Contingent derivatives and regularization for noncoercive inverse problems

We study the inverse problem of parameter identification in non-coercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map by using the first-order and the second-order contingent derivatives. We explore the inverse problem by using the output least-squares and the modified output least-squares objectives. By regularizing the non-coercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

The relationship between psychosocial factors and student success in athletic training students

Many athletic training (AT) programs are not meeting accreditation standards that involve measures of student success, causing programs to lose their accreditation and showing students that their program may not adequately prepare them for a successful career. Studies have shown that psychosocial factors, including psychological needs (autonomy, competence, and relatedness), and motivational factors such as self-efficacy, types of motivation, and identity may increase measures of student success, including persistence and academic performance. The purpose of this quantitative, cross-sectional study was to examine the relationships between psychological needs (autonomy, competence, and relatedness), self-efficacy, types of motivation (controlled and autonomous), identity (academic and athletic trainer), and measures of student success (persistence, intentions to leave, perceived academic performance, and grade point average) in AT students. Participants included 167 National Athletic Trainers' Association members who held a non-certified student membership for the 2020 calendar year, who completed self-reported scales through Qualtrics in fall 2020. Preliminary analyses included exploratory factor and reliability analyses. The main analyses for the iii iii study estimated a path model in which student success was specified to be predicted by psychological needs directly and indirectly through measures of motivation (self-efficacy, types of motivation, and identity). Results showed that competence was one of the most significant predictors of measures of student success, directly and indirectly predicting all measures of student success. Indirectly, competence predicted measures of student success through autonomous motivation and identity (academic and athletic trainer). Results also showed that types of motivation (controlled and autonomous) and identity (academic and athletic trainer) were direct predictors of student success as well. Additionally, autonomy was a significant direct predictor of persistence and predicted intentions to leave indirectly through controlled motivation. AT students should be provided opportunities to practice their AT skills and knowledge and make choices regarding patient care in real-life situations. Additionally, AT students should be provided opportunities to make choices regarding their learning environment, deciding how they research and study material outside of class, using time in class to practice AT skills and knowledge. Through these opportunities, increased competence, autonomy, autonomous motivation, and academic identity may positively influence measures of student success

Chemical availability of fallout radionuclides in cryoconite

Atmospheric deposition on glaciers is a major source of legacy fallout radionuclides (FRNs) accumulating in cryoconite, a dark granular material with surface properties that efficiently bind FRN contaminants (specifically 137Cs; 210Pb; 241Am). Cryoconite-bound FRNs in glaciers can be released when they interact with and are transported by glacial meltwater, resulting in the discharge of amassed particulate contaminants into aquatic and terrestrial environments downstream. The environmental consequences of FRN release from the cryosphere are poorly understood, including impacts of cryoconite-sourced FRNs for alpine food chains. Consequently, there is limited understanding of potential health risks to humans and animals associated with the consumption of radiologically-contaminated meltwater. To assess the chemical availability of cryoconite-adsorbed FRNs we used a three-stage sequential chemical extraction method, applied to cryoconite samples from glaciers in Sweden and Iceland, with original FRN activity concentrations up to 3300 Bq kg−1 for 137Cs, 10,950 Bq kg−1 for unsupported 210Pb (210Pbun) and 24.1 Bq kg−1 for 241Am, and orders of magnitude above regional backgrounds. Our results demonstrate that FRNs attached to cryoconite are solubilized to different degrees, resulting in a stage-wise release of 210Pbun involving significant stepwise solubilization, while 137Cs and 241Am tend to be retained more in the particulate phase. This work provides an insight into the vulnerability of pristine glacial environments to the mobilization of FRN-contaminated particles released during glacier melting, and their potential impact on glacial-dependent ecology

Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case

International audienceIn this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical La-grange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations. 1. Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Latt es and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial ill-posed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary

A feeding inhibition based prediction of the toxic effect of dissolved metal mixtures upon Echinogammarus marinus (Crustacea: Amphipoda) at field relevant concentrations across a latitudinal gradient

