Numerical controllability of the wave equation through primal methods and Carleman estimates

This paper deals with the numerical computation of boundary null controls for the 1D wave equation with a potential. The goal is to compute an approximation of controls that drive the solution from a prescribed initial state to zero at a large enough controllability time. We do not use in this work duality arguments but explore instead a direct approach in the framework of global Carleman estimates. More precisely, we consider the control that minimizes over the class of admissible null controls a functional involving weighted integrals of the state and of the control. The optimality conditions show that both the optimal control and the associated state are expressed in terms of a new variable, the solution of a fourth-order elliptic problem defined in the space-time domain. We first prove that, for some specific weights determined by the global Carleman inequalities for the wave equation, this problem is well-posed. Then, in the framework of the finite element method, we introduce a family of finite-dimensional approximate control problems and we prove a strong convergence result. Numerical experiments confirm the analysis. We complete our study with several comments

Numerical null controllability of the 1D heat equation: primal methods

This paper deals with the numerical computation of distributed null controls for the 1D heat equation, with Dirichlet boundary conditions. The goal is to compute a control that drives (a numerical approximation of) the solution from a prescribed initial state at t = 0 to zero at t = T. Using ideas from Fursikov and Imanuvilov [18], we consider the control that minimizes over the class of admissible null controls a functional that involves weighted integrals of the state and the control, with weights that blow up near T. The optimality system is equivalent to a di erential problem that is fourth-order in space and second-order in time. We rst address the numerical solution of the corresponding variational formulation by introducing a space-time nite element that is C1 in space and C0 in time. We prove a strong convergence result for the approximate controls and then we present some numerical experiments. IWe also introduce a mixed variational formulation and we prove well-posedness through a suitable inf-sup condition. We introduce a (non-conformal) C0 nite element approximation and we provide new numerical results. In both cases, thanks to an appropriate change of variable, we observe a polynomial dependance of the condition number with respect to the discretization parameter. Furthermore, with this second method, the initial and nal conditions are satis ed exactly

Numerical null controllability of the 1D heat equation: Carleman weights an duality

This paper deals with the numerical computation of distributed null controls for the 1D heat equation. The goal is to compute a control that drives (a numerical approximation of) the solution from a prescribed initial state at t = 0 exactly to zero at t = T. We extend the earlier contribution of Carthel, Glowinski and Lions [5], which is devoted to the computation of minimal L2-norm controls. We start from some constrained extremal problems introduced by Fursikov and Imanuvilov [15]) and we apply appropriate duality techniques. Then, we introduce numerical approximations of the associated dual problems and we apply conjugate gradient algorithms. Finally, we present several experiments, we highlight the in uence of the weights and we analyze this approach in terms of robustness and e fficiency

Simulation numérique de la propagation d'une source laser incohérente dans une fibre optique

International audienceLe présent travail concerne les lasers à fibre impulsionnels de puissance de type MOPFA (oscillateur laser maître suivi d'un amplificateur à fibre). Un travail expérimental a permis d'établir que les non-linéarités observées (effet Kerr, mélange à quatre ondes, effet Raman) pouvaient être de nature très différentes selon les caractéristiques de la source issue du laser maître sans toutefois permettre de déterminer si la statistique des photons est seule responsable des différents scénarios non-linéaires observés. Nous avons développé un code de simulation numérique afin de pouvoir valider l'hypothèse selon laquelle les propriétés du laser maître en termes de cohérence jouent un rôle prépondérant dans la manifestation des non-linéarités

Inference of geostatistical hyperparameters with the correlated pseudo-marginal method

We consider non-linear Bayesian inversion problems targeting the geostatistical hyperparameters of a random field describing hydrogeological or geophysical properties given hydrogeological or geophysical data. This problem is of particular importance in the non-ergodic setting as there are no analytical upscaling relationships linking the data to the hyperparameters, such as, mean, standard deviation, and integral scales. Full inversion of the hyperparameters and the local properties of the field (typically involving many thousands of unknowns) brings substantial computational challenges, such that simplifying model assumptions (e.g., homogeneity or ergodicity) are typically made. To prevent the errors resulting from such simplified assumptions while also circumventing the burden of high-dimensional full inversions, we use a pseudo-marginal Metropolis–Hastings algorithm that treats the random field as latent variables. In this random effects model, the intractable likelihood of observing the data given the hyperparameters is estimated by Monte Carlo averaging over realizations of the random field. To increase the efficiency of the method, low-variance approximations of the likelihood ratio are obtained by using importance sampling and by correlating the samples used in the proposed and current steps of the Markov chain. We assess the performance of this correlated pseudo-marginal method by considering two representative inversion problems involving diffusion-based and wave-based physics, respectively, in which we infer the hyperparameters of (1) hydraulic conductivity fields using apparent hydraulic conductivity data in a data-poor setting and (2) fracture aperture fields using borehole ground-penetrating radar (GPR) reflection data in a more data-rich setting. For the first test case, we find that the correlated pseudo-marginal method generates similar estimates of the geostatistical mean as classical rejection sampling, while an inversion assuming ergodicity provides biased estimates. For the second test case, we find that the correlated pseudo-marginal method estimates the hyperparameters well, while rejection sampling is computationally unfeasible and a simplified model assuming homogeneity leads to biased estimates

