A study on iterative methods for solving Richards` equation

This work concerns linearization methods for efficiently solving the Richards` equation,a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media.The discretization of Richards` equation is based on backward Euler in time and Galerkin finite el-ements in space. The most valuable linearization schemes for Richards` equation, i.e. the Newtonmethod, the Picard method, the Picard/Newton method and theLscheme are presented and theirperformance is comparatively studied. The convergence, the computational time and the conditionnumbers for the underlying linear systems are recorded. The convergence of theLscheme is theo-retically proved and the convergence of the other methods is discussed. A new scheme is proposed,theLscheme/Newton method which is more robust and quadratically convergent. The linearizationmethods are tested on illustrative numerical examples

Fluid-limit Cosmological Simulations Starting from the Big Bang

The cosmic large-scale structure (LSS) provides a unique testing ground for connecting fundamental physics to astronomical observations. Modelling the LSS requires numerical $N$-body simulations or perturbative techniques that both come with distinct shortcomings. Here we present the first unified numerical approach, enabled by new time integration and discreteness reduction schemes, and demonstrate its convergence at the field level. In particular, we show that our simulations (1) can be initialised directly at time zero, and (2) can be made to agree with high-order Lagrangian perturbation theory in the fluid limit. This allows fast, self-consistent, and UV-complete forward modelling of LSS observables.Comment: 5+10 pages, 4+7 figures. Comments are very welcome

Bayesian Simulation-based Inference for Cosmological Initial Conditions

Reconstructing astrophysical and cosmological fields from observations is challenging. It requires accounting for non-linear transformations, mixing of spatial structure, and noise. In contrast, forward simulators that map fields to observations are readily available for many applications. We present a versatile Bayesian field reconstruction algorithm rooted in simulation-based inference and enhanced by autoregressive modeling. The proposed technique is applicable to generic (non-differentiable) forward simulators and allows sampling from the posterior for the underlying field. We show first promising results on a proof-of-concept application: the recovery of cosmological initial conditions from late-time density fields.Comment: Accepted for the NeurIPS 2023 workshop Machine Learning and the Physical Sciences; 5 pages, 1 figur

LOAD CONDITION OF THE WRIST DURING THE FORWARD HANDSPRING, THE FORWARD HANDSPRING WITH ULNAR DEVIATED HAND POSITIONING AND THE BACKWARD HANDSPRING

The aim of this research was to deterime the loading conditions throughout the forward handspring, the forward handspring with ulnar deviated hand positioning and the backward handspring using an inverse dynamics approach based on simultaneously acquired kinetic and kinematic data. 14 gymnasts performed five of each movement. The range of motion (ROM) around the pronation/supination axis in the forward handspring with ulnar deviated hands was significantly higher than in the two other executions. The calculated moment acting on the wrist during backward handsprings exceeded the ones during the forward executions significantly. Due to the knowledge of the loading conditions, long-term damages can be estimated and minimized in such repetitively excessive motions

Harnessing Policy Complementarities to Conserve Energy: Evidence from a Natural Field Experiment

The literature has shown the power of social norms to promote residential energy conservation, particularly among high usage users. This study uses a natural field experiment with nearly 200,000 US households to explore whether a financial rewards program can complement such approaches. We observe strong impacts of the program, particularly amongst low-usage and lowvariance households, customers who typically are less responsive to normative messaging. Our data thus suggest important policy complementarities between behavioral and financial incentives: whereas non-pecuniary interventions disproportionately affect intense users, financial incentives are able to substantially affect the low-user, “sticky households.