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

A review on sparse solutions in optimal control of partial differential equations

In this paper a review of the results on sparse controls for partial differential equations is presented. There are two different approaches to the sparsity study of control problems. One approach consists of taking functions to control the system, putting in the cost functional a convenient term that promotes the sparsity of the optimal control. A second approach deals with controls that are Borel measures and the norm of the measure is involved in the cost functional. The use of measures as controls allows to obtain optimal controls supported on a zero Lebesgue measure set, which is very interesting for practical implementation. If the state equation is linear, then we can carry out a complete analysis of the control problem with measures. However, if the equation is nonlinear the use of measures to control the system is still an open problem, in general, and the use of functions to control the system seems to be more appropriate.This work was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2014-57531-P

Cryoconite: an efficient accumulator of radioactive fallout in glacial environments

Abstract. Cryoconite is rich in natural and artificial radioactivity, but a discussion about its ability to accumulate radionuclides is lacking. A characterization of cryoconite from two Alpine glaciers is presented here. Results confirm that cryoconite is significantly more radioactive than the matrices usually adopted for the environmental monitoring of radioactivity, such as lichens and mosses, with activity concentrations exceeding 10 000 Bq kg−1 for single radionuclides. This makes cryoconite an ideal matrix to investigate the deposition and occurrence of radioactive species in glacial environments. In addition, cryoconite can be used to track environmental radioactivity sources. We have exploited atomic and activity ratios of artificial radionuclides to identify the sources of the anthropogenic radioactivity accumulated in our samples. The signature of cryoconite from different Alpine glaciers is compatible with the stratospheric global fallout and Chernobyl accident products. Differences are found when considering other geographic contexts. A comparison with data from literature shows that Alpine cryoconite is strongly influenced by the Chernobyl fallout, while cryoconite from other regions is more impacted by events such as nuclear test explosions and satellite reentries. To explain the accumulation of radionuclides in cryoconite, the glacial environment as a whole must be considered, and particularly the interaction between ice, meltwater, cryoconite and atmospheric deposition. We hypothesize that the impurities originally preserved into ice and mobilized with meltwater during summer, including radionuclides, are accumulated in cryoconite because of their affinity for organic matter, which is abundant in cryoconite. In relation to these processes, we have explored the possibility of exploiting radioactivity to date cryoconite. </jats:p

Sparse initial data indentification for parabolic pde and its finite element approximations

We address the problem of inverse source identification for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability so that the target is not required to be achieved exactly but only in an approximate sense. We prove an approximate inversion result and derive a characterization of the optimal initial measures by means of duality and the minimization of a suitable quadratic functional on the solutions of the adjoint system. We prove the sparsity of the optimal initial measures showing that they are supported in sets of null Lebesgue measure. As a consequence, approximate controllability can be achieved efficiently by means of controls that are activated in a finite number of pointwise locations. Moreover, we discuss the finite element numerical approximation of the control problem providing a convergence result of the corresponding optimal measures and states as the discretization parameters tend to zero.The first author was supported by Spanish Ministerio de Economía y Competitividad under project MTM2011-22711. The third author was supported by the Advanced Grant NUMERIWAVES/FP7-246775 of the European Research Council Executive Agency, FA9550-14-1-0214 of the EOARD-AFOSR, FA9550-15-1-0027 of AFOSR, the BERC 2014-2017 program of the Basque Government, the MTM2011-29306 and SEV-2013-0323 Grants of the MINECO, the CIMI-Toulouse Excellence Chair in PDEs, Control and Numerics and a Humboldt Award at the University of Erlangen-Nürnberg

Cryoconite as an efficient monitor for the deposition of radioactive fallout in glacial environments

&amp;lt;p&amp;gt;&amp;lt;strong&amp;gt;Abstract.&amp;lt;/strong&amp;gt; Cryoconite is extremely rich in natural and artificial radionuclides, but a comprehensive discussion about its ability to accumulate radioactivity is lacking. A characterization of cryoconite from two Alpine glaciers is presented and discussed. Results confirm that cryoconite is among the most radioactive environmental matrices, with activity concentrations exceeding 10,000&amp;amp;#8201;Bq&amp;amp;#8201;kg&amp;lt;sup&amp;gt;&amp;amp;#8722;1&amp;lt;/sup&amp;gt; for single radionuclides. Atomic and activity ratios of Pu and Cs radioactive isotopes reveal that the artificial radioactivity of Alpine cryoconite is mostly related to the stratospheric fallout from nuclear weapon tests and to the 1986 Chernobyl accidents. The signature of cryoconite radioactivity is thus influenced by both local and more widespread events. The extreme accumulation of radioactivity in cryoconite can be explained only considering the glacial environment as a whole, and particularly the interaction between ice, meltwater, cryoconite and atmospheric deposition. Cryoconite is an ideal monitor to investigate the deposition and occurrence of natural and artificial radioactive species in glacial environment.&amp;lt;/p&amp;gt; </jats:p

Functional Dissection of the Proton Pumping Modules of Mitochondrial Complex I

A catalytically active subcomplex of respiratory chain complex I lacks 14 of its 42 subunits yet retains half of its proton-pumping capacity, indicating that its membrane arm has two pump modules

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

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

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