Optimal shape and location of sensors or actuators in PDE models

We investigate the problem of optimizing the shape and location of sensors and actuators for evolution systems driven by distributed parameter systems or partial differential equations (PDE). We consider wave, Schrödinger and heat equations on an arbitrary domain Ω, in any space dimension, and with suitable boundary conditions (if there is a boundary) which can be of Dirichlet, Neumann, mixed or Robin type. This kind of problem is frequently encountered in applications where one aims, for instance, at maximizing the quality of reconstruction of the solution, using only a partial observation. From the mathematical point of view, using probabilistic considerations we model this problem as that of maximizing the so-called randomized observability constant, over all possible subdomains of Ω having a prescribed measure. The spectral analysis of this problem reveals intimate connections with the theory of quantum chaos. More precisely, we provide a solution to this problem when the domain Ω satisfies suitable quantum ergodicity assumptions

Complexity and regularity of maximal energy domains for the wave equation with fixed initial data

We consider the homogeneous wave equation on a bounded open connected subset Ω of IRn. Some initial data being specified, we consider the problem of determining a measurable subset ω of Ω maximizing the L2-norm of the restriction of the corresponding solution to ω over a time interval [0, T], over all possible subsets of Ω having a certain prescribed measure. We prove that this problem always has at least one solution and that, if the initial data satisfy some analyticity assumptions, then the optimal set is unique and moreover has a finite number of connected components. In contrast, we construct smooth but not analytic initial conditions for which the optimal set is of Cantor type and in particular has an infinite number of connected components

Optimal location of controllers for the one-dimensional wave equation

In this paper, we consider the homogeneous one-dimensional wave equation defined on (0,π). For every subset ωâŠ[0,π] of positive measure, every T≥2π, and all initial data, there exists a unique control of minimal norm in L2(0,T;L2(ω)) steering the system exactly to zero. In this article we consider two optimal design problems. Let L∈(0,1). The first problem is to determine the optimal shape and position of ω in order to minimize the norm of the control for given initial data, over all possible measurable subsets ω of [0,π] of Lebesgue measure Lπ. The second problem is to minimize the norm of the control operator, over all such subsets. Considering a relaxed version of these optimal design problems, we show and characterize the emergence of different phenomena for the first problem depending on the choice of the initial data: existence of optimal sets having a finite or an infinite number of connected components, or nonexistence of an optimal set (relaxation phenomenon). The second problem does not admit any optimal solution except for L=1/2. Moreover, we provide an interpretation of these problems in terms of a classical optimal control problem for an infinite number of controlled ordinary differential equations. This new interpretation permits in turn to study modal approximations of the two problems and leads to new numerical algorithms. Their efficiency will be exhibited by several experiments and simulations

In-situ fines migration and grains redistribution induced by mineral reactions – Implications for clogging during water injection in carbonate aquifers

Water injection into an aquifer is generally motivated by one of three objectives: disposal, managed aquifer recharge (MAR), or aquifer storage and recovery (ASR). Any of these would be undermined if an injection well were to become clogged. This paper investigates whether mineral reactions can cause mobilization of fines and rock grains, and if so, how this would affect clogging. Injection experiments are performed on Edwards Brown (dolomite) and Indiana limestone core samples. X-ray Powder Diffraction analysis of the rocks shows that no clays are present. Filtered-deaired deionized water and pure salts are used to prepare the injection fluids. The core samples are subjected to four sequential injections of fluids: at salinities 44,580 mg/L (referred to as “seawater”), 14,860 mg/L, 7,430 mg/L, and 0 mg/L (deionized water). These salinities are selected to represent disposal, and less saline fluids to represent MAR and ASR projects. Pressure difference is recorded across the core sample at each stage and is used to calculate permeability. The effluent samples are collected to characterize produced fines and elements. The increase in the pH of the effluent samples suggest mineral reactions, which is supported by an increase in the concentration of chemical elements in the effluent samples. Scanning Electron Microscopy (SEM) images show pore enlargement due to dissolution and depict pore blockage due to fines migration, grains redistribution, and mineral precipitation. Mineral reactions dissolved the grain's surface and intergranular cement, releasing silicate fines and rock grains, which in turn reduce the permeability of the rock by 68 % to 99.9 %

A Novel and Efficient Gene Transfer Strategy Reduces Glial Reactivity and Improves Neuronal Survival and Axonal Growth In Vitro

