Comparison of Magnetic Anomalies of Lithospheric Origin Measured by Satellite and Airborne Magnetometers over Western Canada

Crustal magnetic anomaly data from the OGO 2, 4 and 6 (Pogo) satellites are compared with upward-continued aeromagnetic data between 50 deg -85 deg N latitude and 220 deg - 260 deg E longitude. Agreement is good both in anomaly location and in amplitude, giving confidence that it is possible to proceed with the derivation and interpretation of satellite anomaly maps in all parts of the globe. The data contain a magnetic high over the Alpha ridge suggesting continental composition and a magnetic low over the southern Canada basin and northern Canadian Arctic islands (Sverdrup basin). The low in the Sverdrup basin corresponds to a region of high heat flow, suggesting a shallow Curie isotherm. A ridge of high field, with two distinct peaks in amplitude, is found over the northern portion of the platform deposits and a relative high is located in the central portion of the Churchill province. No features are present to indicate a magnetic boundary between Slave and Bear provinces, but a trend change is evident between Slave and Churchill provinces. South of 60 deg latitude a broad magnetic low is located over very thick (40-50 km) crust, interpreted to be a region of low magnetization

The Cluster Distribution as a Test of Dark Matter Models. IV: Topology and Geometry

We study the geometry and topology of the large-scale structure traced by galaxy clusters in numerical simulations of a box of side 320 $h^{-1}$ Mpc, and compare them with available data on real clusters. The simulations we use are generated by the Zel'dovich approximation, using the same methods as we have used in the first three papers in this series. We consider the following models to see if there are measurable differences in the topology and geometry of the superclustering they produce: (i) the standard CDM model (SCDM); (ii) a CDM model with $\Omega_0=0.2$ (OCDM); (iii) a CDM model with a `tilted' power spectrum having $n=0.7$ (TCDM); (iv) a CDM model with a very low Hubble constant, $h=0.3$ (LOWH); (v) a model with mixed CDM and HDM (CHDM); (vi) a flat low-density CDM model with $\Omega_0=0.2$ and a non-zero cosmological $\Lambda$ term ($\Lambda$CDM). We analyse these models using a variety of statistical tests based on the analysis of: (i) the Euler-Poincar\'{e} characteristic; (ii) percolation properties; (iii) the Minimal Spanning Tree construction. Taking all these tests together we find that the best fitting model is $\Lambda$CDM and, indeed, the others do not appear to be consistent with the data. Our results demonstrate that despite their biased and extremely sparse sampling of the cosmological density field, it is possible to use clusters to probe subtle statistical diagnostics of models which go far beyond the low-order correlation functions usually applied to study superclustering.Comment: 17 pages, 7 postscript figures, uses mn.sty, MNRAS in pres

Extreme events and event size fluctuations in biased random walks on networks

Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the context of complex networks. This was motivated by the occurrence of rare events such as traffic jams, floods, and power black-outs which take place on networks. In this work, we study extreme events in a generalized random walk model in which the walk is preferentially biased by the network topology. The walkers preferentially choose to hop toward the hubs or small degree nodes. In this setting, we show that extremely large fluctuations in event-sizes are possible on small degree nodes when the walkers are biased toward the hubs. In particular, we obtain the distribution of event-sizes on the network. Further, the probability for the occurrence of extreme events on any node in the network depends on its 'generalized strength', a measure of the ability of a node to attract walkers. The 'generalized strength' is a function of the degree of the node and that of its nearest neighbors. We obtain analytical and simulation results for the probability of occurrence of extreme events on the nodes of a network using a generalized random walk model. The result reveals that the nodes with a larger value of 'generalized strength', on average, display lower probability for the occurrence of extreme events compared to the nodes with lower values of 'generalized strength'

