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Inexact Newton methods and the method of lines for solving Richards' equation in two space dimensions

Richards' equation (RE) is often used to model flow in unsaturated porous media. This model captures physical effects, such as sharp fronts in fluid pressures and saturations, which are present in more complex models of multiphase flow. The numerical solution of RE is difficult not only because of these physical effects but also because of the mathematical problems that arise in dealing with the nonlinearities. The method of lines has been shown to be very effective for solving RE in one space dimension. When solving RE in two space dimensions, direct methods for solving the linearized problem for the Newton step are impractical. In this work, we show how the method of lines and Newton-iterative methods, which solve linear equations with iterative methods, can be applied to RE in two space dimensions. We present theoretical results on convergence and use that theory to design an adaptive method for computation of the linear tolerance. Numerical results show the method to be effective and robust compared with an existing approach.     

Interstellar holography

The dynamic spectrum of a radio pulsar is an in-line digital hologram of the ionized interstellar medium. It has previously been demonstrated that such holograms permit image reconstruction, in the sense that one can determine an approximation to the complex electric field values as a function of Doppler shift and delay, but to date the quality of the reconstructions has been poor. Here we report a substantial improvement in the method which we have achieved by simultaneous optimization of the thousands of coefficients that describe the electric field. For our test spectrum of PSR B0834+06 we find that the model provides an accurate representation of the data over the full 63 dB dynamic range of the observations: residual differences between model and data are noise like. The advent of interstellar holography enables detailed quantitative investigation of the interstellar radio-wave propagation paths for a given pulsar at each epoch of observation. We illustrate this using our test data which show the scattering material to be structured and highly anisotropic. The temporal response of the medium exhibits a scattering tail which extends to beyond  100 μs  , and the centroid of the pulse at this frequency and this epoch of observation is delayed by approximately  15 μs  as a result of multipath propagation in the interstellar medium.     

What happens after climate change adaptation projects end: A community-based approach to ex-post assessment of adaptation projects

Over the last decade, hundreds of climate change adaptation projects have been funded and implemented. Despite the importance of these first-generation adaptation projects for establishing funders and implementors’ “best practices,” very little is known about how early adaptation projects have endured, to what ends, and for whom. In this article, I propose a community-based methodology for ex-post assessment of climate change adaptation projects. This methodology contributes to recognitional justice by asking the individuals and collectives tasked with sustaining adaptation initiatives to define adaptation success and what criteria for success should be assessed. I apply this subjective assessment approach in 10 communities across Ecuador that participated in an internationally funded adaptation project that concluded in 2015. My analysis draws together participatory mapping, walking interviews with local leaders, participant observation, and surveys with former project participants. The results highlight that even adaptation projects that were deemed highly successful at their closure have uncertain futures. I find that the sustainability mechanisms that were envisioned by project implementors have not functioned, and communities are shouldering the burden of reviving failing adaptation interventions. These findings highlight that the current model of episodic funding for climate change adaptation projects and evaluation processes needs to be revisited to acknowledge the long-term challenges faced by communities. This analysis also calls attention to the importance of ex-post assessment for adaptation projects and the potential of subjective assessment approaches for building more ontological and epistemological pluralism in understandings of successful climate change adaptation.