Background: The lack of axonal regeneration in the central nervous system is attributed among other factors to the formation of a glial scar. This cellular structure is mainly composed of reactive astrocytes that overexpress two intermediate filament proteins, the glial fibrillary acidic protein (GFAP) and vimentin. Indeed, in vitro, astrocytes lacking GFAP or both GFAP and vimentin were shown to be the substrate for increased neuronal plasticity. Moreover, double knockout mice lacking both GFAP and vimentin presented lower levels of glial reactivity in vivo, significant axonal regrowth and improved functional recovery in comparison with wild-type mice after spinal cord hemisection. From these results, our objective was to develop a novel therapeutic strategy for axonal regeneration, based on the targeted suppression of astroglial reactivity and scarring by lentiviral-mediated RNA-interference (RNAi). Methods and Findings: In this study, we constructed two lentiviral vectors, Lv-shGFAP and Lv-shVIM, which allow efficient and stable RNAi-mediated silencing of endogenous GFAP or vimentin in vitro. In cultured cortical and spinal reactive astrocytes, the use of these vectors resulted in a specific, stable and highly significant decrease in the corresponding protein levels. In a second model -scratched primary cultured astrocytes- Lv-shGFAP, alone or associated with Lv-shVIM, decreased astrocytic reactivity and glial scarring. Finally, in a heterotopic coculture model, cortical neurons displayed higher survival rates and increased neurite growth when cultured with astrocytes in which GFAP and vimentin had been invalidated by lentiviral-mediated RNAi. Conclusions: Lentiviral-mediated knockdown of GFAP and vimentin in astrocytes show that GFAP is a key target for modulating reactive gliosis and monitoring neuron/glia interactions. Thus, manipulation of reactive astrocytes with the Lv-shGFAP vector constitutes a promising therapeutic strategy for increasing glial permissiveness and permitting axonal regeneration after central nervous system lesions. Copyright: © 2009 Desclaux et al.This work was supported by the Centre National de la Recherche Scientifique (CNRS), the Institut National de la Sante et de la Recherche Medicale (INSERM), the Universite Pierre et Marie Curie - Paris 6 (UPMC), the Universite de Montpellier 2, Verticale, Demain Debout, and the Institut de Recherche sur la Moelle epiniere et l’Encephale (IRME).Peer Reviewe

Anatomical study of serotonergic innervation and 5-HT1A receptor in the human spinal cord

Serotonergic innervation of the spinal cord in mammals has multiple roles in the control of motor, sensory and visceral functions. In rats, functional consequences of spinal cord injury at thoracic level can be improved by a substitutive transplantation of serotonin (5-HT) neurons or regeneration under the trophic influence of grafted stem cells. Translation to either pharmacological and/or cellular therapies in humans requires the mapping of the spinal cord 5-HT innervation and its receptors to determine their involvement in specific functions. Here, we have performed a preliminary mapping of serotonergic processes and serotonin-lA (5-HT1A) receptors in thoracic and lumbar segments of the human spinal cord. As in rodents and non-human primates, 5-HT profiles in human spinal cord are present in the ventral horn, surrounding motoneurons, and also contact their presumptive dendrites at lumbar level. 5-HT1A receptors are present in the same area, but are more densely expressed at lumbar level. 5-HT profiles are also present in the intermediolateral region, where 5-HT1A receptors are absent. Finally, we observed numerous serotonergic profiles in the superficial part (equivalent of Rexed lamina II) of the dorsal horn, which also displayed high levels of 5-HT1A receptors. These findings pave the way for local specific therapies involving cellular and/or pharmacological tools targeting the serotonergic system

Illegals abortions and utero-digestives lesions: retrospective study of 12 cases in the Department of Gynecology and Obstetrics at the Treichville teaching hospital (Abidjan, Cote D’ivoire)

