The WaveGyro

The WaveGyro – A new Concept for Ocean Wave Energy Capture (Master Thesis by Gebhard Waizmann, University of Southampton 22.09.2011) Abstract Climate change, environmental pollution and the proceeding resource depletion give awareness of the necessity towards more sustainable energy economics. Energy from ocean waves may once play a contributing role towards this step but is as yet in its fledgling stages. This is mainly due to the harsh sea environment, which implies the need for simple and robust wave energy converter. The work presented in this thesis picks up this thought when dealing with the so-called WaveGyro. Introductory chapters explain how this novel concept arose, followed by a detailed explanation of the working principle. The WavGyro utilizes gyroscopes to provide an internal reaction moment against the wave excitation. This internal reaction permits designing a completely enclosed and thus environmentally resistant device. The gyroscopic precession is used to convert the wave-induced moment into a moment that accelerates the flywheels. Equations of motion, which describe the gyroscope kinetics, are deduced. The gyroscopic motions and moment is then implemented into the first-order wave hydrodynamics. Two main approaches to describe the wave excitation are presented. The first approach is superposition of radiation and exci-tation and the second approach makes use of the relative motion principle, which relates the excitation to the extent of displacement. Both approaches are employed to deduce the maximum power capture condition in relation to the device’s dimensions and operational parameters. The influence of real sea state, analytically expressed by the Pierson-Moskowitz spec-trum, on the optimum power analysis is considered and implementation methods are de-veloped. Subsequently the spin-up mechanism is explained and examined; this is the mechanism converting the precession moment into torque accelerating the flywheel. It is shown that a simple configuration, composed of an ordinary cogwheel and a sprag-clutch only is not sufficient for this mechanism. Ideas for alternative mechanisms are considered but require further investigation to allow conclusive results. Finally, an approximate plan for the design of model is developed, which includes basic considerations of scaling laws. Recommendations for further theoretical and practical work on the WaveGyro are provided

The strongest gravitational lenses: IV. The order statistics of the largest Einstein radii with cluster mergers

Based on techniques developed in the previous papers of this series, we investigate the impact of galaxy-cluster mergers on the order statistics of the largest Einstein radii. We show that the inclusion of mergers significantly shifts the extreme value distribution of the largest Einstein radius to higher values, typically increasing the expected value by ${\sim}10\%$. A comparison with current data reveals that the largest observed Einstein radius agrees excellently well with the theoretical predictions of the $\Lambda$CDM model at redshifts $z > 0.5$. At redshifts $z < 0.5$, our results are somewhat more controversial. Although cluster mergers also increase the expected values of the order statistics of the $n$ largest Einstein radii by ${\sim}10\%$, the theoretically expected values are notably lower (${\sim}3\sigma$ deviation for $n = 12$) than the largest Einstein radii of a selected sample of SDSS clusters in the redshift range $0.1 \leq z \leq 0.55$. The uncertainties of the observed Einstein radii are still large, however, and thus the measurements need to be carefully revised in future works. Therefore, given the premature state of current observational data, overall, there is still no reliable statistical evidence for observed Einstein radii to exceed the theoretical expectations of the standard cosmological model.Comment: 9 pages, 7 figures, 1 table; accepted for publication in A&

The strongest gravitational lenses: III. The order statistics of the largest Einstein radii

The Einstein radius (ER) of a gravitational lens encodes information about decisive quantities such as halo mass, concentration, triaxiality, and orientation with respect to the observer. Thus, the largest Einstein radii can potentially be utilised to test the predictions of the LCDM model. Hitherto, studies have focussed on the single largest observed ER. We extend those studies by employing order statistics to formulate exclusion criteria based on the n largest Einstein radii and apply these criteria to the strong lensing analysis of 12 MACS clusters at z>0.5. We obtain the order statistics of Einstein radii by a MC approach, based on the semi-analytic modelling of the halo population on the past lightcone. After sampling the order statistics, we fit a GEV distribution to the first-order distribution, which allows us to derive analytic relations for the order statistics of the Einstein radii. We find that the Einstein radii of the 12 MACS clusters are not in conflict with the LCDM expectations. Our exclusion criteria indicate that, in order to exhibit tension with the concordance model, one would need to observe approximately twenty Einstein radii >30", ten >35" or five >42" in the range of 0.5<z<1.0 on the full sky. Furthermore, we find that, with increasing order, the haloes with the largest Einstein radii are on average less aligned along the line-of-sight and less triaxial. In general, the cumulative distribution functions steepen for higher orders, giving them better constraining power. (abridged)Comment: 8 pages, 6 figures, accepted for publication in Astronomy and Astrophysic

On the modelling of the excesses of galaxy clusters over high-mass thresholds

In this work we present for the first time an application of the Pareto approach to the modelling of the excesses of galaxy clusters over high-mass thresholds. The distribution of those excesses can be described by the generalized Pareto distribution (GPD), which is closely related to the generalized extreme value (GEV) distribution. After introducing the formalism, we study the impact of different thresholds and redshift ranges on the distributions, as well as the influence of the survey area on the mean excess above a given mass threshold. We also show that both the GPD and the GEV approach lead to identical results for rare, thus high-mass and high-redshift, clusters. As an example, we apply the Pareto approach to ACT-CL J0102-4915 and SPT-CL J2106-5844 and derive the respective cumulative distribution functions of the exceedance over different mass thresholds. We also study the possibility to use the GPD as a cosmological probe. Since in the maximum likelihood estimation of the distribution parameters all the information from clusters above the mass threshold is used, the GPD might offer an interesting alternative to GEV-based methods that use only the maxima in patches. When comparing the accuracy with which the parameters can be estimated, it turns out that the patch-based modelling of maxima is superior to the Pareto approach. In an ideal case, the GEV approach is capable to estimate the location parameter with a percent level precision for less than 100 patches. This result makes the GEV based approach potentially also interesting for cluster surveys with a smaller area.Comment: 10 pages, 8 figures, MNRAS accepted, minor modifications to match the accepted versio