Risk assessment of metals in the environment is performed mainly with toxicity evaluations on single metals, which is largely inadequate since these substances occur in mixtures. The development of models predicting combined toxic effects on the basis of the concentration-response relationships of individual compounds has emerged as an answer. In the present study, metal effects on post-exposure anorexia (the concept of FdC(50)-concentration causing 50% of feeding inhibition-is implemented) in Echinogammarus marinus, a widely distributed gammarid amphipod, were assessed and compared with modelled ones obtained through the application of the concentration addition (CA) model, which represents a reasonable worst-case scenario for the risk assessment of metal mixtures. Data were validated using in situ experiments performed along a latitudinal gradient (Iceland, Scotland and Portugal) aiming at establishing a geographic profile of autochthonous population susceptibilities to metals. For all of the metals studied concentrations in the water column at exposure sites were in good agreement with feeding inhibition levels. Models gave low to relatively high percentage agreement between predictions and experimental data. Boreal populations demonstrated higher susceptibility to single metals, but not to mixture exposures. Meridional populations denoted lower susceptibilities with higher FdC(50).FCTSFRH/BPD/26689/2006SMC - IHP/ARIEC - Marie Curie Actions -EC-IH

Does Non-Moral Ignorance Exculpate? Situational Awareness and Attributions of Blame and Forgiveness

In this paper, we set out to test empirically an idea that many philosophers find intuitive, namely that non-moral ignorance can exculpate. Many philosophers find it intuitive that moral agents are responsible only if they know the particular facts surrounding their action. Our results show that whether moral agents are aware of the facts surrounding their action does have an effect on people’s attributions of blame, regardless of the consequences or side effects of the agent’s actions. In general, it was more likely that a situationally aware agent will be blamed for failing to perform the obligatory action than a situationally unaware agent. We also tested attributions of forgiveness in addition to attributions of blame. In general, it was less likely that a situationally aware agent will be forgiven for failing to perform the obligatory action than a situationally unaware agent. When the agent is situationally unaware, it is more likely that the agent will be forgiven than blamed. We argue that these results provide some empirical support for the hypothesis that there is something intuitive about the idea that non-moral ignorance can exculpate

Modelling the transfer of supraglacial meltwater to the bed of Leverett Glacier, Southwest Greenland

This is the final version of the article. Available from EGU via the DOI in this record.Meltwater delivered to the bed of the Greenland Ice Sheet is a driver of variable ice-motion through changes in effective pressure and enhanced basal lubrication. Ice surface velocities have been shown to respond rapidly both to meltwater production at the surface and to drainage of supraglacial lakes, suggesting efficient transfer of meltwater from the supraglacial to subglacial hydrological systems. Although considerable effort is currently being directed towards improved modelling of the controlling surface and basal processes, modelling the temporal and spatial evolution of the transfer of melt to the bed has received less attention. Here we present the results of spatially distributed modelling for prediction of moulins and lake drainages on the Leverett Glacier in Southwest Greenland. The model is run for the 2009 and 2010 ablation seasons, and for future increased melt scenarios. The temporal pattern of modelled lake drainages are qualitatively comparable with those documented from analyses of repeat satellite imagery. The modelled timings and locations of delivery of meltwater to the bed also match well with observed temporal and spatial patterns of ice surface speed-ups. This is particularly true for the lower catchment ( < 1000 m a.s.l.) where both the model and observations indicate that the development of moulins is the main mechanism for the transfer of surface meltwater to the bed. At higher elevations (e.g. 1250-1500 m a.s.l.) the development and drainage of supraglacial lakes becomes increasingly important. At these higher elevations, the delay between modelled melt generation and subsequent delivery of melt to the bed matches the observ ed delay between the peak air temperatures and subsequent velocity speed-ups, while the instantaneous transfer of melt to the bed in a control simulation does not. Although both moulins and lake drainages are predicted to increase in number for future warmer climate scenarios, the lake drainages play an increasingly important role in both expanding the area over which melt accesses the bed and in enabling a greater proportion of surface melt to reach the bed.We acknowledge the College of Physical Sciences, University of Aberdeen, the Leverhulme Trust through a Study Abroad Studentship and the Swedish Radiation Safety Authority, for funding awarded to C. Clason. Data collection was supported by the UK Natural Environment Research Council (through a studentship to I. Bartholomew and grants to P. Nienow and D. Mair) and the Edinburgh University Moss Centenary Scholarship (I. Bartholomew)

ITERATED QUASI-REVERSIBILITY METHOD APPLIED TO ELLIPTIC AND PARABOLIC DATA COMPLETION PROBLEMS

International audienceWe study the iterated quasi-reversibility method to regularize ill-posed elliptic and parabolic problems: data completion problems for Poisson's and heat equations. We define an abstract setting to treat both equations at once. We demonstrate the convergence of the regularized solution to the exact one, and propose a strategy to deal with noise on the data. We present numerical experiments for both problems: a two-dimensional corrosion detection problem and the one-dimensional heat equation with lateral data. In both cases, the method prove to be efficient even with highly corrupted data