A finite element data assimilation method for the wave equation

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions are used for the approximation in space and backward differentiation is used in time. Stabilizing terms are added on the discrete level. The design of these terms is driven by numerical stability and the stability of the continuous problem, with the objective of minimizing the computational error. Error estimates are then derived that are optimal with respect to the approximation properties of the numerical scheme and the stability properties of the continuous problem. The effects of discretizing the (smooth) domain boundary and other perturbations in data are included in the analysis

A priori and a posteriori analysis of non-conforming finite elements with face penalty for advection-diffusion equations

We analyse a non-conforming finite-element method to approximate advection-diffusion-reaction equations. The method is stabilized by penalizing the jumps of the solution and those of its advective derivative across mesh interfaces. The a priori error analysis leads to (quasi-)optimal estimates in the mesh size (sub-optimal by order ½ in the L2-norm and optimal in the broken graph norm for quasi-uniform meshes) keeping the Péclet number fixed. Then, we investigate a residual a posteriori error estimator for the method. The estimator is semi-robust in the sense that it yields lower and upper bounds of the error which differ by a factor equal at most to the square root of the Péclet number. Finally, to illustrate the theory we present numerical results including adaptively generated meshe

The effect of exposure to low frequency electromagnetic fields (EMF) as an integral part of the housing system on anxiety-related behaviour, cognition and welfare in two strains of laboratory mouse.

Electromagnetic field (EMF) technology has the potential to improve scientific data capture and welfare assessment by allowing automated data collection from individual cages. How- ever, it is important to determine any impact that a new technology itself may have on animal welfare, and previous studies have found contrasting results of EMF on laboratory rodent anxiety-like behaviour and cognition. We therefore investigated whether there was an effect of low frequency EMF experienced continuously over a six-week period, as an integral part of the animal housing system, on measures of mouse anxiety-related behaviour, cognition and welfare. We housed mice (N = 80) of two strains (BALB/cAnNCrl and C57BL/6NCrl) separately in Individually Ventilated Cages (IVCs) in groups of four, either with the EMF plate turned ‘on’ or ‘off’ (n = 5). Some measures, e.g. food and water utilisation, were col- lected at regular intervals, whereas measures of anxiety-like behaviour (e.g. open field test) and cognitive performance (novel-object recognition test) were collected only at the end of the study. We found expected strong strain differences in most measures, e.g. latency to leave the starting square in an open field test, with C57BL/6NCrl mice moving away sooner, and interactions between strain and time for those measures recorded at more than one time point, e.g. significant weight gain over time for both strains, but with BALB/cAnNCrl mice weighing more. However, we found no significant effects of treatment (EMF ‘on’/‘off’) for any of the measures collected. These results indicate that, for the measures recorded here, there was no measurable impact on the behaviour and welfare of low frequency EMF exposure experienced continuously over a six-week period. Housing systems that include EMF monitoring technology may therefore be suitable for use without influencing either ani- mal welfare or scientific outcomes

Quadratic Poisson brackets compatible with an algebra structure

Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.Comment: 6 page

The "exterior approach" applied to the inverse obstacle problem for the heat equation

International audienceIn this paper we consider the " exterior approach " to solve the inverse obstacle problem for the heat equation. This iterated approach is based on a quasi-reversibility method to compute the solution from the Cauchy data while a simple level set method is used to characterize the obstacle. We present several mixed formulations of quasi-reversibility that enable us to use some classical conforming finite elements. Among these, an iterated formulation that takes the noisy Cauchy data into account in a weak way is selected to serve in some numerical experiments and show the feasibility of our strategy of identification. 1. Introduction. This paper deals with the inverse obstacle problem for the heat equation, which can be described as follows. We consider a bounded domain D ⊂ R d , d ≥ 2, which contains an inclusion O. The temperature in the complementary domain Ω = D \ O satisfies the heat equation while the inclusion is characterized by a zero temperature. The inverse problem consists, from the knowledge of the lateral Cauchy data (that is both the temperature and the heat flux) on a subpart of the boundary ∂D during a certain interval of time (0, T) such that the temperature at time t = 0 is 0 in Ω, to identify the inclusion O. Such kind of inverse problem arises in thermal imaging, as briefly described in the introduction of [9]. The first attempts to solve such kind of problem numerically go back to the late 80's, as illustrated by [1], in which a least square method based on a shape derivative technique is used and numerical applications in 2D are presented. A shape derivative technique is also used in [11] in a 2D case as well, but the least square method is replaced by a Newton type method. Lastly, the shape derivative together with the least square method have recently been used in 3D cases [18]. The main feature of all these contributions is that they rely on the computation of forward problems in the domain Ω × (0, T): this computation obliges the authors to know one of the two lateral Cauchy data (either the temperature or the heat flux) on the whole boundary ∂D of D. In [20], the authors introduce the so-called " enclosure method " , which enables them to recover an approximation of the convex hull of the inclusion without computing any forward problem. Note however that the lateral Cauchy data has to be known on the whole boundary ∂D. The present paper concerns the " exterior approach " , which is an alternative method to solve the inverse obstacle problem. Like in [20], it does not need to compute the solution of the forward problem and in addition, it is applicable even if the lateral Cauchy data are known only on a subpart of ∂D, while no data are given on the complementary part. The " exterior approach " consists in defining a sequence of domains that converges in a certain sense to the inclusion we are looking for. More precisely, the nth step consists, 1. for a given inclusion O n , in approximating the temperature in Ω n × (0, T) (Ω n := D \ O n) with the help of a quasi-reversibility method, 2. for a given temperature in Ω n × (0, T), in computing an updated inclusion O n+1 with the help of a level set method. Such " exterior approach " has already been successfully used to solve inverse obstacle problems for the Laplace equation [5, 4, 15] and for the Stokes system [6]. It has also been used for the heat equation in the 1D case [2]: the problem in this simple case might be considered as a toy problem since the inclusion reduces to a point in some bounded interval. The objective of the present paper is to extend the " exterior approach " for the heat equation to any dimension of space, with numerical applications in the 2D case. Let us shed some light on the two steps o

