Two-body motion in the post-Newtonian approximation

The motion of two massive particles is considered within the framework of the first post-Newtonian approximation. The system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables. Closed-form solutions for the Delaunay elements in the phase space are obtained. The bridge between the phase space and the state space of the Lagrangian of the motion is provided by a velocity-dependent Legendre transformation. By explicit inversion of this transformation, expressions for the Keplerian elements in the state space are obtained from the Delaunay element solutions.     

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A friction damped base isolation system with fail-safe characteristics

An experimental study of a Coulomb friction damped aseismic base isolation system with fail-safe characteristics is described in this paper. The base isolation system utilized commercially made natural rubber bearings and a skid system which comes into operation at preset-levels of relative horizontal displacement between the structure and the foundation. The fail-safe skid provides hysteretic damping and prevents failure of the isolation system in the event of displacements larger than those assumed in the original design. The isolation system can be designed for an earthquake which can be reasonably expected within the lifetime of the structure; in the event of an earthquake of unanticipated intensity the failsafe system will prevent collapse of the structure. The testing of the system involved an 80,000lb model, approximately 1/3 scale to a real structure mounted on the 20′ × 20′ shaking table at EERC and subject to a variety of earthquake inputs. The results show that the hysteretic effect of the fail-safe system does not greatly increase the accelerations experienced by the structure but considerably reduces the relative displacements at the isolation bearings. The action of the fail-safe system was tested by using an earthquake input that produced a resonant response in the isolated mode of the model. The stability limit of the isolation system was exceeded and the bearings failed but complete failure of the isolation system and thus collapse of the model was prevented by the fail-safe system. The implementation of the system in full scale structures poses no technical or construction problems. An equivalent linearization technique was developed for this system for design purposes using response spectra. The accuracy of this approach was verified by comparison with the experimental results.     

Training Images from Process-Imitating Methods

The lack of a suitable training image is one of the main limitations of the application of multiple-point statistics (MPS) for the characterization of heterogeneity in real case studies. Process-imitating facies modeling techniques can potentially provide training images. However, the parameterization of these process-imitating techniques is not straightforward. Moreover, reproducing the resulting heterogeneous patterns with standard MPS can be challenging. Here the statistical properties of the paleoclimatic data set are used to select the best parameter sets for the process-imitating methods. The data set is composed of 278 lithological logs drilled in the lower Namoi catchment, New South Wales, Australia. A good understanding of the hydrogeological connectivity of this aquifer is needed to tackle groundwater management issues. The spatial variability of the facies within the lithological logs and calculated models is measured using fractal dimension, transition probability, and vertical facies proportion. To accommodate the vertical proportions trend of the data set, four different training images are simulated. The grain size is simulated alongside the lithological codes and used as an auxiliary variable in the direct sampling implementation of MPS. In this way, one can obtain conditional MPS simulations that preserve the quality and the realism of the training images simulated with the process-imitating method. The main outcome of this study is the possibility of obtaining MPS simulations that respect the statistical properties observed in the real data set and honor the observed conditioning data, while preserving the complex heterogeneity generated by the process-imitating method. In addition, it is demonstrated that an equilibrium of good fit among all the statistical properties of the data set should be considered when selecting a suitable set of parameters for the process-imitating simulations.     

Variable Grid Method: An Intuitive Approach for Simultaneously Quantifying and Visualizing Spatial Data and Uncertainty

Efforts to develop applications and methods that effectively quantify and communicate uncertainty associated with spatial data remains a focus within many scientific communities. However, the inherent complexity of uncertainty makes it difficult to define, characterize, and represent. Frequently, the products of spatial and spatio‐temporal data are presented without a clear explanation of the inherent uncertainty underlying the data. As uses and applications for spatial data and their products continues to increase, so does the importance for utilizing reliable approaches to effectively communicate spatial data along with their inherent uncertainties. To address this need, the Variable Grid Method (VGM) was developed as an intuitive approach that simultaneously communicates both spatial patterns and trends and the uncertainty associated with data or their analyses. This article details the VGM approach and demonstrates the utility of the VGM to provide critical information about the relationship between uncertainty and spatial data, necessary to support the increasing utilization of spatial information for a wide range of research and other needs.     

A crustal seismic velocity model for the UK, Ireland and surrounding seas

A regional model of the 3-D variation in seismic P -wave velocity structure in the crust of NW Europe has been compiled from wide-angle reflection/refraction profiles. Along each 2-D profile a velocity–depth function has been digitised at 5 km intervals. These 1-D velocity functions were mapped into three dimensions using ordinary kriging with weights determined to minimise the difference between digitised and interpolated values. An analysis of variograms of the digitised data suggested a radial isotropic weighting scheme was most appropriate. Horizontal dimensions of the model cells are optimised at 40 × 40 km and the vertical dimension at 1 km. The resulting model provides a higher resolution image of the 3-D variation in seismic velocity structure of the UK, Ireland and surrounding areas than existing models. The construction of the model through kriging allows the uncertainty in the velocity structure to be assessed. This uncertainty indicates the high density of data required to confidently interpolate the crustal velocity structure, and shows that for this region the velocity is poorly constrained for large areas away from the input data.     

