Fooled by bursts. A Goal per Minute model for the World Cup

On the occasion of the last FIFA World Cup in Brazil, The Economist published a plot depicting how many goals have been scored in all World Cup competitions until present, minute by minute. The plot was followed by a naive and poorly grounded qualitative analysis. In the present article we use The Economist dataset to check its conclusions, update previous results from literature and offer a new model. In particular, it will be shown that first and second half game have different scoring rates. In the first half the scoring rate can be considered constant. In the second it increases linearly with time

Optimal on-off cooperative manoeuvers for long-term satellite cluster flight

When a group of satellites is equipped with a particulary simple propul- sion system, e.g. cold-gas thrusters, constraints on the thrust level and total propellant mass renders cluster-keeping extremely challenging. This is even more pronounced in disaggregated space architectures, in which a satellite is formed by clustering a number of heterogenous, free-flying modules. The research described in this paper develops guidance laws aimed at keeping the relative distances between the cluster modules bounded for long mission lifetimes, typically more than a year, while utilizing constant-magnitude low-thrust, with a characteristic on-off profile. A cooperative guidance law capable of cluster establishment and maintenance under realistic environ- mental perturbations is developed. The guidance law is optimized for fuel consumption, subject to relative distance constraints. Some of the solutions found to the optimal guidance problem require only a single maneuver arc to keep the cluster within relatively close distances for an entire year

Autonomous satellite constellation for enhanced Earth coverage using coupled selection equations

This paper presents a novel solution to the problem of autonomous task allocation for a self-organising constellation of small satellites in Earth orbit. The method allows the constellation members to plan manoeuvres to cluster themselves above particular target longitudes on the Earth’s surface. This is enabled through the use of Coupled Selection Equations, which represent a dynamical systems approach to combinatorial optimisation problems, and whose solution tends towards a Boolean matrix which describes pairings of the satellites and targets which solves the relevant assignment problems. Satellite manoeuvres are actuated using a simple control law which incorporates the results of the Coupled Selection Equations. Three demonstrations of the efficacy of the method are given in order of increasing complexity - first with an equal number of satellites and targets, then with a surplus of satellites, including agent failure events, and finally with a constellation of two different satellite types. The method is shown to provide efficient solutions, whilst being computationally non-intensive, quick to converge and robust to satellite failures. Proposals to extend the method for on-board processing on a distributed architecture are discussed

Self-organising satellite constellation in geostationary Earth orbit

This paper presents a novel solution to the problem of autonomous task allocation for a self-organizing satellite constellation in Earth orbit. The method allows satellites to cluster themselves above targets on the Earth’s surface. This is achieved using Coupled Selection Equations (CSE) - a dynamical systems approach to combinatorial optimization whose solution tends asymptotically towards a Boolean matrix describing the pairings of satellites and targets which solves the relevant assignment problems. Satellite manoeuvers are actuated by an Artificial Potential Field method which incorporates the CSE output. Three demonstrations of the method’s efficacy are given - first with equal numbers of satellites and targets, then with a satellite surplus, including agent failures, and finally with a fractionated constellation. Finally, a large constellation of 100 satellites is simulated to demonstrate the utility of the method in future swarm mission scenarios. The method provides efficient solutions with quick convergence, is robust to satellite failures, and hence appears suitable for distributed, on-board autonomy

Integration of conventional and unconventional Instrument Transformers in Smart Grids

In this thesis the reader will be guided towards the role of Instrument Transformers inside the always evolving Smart Grid scenario. In particular, even non-experts or non-metrologists will have the chance to follow the main concepts presented; this, because the basic principles are always presented before moving to in-deep discussions. The chapter including the results of the work is preceded by three introductive chapters. These, contain the basic principles and the state of the art necessary to provide the reader the tools to approach the results chapter. The first three chapters describe: Instrument Transformers, Standards, and Metrology. In the first chapter, the studied Instrument Transformers are described and compared with particular attention to their accuracy parameters. In the second chapter instead, two fundamental international documents, concerning Instrument Transformers, are analysed: the IEC 61869 series and the EN 50160. This has been done to be completely aware of how transformers are standardized and regulated. Finally, the last introductive chapter presents one of the pillars of this work: metrology and the role of uncertainty. In the core of the work Instrument Transformers integration in Smart Grid is distinguished in two main topics. The first assesses the transformers behaviour, in terms of accuracy, when their normal operation is affected by external quantities. The second exploits the current and voltage measurements obtained from the transformers to develop new algorithm and techniques to face typical and new issue affecting Smart Grids. In the overall, this thesis has a bifold aim. On one hand it provides a quite-detailed overview on Instrument Transformers technology and state of the art. On the other hand, it describes issues and novelties concerning the use of the transformers among Smart Grids, focusing on the role of uncertainty when their measurements are used for common and critical applications