Guidance Notes for commercial offices: Safe return to work during COVID-19

This report explores multiple strategies and control measures for preventing or limiting the transmission of the SARS-CoV-2 virus in indoor office workplaces. It has been commissioned by Savile Row Projects Ltd to ensure that, in collaboration with its clients and supply chain, its work on the design, installation and operation of office interiors is executed in light of what is known about the disease. The background study on which this report is based focuses on three areas of advice: clinical, behavioural and built environment

Young peoples’ reflections on what teachers think about family obligations that conflict with school: A focus on the non-normative roles of young caring and language brokering

In “Western” contexts school attendance is central for an ‘ideal’ childhood. However, many young people engage with home roles that conflict with school expectations. This paper explores perceptions of that process in relation two home activities - language brokering and young caring. We interviewed 46 young people and asked them to reflect on what the teacher would think when a child had to miss school to help a family member. This paper discusses the young people’s overall need to keep their out-of-school lives private from their teachers

Targeting Net Zero Energy at Marine Corps Base Hawaii, Kaneohe Bay: Preprint

This paper summarizes the results of an NREL assessment of Marine Corps Base Hawaii (MCBH), Kaneohe Bay to appraise the potential of achieving net zero energy status through energy efficiency, renewable energy, and hydrogen vehicle integration. In 2008, the U.S. Department of Defense's U.S. Pacific Command partnered with the U.S. Department of Energy's (DOE's) National Renewable Energy Laboratory (NREL) to assess opportunities for increasing energy security through renewable energy and energy efficiency at Hawaii military installations. DOE selected Marine Corps Base Hawaii (MCBH), Kaneohe Bay, to receive technical support for net zero energy assessment and planning funded through the Hawaii Clean Energy Initiative (HCEI). NREL performed a comprehensive assessment to appraise the potential of MCBH Kaneohe Bay to achieve net zero energy status through energy efficiency, renewable energy, and hydrogen vehicle integration. This paper summarizes the results of the assessment and provides energy recommendations. The analysis shows that MCBH Kaneohe Bay has the potential to make significant progress toward becoming a net zero installation. Wind, solar photovoltaics, solar hot water, and hydrogen production were assessed, as well as energy efficiency technologies. Deploying wind turbines is the most cost-effective energy production measure. If the identified energy projects and savings measures are implemented, the base will achieve a 96% site Btu reduction and a 99% source Btu reduction. Using excess wind and solar energy to produce hydrogen for a fleet and fuel cells could significantly reduce energy use and potentially bring MCBH Kaneohe Bay to net zero. Further analysis with an environmental impact and interconnection study will need to be completed. By achieving net zero status, the base will set an example for other military installations, provide environmental benefits, reduce costs, increase energy security, and exceed its energy goals and mandates

Tests of Lorentz violation in muon antineutrino to electron antineutrino oscillations

A recently developed Standard-Model Extension (SME) formalism for neutrino oscillations that includes Lorentz and CPT violation is used to analyze the sidereal time variation of the neutrino event excess measured by the Liquid Scintillator Neutrino Detector (LSND) experiment. The LSND experiment, performed at Los Alamos National Laboratory, observed an excess, consistent with neutrino oscillations, of ${\bar\nu}_e$ in a beam of ${\bar\nu}_\mu$. It is determined that the LSND oscillation signal is consistent with no sidereal variation. However, there are several combinations of SME coefficients that describe the LSND data; both with and without sidereal variations. The scale of Lorentz and CPT violation extracted from the LSND data is of order $10^{-19}$ GeV for the SME coefficients $a_L$ and $E \times c_L$. This solution for Lorentz and CPT violating neutrino oscillations may be tested by other short baseline neutrino oscillation experiments, such as the MiniBooNE experiment.Comment: 10 pages, 10 figures, 2 tables, uses revtex4 replaced with version to be published in Physical Review D, 11 pages, 11 figures, 2 tables, uses revtex