On a novel approach using massive clusters at high redshifts as cosmological probe

In this work we propose a novel method for testing the validity of the fiducial LCDM cosmology by measuring the cumulative distribution function of the most massive haloes in a sample of subvolumes of identical size tiled on the sky at a fixed redshift. The fact that the most massive clusters probe the high-mass tail of the mass function, where the difference between LCDM and alternative cosmological models is strongest, makes our method particularly interesting as a cosmological probe. We utilise general extreme value statistics (GEV) to obtain a cumulative distribution function of the most massive objects in a given volume. We sample this distribution function according to the number of patches covered by the survey area for a range of different "test cosmologies" and for differently accurate mass estimations of the haloes. By fitting this sample with the GEV distribution function, we can study which parameters are the most sensitive with respect to the test cosmologies. We find that the peak of the probability distribution function of the most massive halo is well suited to test the validity of the fiducial LCDM model, once we are able to establish a sufficiently complete large-area survey with M_lim=10^14.5 M_sun/h (M_lim=10^14 M_sun/h) at redshifts above z=1 (z=1.5). Being of cumulative nature the proposed measure is robust and an accuracy of 20-30% in the cluster masses would be sufficient to test for alternative models. Since one only needs the most massive system in each angular patch, this method would be ideally suited as a first fast consistency check before going into a more complex statistical analysis of the observed halo sample.Comment: 11 pages, 13 figures, 1 Table, MNRAS accepted versio

On finding galaxy clusters with Planck and the spherical collapse model in different Dark Energy cosmologies

One of the main objectives of the Planck mission is to perform a full-sky cluster survey based on the Sunyaev-Zel'dovich (SZ) effect, which leads to the question of how such a survey would be affected by cosmological models with a different history of structure formation than LCDM. To answer this question, I developed a fast semi-analytic approach for simulating full-sky maps of the Compton-y parameter, ready to be fed into a realistic simulation pipeline. I also implemented a filter and detection pipeline based on spherical multi-frequency matched filters, that was used to study the expected SZ cluster sample of Planck. It turned out that realistic samples will comprise ~1000 clusters at low rate of contamination, significantly lower than originally anticipated. Driven by wrong estimates of the impact of early dark energy models on structure formation, we studied the spherical collapse model in dark energy model, finding that models with varying equation-of-state have a negligible impact on the structure formation. Yet, the different expansion history for the different models can be detected via volume effects, when counting objects in a known volume. Furthermore, it turned out that the different expansion history strongly affects the angular SZ power spectra for the various models, making them an interesting tool to distinguish and constrain alternative cosmologies

Testing Cosmology with Extreme Galaxy Clusters

Motivated by recent suggestions that a number of observed galaxy clusters have masses which are too high for their given redshift to occur naturally in a standard model cosmology, we use Extreme Value Statistics to construct confidence regions in the mass-redshift plane for the most extreme objects expected in the universe. We show how such a diagram not only provides a way of potentially ruling out the concordance cosmology, but also allows us to differentiate between alternative models of enhanced structure formation. We compare our theoretical prediction with observations, placing currently observed high and low redshift clusters on a mass-redshift diagram and find -- provided we consider the full sky to avoid a posteriori selection effects -- that none are in significant tension with concordance cosmology.Comment: 5 pages, 3 figures. Small correction to contours in figure 1. Conclusions unchange

An algorithm for the reconstruction of the projected gravitational potential of galaxy clusters from galaxy kinematics

In this work we develop a method to incorporate the information from galaxy kinematics into the reconstruction of the two-dimensional, projected gravitational potential of galaxy clusters. We start by deprojecting the observed line-of-sight velocity dispersions of cluster galaxies with an application of Bayes' theorem, the Richardson-Lucy method, requiring the assumption of a shape for the cluster. Assuming spherical symmetry, after the deprojection we obtain an effective galaxy pressure, i.e. the density-weighted radial velocity dispersions of the cluster galaxies, which is then related to the three-dimensional gravitational potential by using the tested assumption of a polytropic relation between the effective galaxy pressure and the density. The two-dimensional gravitational potential can finally be found by straightforward projection along the line of sight. We test the method with a numerically simulated triaxial galaxy cluster and the galaxies identified therein and perform the reconstruction for three different lines of sight, initially assuming sphericity. Expanding the gravitational potential in the cluster's geometrical ellipticities yields second-order corrections to the spherical reconstruction. By comparing our results with the projected gravitational potential directly obtained from the simulation, we show that the deviation between the projected potential obtained with our reconstruction method and the potential directly extracted from the simulation is $\lesssim10~\%$ within approximately the virial radius ($1.5\,h^{-1}\mathrm{Mpc}$) from the cluster centre in the case of a spherical cluster and remains moderate (below $10\,\%-25\,\%$) within the same radius in the case of an ellipsoidal cluster

Improved estimations of stochastic chemical kinetics by finite state expansion

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations, and multi-stability.Comment: 33 pages, 9 figure