The PSCz Galaxy Power Spectrum Compared to N-Body Simulations

By comparing the PSCz galaxy power spectrum with haloes from nested and phased N-body simulations, we try to understand how IRAS infrared-selected galaxies populate dark-matter haloes. We pay special attention to the way we identify haloes in the simulations.Comment: 2 pages, 1 figure, to appear in "The IGM/Galaxy Connection: The Distribution of Baryons at z=0," eds. J.L. Rosenberg and M.E. Putma

A Search for Gravitational Milli–Lenses

We have searched for gravitational milli–lens systems by examining VLBI maps of ~ 300 flat–spectrum radio sources. So far we have followed up 7 candidates, with separations in the range 2–20 mas. None have been confirmed as lenses but several of them can not yet be definitively ruled out. If there are no milli-lenses in this sample then uniformly–distributed black holes of 10^6 to 10^8 M_⊙ cannot contribute more than ~ 1% of the closure density

Effect of the Berendsen thermostat on dynamical properties of water

The effect of the Berendsen thermostat on the dynamical properties of bulk SPC/E water is tested by generating power spectra associated with fluctuations in various observables. The Berendsen thermostat is found to be very effective in preserving temporal correlations in fluctuations of tagged particle quantities over a very wide range of frequencies. Even correlations in fluctuations of global properties, such as the total potential energy, are well-preserved for time periods shorter than the thermostat time constant. Deviations in dynamical behaviour from the microcanonical limit do not, however, always decrease smoothly with increasing values of the thermostat time constant but may be somewhat larger for some intermediate values of $\tau_B$, specially in the supercooled regime, which are similar to time scales for slow relaxation processes in bulk water.Comment: 21 pages, 5 figures, To be published in Mol. Phy

Joining Forces of Bayesian and Frequentist Methodology: A Study for Inference in the Presence of Non-Identifiability

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take advantage of both Bayesian and frequentist methods. The elegance of Bayesian methodology is founded in the propagation of information content provided by experimental data and prior assumptions to the posterior probability distribution of model predictions. However, for complex applications experimental data and prior assumptions potentially constrain the posterior probability distribution insufficiently. In these situations Bayesian Markov chain Monte Carlo sampling can be infeasible. From a frequentist point of view insufficient experimental data and prior assumptions can be interpreted as non-identifiability. The profile likelihood approach offers to detect and to resolve non-identifiability by experimental design iteratively. Therefore, it allows one to better constrain the posterior probability distribution until Markov chain Monte Carlo sampling can be used securely. Using an application from cell biology we compare both methods and show that a successive application of both methods facilitates a realistic assessment of uncertainty in model predictions.Comment: Article to appear in Phil. Trans. Roy. Soc.

A level-set method for the evolution of cells and tissue during curvature-controlled growth

Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or cell behavioural in nature. The control of geometry on tissue growth has been evidenced in many in-vivo and in-vitro experiments, including bone remodelling, wound healing, and tissue engineering scaffolds. In this paper, we propose a generalisation of a mathematical model that captures the mechanistic influence of curvature on the joint evolution of cell density and tissue shape during tissue growth. This generalisation allows us to simulate abrupt topological changes such as tissue fragmentation and tissue fusion, as well as three dimensional cases, through a level-set-based method. The level-set method developed introduces another Eulerian field than the level-set function. This additional field represents the surface density of tissue synthesising cells, anticipated at future locations of the interface. Numerical tests performed with this level-set-based method show that numerical conservation of cells is a good indicator of simulation accuracy, particularly when cusps develop in the tissue's interface. We apply this new model to several situations of curvature-controlled tissue evolutions that include fragmentation and fusion.Comment: 15 pages, 10 figures, 3 supplementary figure

The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit

The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic dynamics including irregular switching of sign of various phase space variables, but details of the mechanisms underlying the complicated dynamics have not previously been investigated. We identify global bifurcations that induce the onset of chaotic dynamics and switching near a heteroclinic cycle of this type, and by construction and analysis of approximate return maps, locate the global bifurcations in parameter space. We find there is a threshold in the size of certain symmetry-breaking terms below which there can be no persistent switching. Our results are illustrated by a numerical example

Chaotic root-finding for a small class of polynomials

In this paper we present a new closed-form solution to a chaotic difference equation, $y_{n+1} = a_2 y_{n}^2 + a_1 y_{n} + a_0$ with coefficient $a_0 = (a_1 - 4)(a_1 + 2) / (4 a_2)$, and using this solution, show how corresponding exact roots to a special set of related polynomials of order $2^p, p \in \mathbb{N}$ with two independent parameters can be generated, for any $p$

Line adsorption in a mean-field density functional model

Recent ideas about the analog for a three-phase contact line of the Gibbs adsorption equation for interfaces are illustrated in a mean-field density-functional model. With $d¥tau$ the infinitesimal change in the line tension $¥tau$ that accompanies the infinitesimal changes $d¥mu_i$ in the thermodynamic field variables $¥mu_i$ and with $¥Lambda_i$ the line adsorptions, the sum $d¥tau + ¥Sigma ¥Lambda_i d¥mu_i$, unlike its surface analog, is not 0. An equivalent of this sum in the model system is evaluated numerically and analytically. A general line adsorption equation, which the model results illustrate, is derived.</p

On the detection and attribution of gravity waves generated by the 20 March 2015 solar eclipse

Internal gravity waves are generated as adjustment radiation whenever a sudden change in forcing causes the atmosphere to depart from its large-scale balanced state. Such a forcing anomaly occurs during a solar eclipse, when the Moon’s shadow cools part of the Earth’s surface. The resulting atmospheric gravity waves are associated with pressure and temperature perturbations, which in principle are detectable both at the surface and aloft. In this study, surface pressure and temperature data from two UK sites at Reading and Lerwick are analysed for eclipse-driven gravity-wave perturbations during the 20 March 2015 solar eclipse over north-west Europe. Radiosonde wind data from the same two sites are also analysed using a moving parcel analysis method, to determine the periodicities of the waves aloft. On this occasion, the perturbations both at the surface and aloft are found not to be confidently attributable to eclipse-driven gravity waves. We conclude that the complex synoptic weather conditions over the UK at the time of this particular eclipse helped to mask any eclipse-driven gravity waves

Eclipse-induced wind changes over the British Isles on the 20 March 2015

The British Isles benefits from dense meteorological observation networks, enabling insights into the still-unresolved effects of solar eclipse events on the near-surface wind field. The near-surface effects of the solar eclipse of 20 March 2015 are derived through comparison of output from the Met Office's operational weather forecast model (which is ignorant of the eclipse) with data from two meteorological networks: the Met Office's land surface station (MIDAS) network and a roadside measurement network operated by Vaisala. Synoptic-evolution relative calculations reveal the cooling and increase in relative humidity almost universally attributed to eclipse events. In addition, a slackening of wind speeds by up to about 2 knots in already weak winds and backing in wind direction of about 20 degrees under clear skies across middle England are attributed to the eclipse event. The slackening of wind speed is consistent with the previously reported boundary layer stabilisation during eclipse events. Wind direction changes have previously been attributed to a large-scale `eclipse-induced cold-cored cyclone', mountain slope flows, and changes in the strength of sea breezes. A new explanation is proposed here by analogy with nocturnal wind changes at sunset and shown to predict direction changes consistent with those observed