Fiscal geographies: “Placing” taxation in urban geography

As the state’s primary means of both redistributing wealth and incentivizing private investment, tax plays an outsized role in a range of critical urban processes, including (re)development, gentrification, financialization, and local and regional governance. We argue, through reference to existing literature in urban and economic geography, as well as our own research on taxation and the state, that urban scholarship could benefit by close and careful engagement with taxation and the tax system. We term this new vein of research “fiscal geographies” and see it as offering potential for more nuanced study of urban political economy, politics, and processes.     

Utilization of a multicriteria least cost path model in an aquatic environment

A critical component of maintaining biodiversity in fragmented habitats is maintaining connectivity among the usable fragments. Least cost path (LCP) analysis is a tool that can be used for predicting the ability of an organism to move from one habitat patch to another, based on geographical features of the landscape and life history traits of the organism. While this analysis has been utilized for terrestrial habitats, it is rarely applied to aquatic environments. Aquatic hypoxic conditions occur when dissolved oxygen falls below 2 mg/L. These conditions can create barriers in the water column that can either force fish to leave a habitat, or avoid that habitat altogether. Using the lower St. Johns River (LSJR) estuary in Florida, USA, as a study system, the ability of an adult silver perch, Bairdiella chrysoura, to escape a large-scale hypoxic event was modeled using a multicriteria LCP approach. Criteria-specific cost grids were constructed based upon current speed, risk of predation, and whether oxygen levels in the habitat area were normoxic (>5.5 mg/L), or hypoxic (<2.0–1.5 mg/L) as a function of water depth for the LSJR. The criteria cost grids were combined using relative weighting to produce the multicriteria cost grid used to implement the LCP analysis. Three origin and destination point locations within the LSJR study area were selected for modeling whether or not a silver perch would be able to escape a hypoxic zone. Since the LCP model will always determine a LCP from the specified origin point location, ecologically relevant swimming capacities for silver perch under normoxic and hypoxic conditions were then applied to assess the model, and to determine whether the fish would be able to reach areas unimpacted by hypoxia. The LCP model and the swimming capacity results for this study predict that under normoxic conditions, fish movement was unimpeded. During the rapidly developing hypoxic event that was modeled, the results from the LCP model indicate that the fish could move outside the hypoxic zone, but when swimming capacities were applied to the model, the silver perch could not escape. Ecologically, the results of this study suggest that silver perch would experience high mortality under a rapidly developing hypoxic event. Additionally, the results of this study indicate that a LCP model can be applied to an aquatic habitat, as long as the cost grids incorporate relevant abiotic and biotic factors.     

Contrasting rainfall generated debris flows from adjacent watersheds at Forest Falls, southern California, USA

Debris flows are widespread and common in many steeply sloping areas of southern California. The San Bernardino Mountains community of Forest Falls is probably subject to the most frequently documented debris flows in southern California. Debris flows at Forest Falls are generated during short-duration high-intensity rains that mobilize surface material. Except for debris flows on two consecutive days in November 1965, all the documented historic debris flows have occurred during high-intensity summer rainfall, locally referred to as ‘monsoon’ or ‘cloudburst’ rains. Velocities of the moving debris range from about 5 km/h to about 90 km/h. Velocity of a moving flow appears to be essentially a function of the water content of the flow. Low velocity debris flows are characterized by steep snouts that, when stopped, have only small amounts of water draining from the flow. In marked contrast are high-velocity debris flows whose deposits more resemble fluvial deposits. In the Forest Falls area two adjacent drainage basins, Snow Creek and Rattlesnake Creek, have considerably different histories of debris flows. Snow Creek basin, with an area about three times as large as Rattlesnake Creek basin, has a well developed debris flow channel with broad levees. Most of the debris flows in Snow Creek have greater water content and attain higher velocities than those of Rattlesnake Creek. Most debris flows are in relative equilibrium with the geometry of the channel morphology. Exceptionally high-velocity flows, however, overshoot the channel walls at particularly tight channel curves. After overshooting the channel, the flows degrade the adjacent levee surface and remove trees and structures in the immediate path, before spreading out with decreasing velocity. As the velocity decreases the clasts in the debris flows pulverize the up-slope side of the trees and often imbed clasts in them. Debris flows in Rattlesnake Creek are relatively slow moving and commonly stop in the channel. After the channel is blocked, subsequent debris flows cut a new channel upstream from the blockage that results in the deposition of new debris-flow deposits on the lower part of the fan. Shifting the location of debris flows on the Rattlesnake Creek fan tends to prevent trees from becoming mature. Dense growths of conifer seedlings sprout in the spring on the late summer debris flow deposits. This repeated process results in stands of even-aged trees whose age records the age of the debris flows.