Calcium carbonate-calcium phosphate mixed cement compositions for bone reconstruction

The feasibility of making calcium carbonate-calcium phosphate (CaCO3-CaP) mixed cements, comprising at least 40 % (w/w) CaCO3 in the dry powder ingredients, has been demonstrated. Several original cement compositions were obtained by mixing metastable crystalline calcium carbonate phases with metastable amorphous or crystalline calcium phosphate powders in aqueous medium. The cements set within at most 1 hour at 37°C in atmosphere saturated with water. The hardened cement is microporous and exhibits weak compressive strength. The setting reaction appeared to be essentially related to the formation of a highly carbonated nanocrystalline apatite phase by reaction of the mestastable CaP phase with part or almost all of the metastable CaCO3 phase. The recrystallization of metastable CaP varieties led to a final cement consisting of a highly carbonated poorly crystalline apatite (PCA) analogous to bone mineral associated with various amounts of vaterite and/or aragonite. The presence of controlled amounts of CaCO3 with a higher solubility than the apatite formed in the well-developed calcium phosphate cements might be of interest to increase resorption rates in biomedical cement and favor its replacement by bone tissue. Cytotoxicity testing revealed excellent cytocompatibility of CaCO3-CaP mixed cement compositions

Preparation, physical-chemical characterisation and cytocompatibility of calcium carbonate cements

The feasibility of calcium carbonate cements involving the recrystallisation of metastable calcium carbonate varieties has been demonstrated. Calcium carbonate cement compositions presented in this paper can be prepared straightforwardly by simply mixing water (liquid phase) with two calcium carbonate phases (solid phase) which can be easily obtained by precipitation. An original cement composition was obtained by mixing amorphous calcium carbonate and vaterite with an aqueous medium. The cement set and hardened within 2 hours at 37°C in an atmosphere saturated with water and the final composition of the cement consisted mostly of aragonite. The hardened cement was microporous and showed poor mechanical properties. Cytotoxicity tests revealed excellent cytocompatibility of calcium carbonate cement compositions. Calcium carbonates with a higher solubility than the marketed calcium phosphate cements might be of interest to increase biomedical cement resorption rates and to favour its replacement by bone tissue

Remote training as a common tool for the different professionals involved in the acute phase after terror attacks across Europe:Perspectives from an expert panel

The acute response after a terror attack may have a crucial impact on the physical and psychological wellbeing of the victims. Preparedness of the professionals involved in the acute response is a key element to ensure effective interventions, and can be improved through trainings. Today in Europe there is a recognized lack of inter-professional and international trainings, which are important, among others, to respond to the needs and the rights of victims affected by a terrorist attack in another country than their home country. In this paper we report the perspectives of an expert panel composed by different categories of professionals on the possible role of interprofessional trainings provided remotely. The experts discussed the pertinence of remote trainings for professionals involved in the acute response of a terror attack, and highlighted their Strengths, Weaknesses, Opportunities and Threats (SWOT analysis). We concluded that, while remote trainings cannot replace in-person trainings, they may be useful to share knowledge about the role and the organization of the different categories of professionals, thus potentially improving response coordination, and to easily share good practices across professionals and countries

The history, systematics, and nomenclature of Thalattosuchia (Archosauria: Crocodylomorpha)

The use of more than one nomenclatural code is becoming increasingly common in some biological sub-disciplines. To minimize nomenclatural instability, we have decided to establish a higher level systematization for Thalattosuchia under both the International Code of Phylogenetic Nomenclature (‘PhyloCode’) and the International Code of Zoological Nomenclature (‘Zoological Code’). We undertook a series of phylogenetic analyses with an expanded dataset to examine the origins of Thalattosuchia within Crocodylomorpha, and determined the clade’s diagnostic characters. Based on these analyses, we provide updated diagnoses for Thalattosuchia and its subclades under both the PhyloCode and Zoological Code. We also introduce two new nomina that are regulated under the PhyloCode (Neothalattosuchia and Euthalattosuchia), and the nomen Dakosaurina, which is registered under both nomenclatural codes. Moreover, we introduce PhyloCode-compliant phylogenetic definitions for Thalattosuchia and its subclades. As we cannot reliably discriminate between the positional hypotheses for Thalattosuchia within Crocodylomorpha, the clades’ origins are as much of a mystery today as they were over a century ago. However, we hope that using the same diagnostic characters to define the same clades, with the same nomina, under both nomenclatural codes will be an example to others to follow