1,721,024 research outputs found
Unique continuation from Cauchy data in unknown non-smooth domains
Full text linkWe consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We perform measurements of current and voltage
type on a (known) part of the boundary of the conductor. We prove that, even if the defects are unknown, the current and voltage measurements at the boundary uniquely determine the corresponding electrostatic potential inside the conductor. A corresponding stability result, related to the stability of Neumann
problems with respect to domain variations, is also proved. Some applications of these results to inverse problems are presented
On Unique Determination of Polyhedral Sets
No full textIn this paper, we develop in detail the geometric constructions that lead to many uniqueness
results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of
measurements. We highlight how unique continuation and a suitable reflection principle are enough to proceed with the constructions without any other assumption on the underlying partial differential equation or the boundary condition.We also aim to keep the geometric constructions and their proofs as simple as possible. To illustrate the applicability of this theory, we show how several uniqueness results present in the literature immediately follow from our arguments. Indeed, we believe that this theory may serve as a roadmap for establishing similar uniqueness results for other partial differential equations or boundary conditions
Sustainability of water supply projects: considerations from two case studies
No full textIn Developing countries, drinking water supply is still an open issue: in sub-Saharan Africa, coverage of improved water supply gains only the 63% (JMP, 2013). Some regions are affected by geogenic contaminants (e.g. fluorides and arsenic) and the lack of access to sanitation facilities and hygiene practices causes a high microbiological contamination of water in the supply chain. The responses to these problems are the several projects on drinking water supply that aim to improve the water availability and quality all over the world. But, how cooperation projects on water supply can be really sustainable? Can implemented technologies still work after the end of the projects? These are questions that every NGO/Association should answer during project elaboration and implementation. The main factors that can be a source of failure for water supply projects are: complexity or costs of technologies (even if implemented at domestic scale), technical management, level of acceptance by the beneficiary community (that, if does not clearly recognize the technology benefits, can make hardly sustainable the entire project) and level of support by the local and/or national Institutions. In order to gain the project sustainability, the activities should be clearly focused after a rigorous assessment in the study area regarding the local availability of human and material resources for the technology implementation, the awareness level of the community in terms of technology need and acceptance, etc. CeTAmb research center (Brescia University) has surveyed two projects on drinking water management in Senegal and Burkina Faso, which have confirmed the importance of these aspects. The sustainability level was evaluated after the project implementation: in the first case study, several deficiencies were arisen in terms of material availability and technology costs, whereas the second case study highlighted successful results in regard to water management system sustainability
Uniqueness for the determination of sound-soft defects in an inhomogeneous planar medium by acoustic boundary measurements
Full text linkWe consider the inverse problem of determining shape and location of sound-soft defects inside a known planar inhomogeneous and anisotropic medium through acoustic imaging at low frequency. In order to determine the defects, we perform acoustic boundary measurements, with prescribed boundary conditions of different types. We prove that at most two, suitably chosen, measurements allow us to uniquely determine multiple defects under minimal regularity assumptions on the defects and the medium containing them. Finally, we treat applications of these results to the case of inverse scattering
Stable determination of sound-soft polyhedral scatterers by a single measurement
Full text linkWe prove optimal stability estimates for the determination of a finite number of sound-soft polyhedral scatterers in R^3 by a single far-field measurement. The admissible multiple polyhedral scatterers satisfy minimal a priori assumptions of Lipschitz type and may include at the same time obstacles, screens and even more complicated scatterers. We characterize any multiple
polyhedral scatterer by a size parameter h which is related to the minimal size of the cells of its boundary. In a first step we show that, provided the error epsilon on the far-field measurement is small enough with respect to h, then the corresponding error, in the Hausdorff distance, on the multiple polyhedral scatterer can be controlled by an explicit function of epsilon which approaches zero,
as epsilon goes to 0, in an essentially optimal, although logarithmic, way. Then, we show how to improve this stability estimate, provided we restrict our attention to multiple polyhedral obstacles and epsilon is even smaller with respect to h. In this case we obtain an explicit estimate essentially of Hoelder type
Reconstruction in the inverse crack problem by variational methods
No full textWe deal with a variational approach to the inverse crack problem, that is the detection and reconstruction of cracks, and other defects, inside a conducting body by performing boundary
measurements of current and voltage type. We formulate such an inverse problem in a free-discontinuity problems framework and propose a novel method for the numerical reconstruction
of the cracks by the available boundary data. The proposed method is amenable to numerical computations and it is justified by a convergence analysis, as the error on the measurements
goes to zero. We further notice that we use the Gamma-convergence approximation of the Mumford–Shah functional due to Ambrosio and Tortorelli as the required regularization term
A variational approach to the reconstruction of cracks by boundary measurements
Full text linkWe consider a conducting body which presents some (unknown) perfectly insulating defects, such as cracks or cavities, for instance. We aim to reconstruct the defects by performing measurements of current and voltage type on a (known and accessible) part of the boundary of the conductor. A crucial step in this reconstruction is the determination of the electrostatic
potential inside the conductor, by the electrostatic boundary measurements performed. Since the defects are unknown,
we state such a determination problem as a free-discontinuity problem for the electrostatic potential in the framework of special functions of bounded variation. We provide a characterisation of the looked for electrostatic potential and we approximate it with the minimum points of a sequence of functionals, which take also in account the error in the measurements. These functionals are related to the so-called Mumford-Shah functional, which acts as a regularizing term and allows us to prove existence of minimizers and Gamma-convergence properties
A remark on a paper by Alessandrini and Vessella
Full text linkWe prove that the Lipschitz constant of the Lipschitz stability result for the inverse conductivity problem proved by G. Alessandrini and S. Vessella behaves exponentially with respect to the number N of regions considered
Uniqueness and stability for the determination of boundary defects by electrostatic measurements
No full textTesi di Ph.D., S.I.S.S.A.-I.S.A.S., Triest
- …