Getting the Measure of the Flatness Problem

The problem of estimating cosmological parameters such as $\Omega$ from noisy or incomplete data is an example of an inverse problem and, as such, generally requires a probablistic approach. We adopt the Bayesian interpretation of probability for such problems and stress the connection between probability and information which this approach makes explicit. This connection is important even when information is ``minimal'' or, in other words, when we need to argue from a state of maximum ignorance. We use the transformation group method of Jaynes to assign minimally--informative prior probability measure for cosmological parameters in the simple example of a dust Friedman model, showing that the usual statements of the cosmological flatness problem are based on an inappropriate choice of prior. We further demonstrate that, in the framework of a classical cosmological model, there is no flatness problem.Comment: 11 pages, submitted to Classical and Quantum Gravity, Tex source file, no figur

Scale-dependent Galaxy Bias

We present a simple heuristic model to demonstrate how feedback related to the galaxy formation process can result in a scale-dependent bias of mass versus light, even on very large scales. The model invokes the idea that galaxies form initially in locations determined by the local density field, but the subsequent formation of galaxies is also influenced by the presence of nearby galaxies that have already formed. The form of bias that results possesses some features that are usually described in terms of stochastic effects, but our model is entirely deterministic once the density field is specified. Features in the large-scale galaxy power spectrum (such as wiggles that might in an extreme case mimic the effect of baryons on the primordial transfer function) could, at least in principle, arise from spatial modulations of the galaxy formation process that arise naturally in our model. We also show how this fully deterministic model gives rise to apparently stochasticity in the galaxy distribution.Comment: 14 pages, 2 figures, typos corrected, discussion added and references corrected; matches version accepted by JCA

A low CMB variance in the WMAP data

We have estimated the CMB variance from the three-year WMAP data, finding a value which is significantly lower than the one expected from Gaussian simulations using the WMAP best-fit cosmological model, at a significance level of 98.7 per cent. This result is even more prominent if we consider only the north ecliptic hemisphere (99.8 per cent). Different analyses have been performed in order to identify a possible origin for this anomaly. In particular we have studied the behaviour of single radiometers and single year data as well as the effect of residual foregrounds and 1/f noise, finding that none of these possibilities can explain the low value of the variance. We have also tested the effect of varying the cosmological parameters, finding that the estimated CMB variance tends to favour higher values of $n_s$ than the one of the WMAP best-fit model. In addition, we have also tested the consistency between the estimated CMB variance and the actual measured CMB power spectrum of the WMAP data, finding a strong discrepancy. A possible interpretation of this result could be a deviation from Gaussianity and/or isotropy of the CMB.Comment: 13 pages, 5 figures. Some new tests added. Section 5 largely modified. Accepted for publication in MNRA

A Counts-in-Cells Analysis of Lyman-break Galaxies at z~3

We have measured the counts-in-cells fluctuations of 268 Lyman-break galaxies with spectroscopic redshifts in six 9 arcmin by 9 arcmin fields at z~3. The variance of galaxy counts in cubes of comoving side length 7.7, 11.9, 11.4 h^{-1} Mpc is \sigma_{gal}^2 ~ 1.3\pm0.4 for \Omega_M=1, 0.2 open, 0.3 flat, implying a bias on these scales of \sigma_{gal} / \sigma_{mass} = 6.0\pm1.1, 1.9\pm0.4, 4.0\pm0.7. The bias and abundance of Lyman-break galaxies are surprisingly consistent with a simple model of structure formation which assumes only that galaxies form within dark matter halos, that Lyman-break galaxies' rest-UV luminosities are tightly correlated with their dark masses, and that matter fluctuations are Gaussian and have a linear power-spectrum shape at z~3 similar to that determined locally (\Gamma~0.2). This conclusion is largely independent of cosmology or spectral normalization \sigma_8. A measurement of the masses of Lyman-break galaxies would in principle distinguish between different cosmological scenarios.Comment: Accepted for publication in ApJ, 16 pages including 4 figure

Computational Study of Turbulent-Laminar Patterns in Couette Flow

Turbulent-laminar patterns near transition are simulated in plane Couette flow using an extension of the minimal flow unit methodology. Computational domains are of minimal size in two directions but large in the third. The long direction can be tilted at any prescribed angle to the streamwise direction. Three types of patterned states are found and studied: periodic, localized, and intermittent. These correspond closely to observations in large aspect ratio experiments.Comment: 4 pages, 5 figure