momentum and the effect of their inertia becomes negligible. The axial component of the electric field first changes sign in this region, causing the fly back. The flow induced in the gas significantly changes this picture in the conditions of typical experiments. A gas plume is induced by the drag of the droplets whose entrainment makes the radius of the spray away from the injection electrode smaller than in a quiescent gas, and convects the droplets across the region of negative axial electric field that appears around the origin of the spray when the flux of droplets is increased. This suppresses fly back and allows much higher fluxes to be reached than are possible in a quiescent gas. The limit of large droplet-to-gas mass ratio is discussed. Migration of satellite droplets to the shroud of the spray is reproduced by the Eulerian model, but this process is also affected by the motion of the gas. The gas flow preferentially pushes satellite droplets from the shroud to the core of the spray when the effect of the inertia of the droplets becomes negligible, and thus opposes the well-established electrostatic/inertial mechanism of segregation and may end up concentrating satellite droplets in an intermediate radial region of the spray.

Critical radius for hot-jet ignition of hydrogen-air mixtures

This study addresses deflagration initiation of lean and stoichiometric hydrogen–air mixtures by the sudden discharge of a hot jet of their adiabatic combustion products. The objective is to compute the minimum jet radius required for ignition, a relevant quantity of interest for safety and technological applications. For sufficiently small discharge velocities, the numerical solution of the problem requires integration of the axisymmetric Navier–Stokes equations for chemically reacting ideal-gas mixtures, supplemented by standard descriptions of the molecular transport terms and a suitably reduced chemical-kinetic mechanism for the chemistry description. The computations provide the variation of the critical radius for hot-jet ignition with both the jet velocity and the equivalence ratio of the mixture, giving values that vary between a few tens microns to a few hundred microns in the range of conditions explored. For a given equivalence ratio, the critical radius is found to increase with increasing injection velocities, although the increase is only moderately large. On the other hand, for a given injection velocity, the smallest critical radius is found at stoichiometric conditions.

Numerical and experimental study of the dynamics of axisymmetric slender liquid bridges

A one-dimensional inviscid slice model has been used to study numerically the influence of axial microgravity on the breaking of liquid bridges having a volume close to that of gravitationless minimum volume stability limit. Equilibrium shapes and stability limits have been obtained as well as the dependence of the volume of the two drops formed after breaking on both the length and the volume of the liquid bridge. The breaking process has also been studied experimentally. Good agreement has been found between theory and experiment for neutrally buoyant systems

Consideration of tip speed limitations in preliminary analysis of minimum COE wind turbines

A relation between Cost Of Energy, COE, maximum allowed tip speed, and rated wind speed, is obtained for wind turbines with a given goal rated power. The wind regime is characterised by the corresponding parameters of the probability density function of wind speed. The non-dimensional characteristics of the rotor: number of blades, the blade radial distributions of local solidity, twist angle, and airfoil type, play the role of parameters in the mentioned relation. The COE is estimated using a cost model commonly used by the designers. This cost model requires basic design data such as the rotor radius and the ratio between the hub height and the rotor radius. Certain design options, DO, related to the technology of the power plant, tower and blades are also required as inputs. The function obtained for the COE can be explored to �nd those values of rotor radius that give rise to minimum cost of energy for a given wind regime as the tip speed limitation changes. The analysis reveals that iso-COE lines evolve parallel to iso-radius lines for large values of limit tip speed but that this is not the case for small values of the tip speed limits. It is concluded that, as the tip speed limit decreases, the optimum decision for keeping minimum COE values can be: a) reducing the rotor radius for places with high weibull scale parameter or b) increasing the rotor radius for places with low weibull scale parameter

Cross Ventilation CFD Modeling: Characterization and Study of Different Façade Openings Configurations at the Refurbishment of a Residential Building in Málaga (Spain)

The opening of new windows on the façade is proposed as a refurbishment strategy in an existing building in Málaga to facilitate cross ventilation of dwellings. The building is a residential block of 140 public housing units for rent for people with low income in Málaga (Spain), property of the City Council. By modeling with Computational Fluid Dynamics (CFD), eleven configurations of openings are studied in two different areas of the main housing type of the building. The quantity of introduced/extracted air into/from the room and the generated airflow patterns are obtained. The modeling allows comparing the different openings configurations to determine the most appropriate ventilation option for every room.

Proposal of a new indicator to define ductility applied to corroded steel reinforcement on concrete structures = Propuesta de un nuevo indicador para definir la ductilidad aplicada a la corrosión del acero de refuerzo en estructuras de hormigón

The carbonation of concrete or the chlorides ingress in such quantity to reach the level of bars is triggers of reinforcement corrosion. One of the most significant effects of reinforcing steel corrosion on reinforced concrete structures is the decline in the ductility-related properties of the steel. Reinforcement ductility has a decisive effect on the overall ductility of reinforced concrete structures. Different Codes classify the type of steel depending on their ductility defined by the minimum values of several parameters. Using indicators of ductility associating different properties can be advantageous on many occasions. It is considered necessary to define the ductility by means of a single parameter that considers strength values and deformation simultaneously. There are a number of criteria for defining steel ductility by a single parameter. The present experimental study addresses the variation in the ductility of concrete-embedded steel bars when exposed to accelerated corrosion. This paper analyzes the suitability of a new indicator of ductility used in corroded bars.