COLA with massive neutrinos

The effect of massive neutrinos on the growth of cold dark matter perturbations acts as a scale-dependent Newton's constant and leads to scale-dependent growth factors just as we often find in models of gravity beyond General Relativity. We show how to compute growth factors for $\Lambda$CDM and general modified gravity cosmologies combined with massive neutrinos in Lagrangian perturbation theory for use in COLA and extensions thereof. We implement this together with the grid-based massive neutrino method of Brandbyge and Hannestad in $\texttt{MG-PICOLA}$ and compare COLA simulations to full $\it N$-body simulations of $\Lambda$CDM and $f(R)$ gravity with massive neutrinos. Our implementation is computationally cheap if the underlying cosmology already has scale-dependent growth factors and it is shown to be able to produce results that match $\it N$-body to percent level accuracy for both the total and CDM matter power-spectra up to $k\lesssim 1 h/$Mpc.Comment: 29 pages, 15 figures, 1 table, version accepted for publication in JCAP, added frame-lagging terms in 2LPT sections (results unaffected) and appendix on comparison to SP

Mixed finite element methods for linear elasticity with weakly imposed symmetry

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a modified form of the Hellinger--Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.Comment: to appear in Mathematics of Computatio

Investigating the degeneracy between modified gravity and massive neutrinos with redshift-space distortions

There is a well known degeneracy between the enhancement of the growth of large-scale structure produced by modified gravity models and the suppression due to the free-streaming of massive neutrinos at late times. This makes the matter power-spectrum alone a poor probe to distinguish between modified gravity and the concordance $\Lambda$CDM model when neutrino masses are not strongly constrained. In this work, we investigate the potential of using redshift-space distortions (RSD) to break this degeneracy when the modification to gravity is scale-dependent in the form of Hu-Sawicki $f(R)$. We find that if the linear growth rate can be recovered from the RSD signal, the degeneracy can be broken at the level of the dark matter field. However, this requires accurate modelling of the non-linearities in the RSD signal, and we here present an extension of the standard perturbation theory-based model for non-linear RSD that includes both Hu-Sawicki $f(R)$ modified gravity and massive neutrinos.Comment: 24 pages, 12 figures, 1 table; corrected typo in prefactors of the '13'-type 1-loop SPT term

Medical Data Architecture Platform and Recommended Requirements for a Medical Data System for Exploration Missions

The Medical Data Architecture (MDA) project supports the Exploration Medical Capability (ExMC) risk to minimize or reduce the risk of adverse health outcomes and decrements in performance due to in-flight medical capabilities on human exploration missions. To mitigate this risk, the ExMC MDA project addresses the technical limitations identified in ExMC Gap Med 07: We do not have the capability to comprehensively process medically- relevant information to support medical operations during exploration missions. This gap identifies that the current in-flight medical data management includes a combination of data collection and distribution methods that are minimally integrated with on-board medical devices and systems. Furthermore, there are a variety of data sources and methods of data collection. For an exploration mission, the seamless management of such data will enable a more medically autonomous crew than the current paradigm of medical data management on the International Space Station. ExMC has recognized that in order to make informed decisions about a medical data architecture framework, current methods for medical data management must not only be understood, but an architecture must also be identified that provides the crew with actionable insight to medical conditions. This medical data architecture will provide the necessary functionality to address the challenges of executing a self-contained medical system that approaches crew health care delivery without assistance from ground support. Hence, the products derived from the third MDA prototype development will directly inform exploration medical system requirements for Level of Care IV in Gateway missions. In fiscal year 2019, the MDA project developed Test Bed 3, the third iteration in a series of prototypes, that featured integrations with cognition tool data, ultrasound image analytics and core Flight Software (cFS). Maintaining a layered architecture design, the framework implemented a plug-in, modular approach in the integration of these external data sources. An early version of MDA Test Bed 3 software was deployed and operated in a simulated analog environment that was part of the Next Space Technologies for Exploration Partnerships (NextSTEP) Gateway tests of multiple habitat prototypes. In addition, the MDA team participated in the Gateway Test and Verification Demonstration, where the MDA cFS applications was integrated with Gateway-in-a-Box software to send and receive medically relevant data over a simulated vehicle network. This software demonstration was given to ExMC and Gateway Program stakeholders at the NASA Johnson Space Center Integrated Power, Avionics and Software (iPAS) facility. Also, the integrated prototypes served as a vehicle to provide Level 5 requirements for the Crew Health and Performance Habitat Data System for Gateway Missions (Medical Level of Care IV). In the upcoming fiscal year, the MDA project will continue to provide systems engineering and vertical prototypes to refine requirements for medical Level of Care IV and inform requirements for Level of Care V