On turbulent particle fountains

We describe new experiments in which particle-laden turbulent fountains with source Froude numbers 20>Fr_{0}>6 are produced when particle-laden fresh water is injected upwards into a reservoir filled with fresh water. We find that the ratio $U$ of the particle fall speed to the characteristic speed of the fountain determines whether the flow is analogous to a single-phase fountain ($U\ll 1$) or becomes a fully separated flow ($U\geqslant 1$). In the single-phase limit, a fountain with momentum flux $M$ and buoyancy flux $B$ oscillates about the mean height, $h_{m}=(1.56\pm 0.04)M^{3/4}B^{-1/2}$, as fluid periodically cascades from the maximum height, $h_{t}=h_{m}+{\rm\Delta}h$, to the base of the tank. Experimental measurements of the speed $u$ and radius $r$ of the fountain at the mean height $h_{m}$, combined with the conservation of buoyancy, suggest that $Fr(h_{m})=u(g^{\prime }r)^{-1/2}\approx 1$. Using these values, we find that the classical scaling for the frequency of the oscillations, ${\it\omega}\sim BM^{-1}$, is equivalent to the scaling $u(h_{m})/r(h_{m})$ for a fountain supplied at $z=h_{m}$ with $Fr=1$ (Burridge & Hunt, J. Fluid Mech., vol. 728, 2013, pp. 91–119). This suggests that the oscillations are controlled in the upper part of the fountain where $Fr\leqslant 1$, and that they may be understood in terms of a balance between the upward supply of a growing dense particle cloud, at the height where $Fr=1$, and the downward flow of this cloud. In contrast, in the separated flow regime, we find that particles do not reach the height at which $Fr=1$: instead, they are transported to the level at which the upward speed of the fountain fluid equals their fall speed. The particles then continuously sediment while the particle-free fountain fluid continues to rise slowly above the height of particle fallout, carried by its momentum.This work has been funded through the BP Institute, EPSRC and Hughes Hall, Cambridge. We gratefully acknowledge the technical assistance of A. Pluck, and the constructive comments of three anonymous referees.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.16

On the transport of heavy particles through an upward displacement-ventilated space

We explore the transport of heavy particles through an upward displacement-ventilated space. The space incorporates a localised source of buoyancy which generates a turbulent buoyant plume. The plume fluid is contaminated with a small concentration of particles, which are subject to gravitational settling. A constant flow of uncontaminated fluid is supplied at a low level into the space, while an equal amount of fluid is vented from the space at a high level. At steady state, a two-layer density stratification develops associated with the source of buoyancy. New laboratory experiments are conducted to explore how particles are transported by this flow. The experiments identify that the upper layer may either become well-mixed in particles or it may develop a vertical stratification in particle concentration, with the particle concentration decreasing with height. We develop a quantitative model which identifies that such stratification develops for larger particle setting speeds, or smaller ventilation rates. In accord with our experiments, the model predicts that the number of particles extracted from the space through the high-level vent is controlled by the magnitude of the particle stratification in the upper layer, and this in turn depends on the particle settling speed relative to the ventilation speed and also the cross-sectional area and height of the space. We compare the predictions of the model with measurements of the flux of particles vented from the space for a range of operating conditions. We explore the relevance of the model for the removal of airborne contaminants by displacement ventilation in hospital rooms, and we discuss how contamination is propagated in the room as a result of lateral mixing of pathogens in the upper layer.This work has been funded through the BP Institute, EPSRC and Hughes Hall, Cambridge. We gratefully acknowledge the technical assistance of A. Pluck, and the constructive comments of Professor C. Noakes, Dr. C. P. Caulfield and of two anonymous referees.This is the author accepted manuscript. The final version is available via CUP at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=9694505&fileId=S0022112015002049

On the transport of heavy particles through a downward displacement-ventilated space

