The relativistic factor in the orbital dynamics of point masses

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations.     

Seismic response of masonry-infilled steel frames via multi-scale finite-element analyses

Effects of masonry infills on the seismic vulnerability of steel frames is studied through multi-scale numerical modelling. First, a micro-modelling approach is utilized to define a homogenized masonry material, calibrated on experimental tests, which is used for modelling the nonlinear response of a one-story, single span, masonry-infilled portal under horizontal loads. Based on results of the micro-model, the constitutive behavior of a diagonal strut macro-element equivalent to the infill panel is calibrated. Then, the diagonal strut is used to model infill panels in the macro-scale analysis of a multi-span multi-story infilled moment-resisting (MR) steel frame. The seismic vulnerability of the MR frame is evaluated through a nonlinear static procedure. Numerical analyses highlight that infills may radically modify the seismic response and the failure mechanism of the frame, hence the importance of the infill correct modelling.     

Controls on monthly estuarine residuals: Eulerian circulation and elevation

The Dee Estuary, at the NW English–Welsh border, is a major asset, supporting: one of the largest wildlife habitats in Europe, industrial importance along the Welsh coastline and residential and recreational usage along the English coast. Understanding of the residual elevation is important to determine the total water levels that inundate intertidal banks, especially during storms. Whereas, improved knowledge of the 3D residual circulation is important in determining particle transport pathways to manage water quality and morphological change. Using mooring data obtained in February–March 2008, a 3D modelling system has been previously validated against in situ salinity, velocity, elevation and wave observations, to investigate the barotropic–baroclinic wave interaction within this estuary under full realistic forcing. The system consists of a coupled circulation-wave-turbulence model (POLCOMS-WAM-GOTM). Using this modelling system the contribution of different processes and their interactions to the monthly residuals in both elevation and circulation is now assessed. By studying a tidally dominated estuary under wave influence, it is found that baroclinicity induced by a weak river flow has greater importance in generating a residual circulation than the waves, even at the estuary mouth. Although the monthly residual circulation is dominated by tidal and baroclinic processes, the residual estuarine surface elevation is primarily influenced by the seasonal external forcing to the region, with secondary influence from the local wind conditions. During storm conditions, 3D radiation stress becomes important for both elevation and circulation at the event scale but is found here to have little impact over monthly time scales.     

Semi-Periodic Sequences and Extraneous Events in Earthquake Forecasting. II: Application,Forecasts for Japan and Venezuela

In order to analyze observed seismicity in central Japan and Venezuela, we applied a new method to identify semi-periodic sequences in the occurrence times of large earthquakes, which allows for the presence of multiple periodic sequences and/or events not belonging to any sequence in the time series. We also explored a scheme for diminishing the effects of a sharp cutoff magnitude threshold in selecting the events to analyze. A main four-event sequence with probability P _c  = 0.991 of not having occurred by chance was identified for earthquakes with M ≥ 8.0 in central Japan. Venezuela is divided, from West to East, into four regions; for each of these, the magnitude ranges and identified sequences are as follows. Region 1: M ≥ 6.0, a six-event sequence with P _c  = 0.923, and a four-event sequence with P _c  = 0.706. Region 2: M ≥ 5.6, a five-event sequence with P _c  = 0.942. Region 3: M ≥ 5.6, a four-event sequence with P _c  = 0.882. Region 4: M ≥ 6.0, a five-event sequence with P _c  = 0.891. Forecasts are made and evaluated for all identified sequences having four or more events and probabilities ≥0.5. The last event of all these sequences was satisfactorily aftcast by previous events. Whether the identified sequences do, in fact, correspond to physical processes resulting in semi-periodic seismicity is, of course, an open question; but the forecasts, properly used, may be useful as a factor in seismic hazard estimation.     

Semi-Periodic Sequences and Extraneous Events in Earthquake Forecasting: I. Theory and Method,Parkfield Application

We present a new method to identify semi-periodic sequences in the occurrence times of large earthquakes, which allows for the presence of multiple semi-periodic sequences and/or events not belonging to any identifiable sequence in the time series. The method, based on the analytic Fourier transform, yields estimates of the departure from periodicity of an observed sequence, and of the probability that the sequence is not due to chance. These estimates are used to make and to evaluate forecasts of future events belonging to each sequence. Numerous tests with synthetic catalogs show that the method is surprisingly capable of correctly identifying sequences, unidentifiable by eye, in complicated time series. Correct identification of a given sequence depends on the number of events it contains, on the sequence’s departure from periodicity, and, in some cases, on the choice of starting and ending times of the analyzed time window; as well as on the total number of events in the time series. Some particular data combinations may result in spectra where significant periods are obscured by large amplitudes artifacts of the transform, but artifacts can be usually recognized because they lack harmonics; thus, in most of these cases, true semi-periodic sequences may not be identified, but no false identifications will be made. A first example of an application of the method to real seismicity data is the analysis of the Parkfield event series. The analysis correctly aftcasts the September 2004 earthquake. Further applications to real data from Japan and Venezuela are shown in a companion paper.     

