119 research outputs found

    Three real-space discretization techniques in electronic structure calculations

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    A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.Comment: 39 pages, 10 figures, accepted to a special issue of "physica status solidi (b) - basic solid state physics" devoted to the CECAM workshop "State of the art developments and perspectives of real-space electronic structure techniques in condensed matter and molecular physics". v2: Minor stylistic and typographical changes, partly inspired by referee comment

    Toward improved prediction of the bedrock depth underneath hillslopes: Bayesian inference of the bottom‐up control hypothesis using high‐resolution topographic data

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    The depth to bedrock controls a myriad of processes by influencing subsurface flow paths, erosion rates, soil moisture, and water uptake by plant roots. As hillslope interiors are very difficult and costly to illuminate and access, the topography of the bedrock surface is largely unknown. This essay is concerned with the prediction of spatial patterns in the depth to bedrock (DTB) using high‐resolution topographic data, numerical modeling, and Bayesian analysis. Our DTB model builds on the bottom‐up control on fresh‐bedrock topography hypothesis of Rempe and Dietrich (2014) and includes a mass movement and bedrock‐valley morphology term to extent the usefulness and general applicability of the model. We reconcile the DTB model with field observations using Bayesian analysis with the DREAM algorithm. We investigate explicitly the benefits of using spatially distributed parameter values to account implicitly, and in a relatively simple way, for rock mass heterogeneities that are very difficult, if not impossible, to characterize adequately in the field. We illustrate our method using an artificial data set of bedrock depth observations and then evaluate our DTB model with real‐world data collected at the Papagaio river basin in Rio de Janeiro, Brazil. Our results demonstrate that the DTB model predicts accurately the observed bedrock depth data. The posterior mean DTB simulation is shown to be in good agreement with the measured data. The posterior prediction uncertainty of the DTB model can be propagated forward through hydromechanical models to derive probabilistic estimates of factors of safety.Key Points:We introduce an analytic formulation for the spatial distribution of the bedrock depthBayesian analysis reconciles our model with field data and quantifies prediction and parameter uncertaintyThe use of a distributed parameterization recognizes geologic heterogeneitiesPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137555/1/wrcr22005.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137555/2/wrcr22005_am.pd

    Systematic Fragmentation Method and the Effective Fragment Potential: An Efficient Method for Capturing Molecular Energies

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