We investigate the transport of relatively heavy, small particles through a downward displacement-ventilated space. A flux of particles is supplied to the space from a localised source at a high level and forms a turbulent particle-laden plume which descends through the space. A constant flow of ambient fluid which does not contain particles is supplied to the space at a high level, while an equal amount of fluid is vented from the space at a low level. As a result of the entrainment of ambient fluid into the particle plume, a return flow is produced in the ambient fluid surrounding the plume in the lower part of the space. At steady state, particles are suspended by this return flow. An interface is formed which separates the ambient fluid in the lower part of the space, which contains particles, from the particle-free ambient fluid in the upper part of the space. New laboratory experiments show that the concentration of particles in the ambient fluid below the interface is larger than the average concentration of particles in the plume fluid at the level of the interface. Hence, as the plume fluid crosses the interface and descends through the particle-laden fluid underneath, it becomes relatively buoyant and forms a momentum-driven fountain. If the fountain fluid impinges on the floor, it then spreads radially over the surface until lifting off. We develop a quantitative model which can predict the height of the interface, the concentration of particles in the lower layer, and the partitioning of the particle flux between the fraction which sediments over the floor and that which is ventilated out of the space. We generalise the model to show that when particles and negatively buoyant fluid are supplied at the top of the space, a three-layer stratification develops in the space at steady state: the upper layer contains relatively low-density ambient fluid in which no particles are suspended; the central layer contains a mixture of ambient and plume fluid in which no particles are suspended; and the lower layer contains a suspension of particles in the same mixture of ambient and plume fluid. We quantify the heights of the two interfaces which separate the three layers in the space and the concentration of particles in suspension in the ambient fluid in the lower layer. We then discuss the relevance of the results for the control of airborne infections in buildings. Our experiments show that the three-layer stratification is subject to intermittent large-scale instabilities when the concentration of particles in the plume at the source is sufficiently small, or the rate of ventilation of the space is sufficiently large: we describe the transient concentration of particles in the space during one of these instabilities.This work has been funded through the BP Institute, EPSRC and Hughes Hall, Cambridge. We gratefully acknowledge the technical assistance of A. Pluck, and the constructive comments of Professor C. Noakes, Dr. C. P. Caulfield and of three anonymous referees.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2015.24

Mixing and reaction in turbulent plumes: The limits of slow and instantaneous chemical kinetics

We investigate the behaviour of a reactive plume in the two limiting cases of slow and instantaneous chemical reactions. New laboratory measurements show that, whereas the slow reaction between the source and entrained chemical species takes place within the whole volume of each eddy in the plume, the fast reaction develops preferentially at the periphery of the eddies. We develop a new model that quantifies the mixing of the reactive buoyant fluids at the Batchelor scale and thereby the progress of the fast reaction. We present a series of new experimental results that suggest that a critical distance from the source, $z_{crit}$, exists at which the volume of fluid that is entrained from the ambient is equal to that which is mixed within the plume at the Batchelor scale. For z>z_{crit}, only a fraction of the entrained fluid is rapidly mixed and reacts with the plume fluid. The results of the new experiments enable us to quantify the distance from the source at which an instantaneous reaction reaches completion, and show that it can be significantly larger than the distance $L_{s}$ at which the stoichiometric dilution of the plume fluid is achieved. In the limit of an instantaneous reaction, the longitudinal profiles of source chemical concentration in the plume depend on $(z_{crit}/L_{s})^{5/6}$. The predictions of the model are validated against the experimental results, and the profiles of source chemical concentration in the plume for slow and fast reactions are compared.</jats:p

Smart characterization of rogowski coils by using a synthetized signal

With the spread of new Low-Power Instrument Transformers (LPITs), it is fundamental to provide models and characterization procedures to estimate and even predict the LPITs\u2019 behavior. In fact, distribution system operators and designers of network models are looking for all forms of information which may help the management and the control of power networks. For this purpose, the paper wants to contribute to the scientific community presenting a smart characterization procedure which easily provides sufficient information to predict the output signal of a Low-Power Current Transformer (LPCT), the Rogowski coil. The presented procedure is based on a synthetized signal applied to the Rogowski coil. Afterwards, the validity of the procedure is assessed within the Matlab environment and then by applying it on three off-the-shelf Rogowski coils. Simulations and experimental tests and results involving a variety of distorted signals in the power quality frequency range and by adopting a quite simple measurement setup demonstrated the effectiveness and the capability of the procedure to correctly estimate the output of the tested device