Background: Traumatic intestinal digestive damage after abortion by endo-uterine manoeuvres are not uncommon. The purpose of this study is to describe the diagnostic, therapeutic and prognostic aspects of these lesions.Methods: This is a retrospective study of 3 years on patients with a uterine lesion associated with a digestive traumatic injury during illegal abortions endo-uterine manoeuvres.Results: 12 patients with a median age of 23, 9 are included. The clinical manifestations are not specific: impairment of the general condition 33.3%; hyperthermia 83.3% (or 10 cases); digestive disorders such as diarrhoea 25%, vomiting 33.3%; abdominal pain 100%; occlusive syndrome 16.7%; acute abdominal syndrome 75%. The seat of traumatic injuries is variable. The lesions were for hail alone in 4 cases (33.3%), colon alone for 2 cases (16.7%), rectum 1 case and epiploon 2 cases. In these 3 cases, the lesions were associated, sitting on both the hail and the colon at a time. All these lesions were associated with uterine perforation of variable siege. The therapeutic management consisted of a small bowel resection with ileostomy in 5 cases or 41.7%; colon resection with colostomy 3 cases or 25%; suture lesions after beveling beiges 5 cases either 41, 7 in 2 cases, we performed haemostasis on the bleeding epiploon. Treatment of the uterine lesion was conservative 75% of the time. The evolution on the 10 patients was favorable, 83.3%. Two patients died early in the operative course after septic shock.Conclusions: The digestive lesions are a factor aggravating the prognosis of post-abortion uterine manoeuvres. Their management must be rapid and requires close collaboration between the digestive surgeon and the Gynecologist

Grafted Human Embryonic Progenitors Expressing Neurogenin-2 Stimulate Axonal Sprouting and Improve Motor Recovery after Severe Spinal Cord Injury

7 p.Background: Spinal cord injury (SCI) is a widely spread pathology with currently no effective treatment for any symptom. Regenerative medicine through cell transplantation is a very attractive strategy and may be used in different non-exclusive ways to promote functional recovery. We investigated functional and structural outcomes after grafting human embryonic neural progenitors (hENPs) in spinal cord-lesioned rats.Methods and Principal Findings: With the objective of translation to clinics we have chosen a paradigm of delayed grafting, i.e., one week after lesion, in a severe model of spinal cord compression in adult rats. hENPs were either naive or engineered to express Neurogenin 2 (Ngn2). Moreover, we have compared integrating and non-integrating lentiviral vectors, since the latter present reduced risks of insertional mutagenesis. We show that transplantation of hENPs transduced to express Ngn2 fully restore weight support and improve functional motor recovery after severe spinal cord compression at thoracic level. This was correlated with partial restoration of serotonin innervations at lumbar level, and translocation of 5HT1A receptors to the plasma membrane of motoneurons. Since hENPs were not detectable 4 weeks after grafting, transitory expression of Ngn2 appears sufficient to achieve motor recovery and to permit axonal regeneration. Importantly, we also demonstrate that transplantation of naive hENPs is detrimental to functional recovery.Conclusions and Significance: Transplantation and short-term survival of Ngn2-expressing hENPs restore weight support after SCI and partially restore serotonin fibers density and 5HT1A receptor pattern caudal to the lesion. Moreover, grafting of naive-hENPs was found to worsen the outcome versus injured only animals, thus pointing to the possible detrimental effect of stem cell-based therapy per se in SCI. This is of major importance given the increasing number of clinical trials involving cell grafting developed for SCI patients.This study was supported by the European Union FP6 "RESCUE" STREP; the "Institut pour la Recherche sur la Moelle Epiniere"; the "Academie de Medecine"; the "Societe Francaise de Neurochirurgie"; "Verticale" and the "Association Demain Debout Aquitaine". The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Unveiling microscopic carrier loss mechanisms in 12 efficient Cu2ZnSnSe4 solar cells

Understanding carrier loss mechanisms at microscopic regions is imperative for the development of high performance polycrystalline inorganic thin film solar cells. Despite the progress achieved for kesterite, a promising environmentally benign and earth abundant thin film photovoltaic material, the microscopic carrier loss mechanisms and their impact on device performance remain largely unknown. Herein, we unveil these mechanisms in state of the art Cu2ZnSnSe4 CZTSe solar cells using a framework that integrates multiple microscopic and macroscopic characterizations with three dimensional device simulations. The results indicate the CZTSe films have a relatively long intragrain electron lifetime of 10 30 amp; 8201;ns and small recombination losses through bandgap and or electrostatic potential fluctuations. We identify that the effective minority carrier lifetime of CZTSe is dominated by a large grain boundary recombination velocity 104 amp; 8201;cm amp; 8201;s amp; 8722;1 , which is the major limiting factor of present device performance. These findings and the framework can greatly advance the research of kesterite and other emerging photovoltaic material