Maximum likelihood algorithm for parametric component separation in cosmic microwave background experiments

We discuss an approach to the component separation of microwave, multifrequency sky maps as those typically produced from cosmic microwave background (CMB) anisotropy data sets. The algorithm is based on the two-step, parametric, likelihood-based technique recently elaborated on by Eriksen et al., where the foreground spectral parameters are estimated prior to the actual separation of the components. In contrast with the previous approaches, we accomplish the former task with help of an analytically derived likelihood function for the spectral parameters, which, we show, yields estimates equal to the maximum likelihood values of the full multidimensional data problem. We then use these estimates to perform the second step via the standard, generalized-least-squares-like procedure. We demonstrate that the proposed approach is equivalent to a direct maximization of the full data likelihood, which is recast in a computationally tractable form. We use the corresponding curvature matrices to characterize statistical properties of the recovered parameters. We incorporate in the formalism some of the essential features of the CMB data sets, such as inhomogeneous pixel domain noise, unknown map offsets as well as calibration errors and study their consequences for the separation. We find that the calibration is likely to have a dominant effect on the precision of the spectral parameter determination for a realistic CMB experiment. We apply the algorithm to simulated data and discuss the results. Our focus is on partial sky, total intensity and polarization, CMB experiments such as planned balloon-borne and ground-based efforts, however, the techniques presented here should be also applicable to the full-sky data as for instance, those produced by the Wilkinson Microwave Anisotropy Probe ( WMAP ) satellite and anticipated from the Planck mission.     

Modelling the cosmological co-evolution of supermassive black holes and galaxies – II. The clustering of quasars and their dark environment

We use semi-analytic modelling on top of the Millennium simulation to study the joint formation of galaxies and their embedded supermassive black holes. Our goal is to test scenarios in which black hole accretion and quasar activity are triggered by galaxy mergers, and to constrain different models for the light curves associated with individual quasar events. In the present work, we focus on studying the spatial distribution of simulated quasars. At all luminosities, we find that the simulated quasar two-point correlation function is fit well by a single power law in the range  0.5 ≲ r ≲ 20  h ⁻¹ Mpc  , but its normalization is a strong function of redshift. When we select only quasars with luminosities within the range typically accessible by today's quasar surveys, their clustering strength depends only weakly on luminosity, in agreement with observations. This holds independently of the assumed light-curve model, since bright quasars are black holes accreting close to the Eddington limit, and are hosted by dark matter haloes with a narrow mass range of a few  10¹²  h ⁻¹ M_⊙  . Therefore, the clustering of bright quasars cannot be used to disentangle light-curve models, but such a discrimination would become possible if the observational samples can be pushed to significantly fainter limits. Overall, our clustering results for the simulated quasar population agree rather well with observations, lending support to the conjecture that galaxy mergers could be the main physical process responsible for triggering black hole accretion and quasar activity.     

Value of perfect ENSO phase predictions for agriculture: evaluating the impact of land tenure and decision objectives

In many places, predictions of regional climate variability associated with the El Niño–Southern Oscillation phenomenon offer the potential to improve farmers’ decision outcomes, by mitigating the negative impacts of adverse conditions or by taking advantage of favorable conditions. While the notion that climate forecasts are potentially valuable has been established, questions of when they may be more or less valuable have proven harder to resolve. Using simulations, we estimate the expected value of seasonal climate information under alternative assumptions about (a) land tenure (ownership vs. short-term leases) and (b) the decision maker’s objective function (expected utility vs. prospect theory value function maximization), employing a full range of plausible parameter values for each objective function. This allows us to show the extent to which the value of information depends on risk preferences, loss aversion, wealth levels and expectations, as well as situational constraints. Our results demonstrate in a non-laboratory decision context that, in some cases, psychologically plausible deviations from expected utility maximization can lead to substantial differences in estimates of the expected value of climate forecasts. Efforts to foster effective use of climate information and forecasts in agriculture must be grounded in a firm understanding of the goals, objectives and constraints of decision makers.