Finite element exterior calculus: from Hodge theory to numerical stability

This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of partial differential equations that are related to differential complexes so that de Rham cohomology and Hodge theory are key tools for the continuous problem. After a brief introduction to finite element methods, the discretization methods we consider, we develop an abstract Hilbert space framework for analyzing stability and convergence. In this framework, the differential complex is represented by a complex of Hilbert spaces and stability is obtained by transferring Hodge theoretic structures from the continuous level to the discrete. We show stable discretization is achieved if the finite element spaces satisfy two hypotheses: they form a subcomplex and there exists a bounded cochain projection from the full complex to the subcomplex. Next, we consider the most canonical example of the abstract theory, in which the Hilbert complex is the de Rham complex of a domain in Euclidean space. We use the Koszul complex to construct two families of finite element differential forms, show that these can be arranged in subcomplexes of the de Rham complex in numerous ways, and for each construct a bounded cochain projection. The abstract theory therefore applies to give the stability and convergence of finite element approximations of the Hodge Laplacian. Other applications are considered as well, especially to the equations of elasticity. Background material is included to make the presentation self-contained for a variety of readers.Comment: 74 pages, 8 figures; reorganized introductory material, added additional example and references; final version accepted by Bulletin of the AMS, added references to codes and adjusted some diagrams. Bulletin of the American Mathematical Society, to appear 201

Double Giant Dipole Resonance in ^{208}Pb

Double-dipole excitations in ^{208}Pb are analyzed within a microscopic model explicitly treating 2p2h-excitations. Collective states built from such 2p2h-excitations are shown to appear at about twice the energy of the isovector giant dipole resonance, in agreement with the experimental findings. The calculated cross section for Coulomb excitation at relativistic energies cannot explain simultaneously the measured single-dipole and double-dipole cross sections, however.Comment: 7 pages, Latex, 5 postscript figure

The emission consequences of using biodiesel and bio ethanol as a fuel for road transport in Denmark

This article explains the emission consequences of using biodiesel and bio ethanol as a fuel for road transport in Denmark calculated in the REBECa project. For the years 2004, 2010, 2015, 2020, 2025 and 2030, two fossil fuel baseline scenarios (FS) are considered characterised by different traffic growth rates. For each FS, two biofuel scenarios (BS1, BS2) are considered with a 5.75 % biodiesel/bio ethanol share in 2010 as a common starting point. From 2010, linear growths are assumed for BS1 (10 % in 2020) and BS2 (25 % in 2030). The emissions presented in this study are vehicle based; a separate Well to Wheels (W-t-W) assessment of the total emission consequences of producing and using biofuels has been conducted in a different part of REBECa. The maximum CO2 emission difference between FS and BS2 becomes 26 % in 2030. The NOx and VOC emission variations between FS and both biofuel scenarios are 3 % or less. For CO and TSP the largest emission differences, 5 % and -12 %, respectively, occur between the FS and BS2 scenarios in 2030. The biofuel emission impacts are insignificant for NOx,VOC, CO and TSP compared to the generally large emission reductions predicted in all scenarios driven by the gradual strengthened emission standards for new vehicles, by far outweighing the emission influence from biofuels and traffic growth. The emission estimates for NOx, VOC, CO and TSP presented in this study are less certain than for CO2 due to the relatively scarce biofuel emission data implemented in the calculations. As a consequence, the obtained emission results must be assessed with care. Bearing in mind these uncertainties, the calculation approach for emissions from biofuel usage presented in this study can be used as a tool to carry out sensitivity analysis, environmental impact assessment studies, or for research purposes as such