2,382 research outputs found

    Contamination source inference in water distribution networks

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    We study the inference of the origin and the pattern of contamination in water distribution networks. We assume a simplified model for the dyanmics of the contamination spread inside a water distribution network, and assume that at some random location a sensor detects the presence of contaminants. We transform the source location problem into an optimization problem by considering discrete times and a binary contaminated/not contaminated state for the nodes of the network. The resulting problem is solved by Mixed Integer Linear Programming. We test our results on random networks as well as in the Modena city network

    On the effect of boundaries in two-phase porous flow

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    In this paper we study a model of an interface between two fluids in a porous medium. For this model we prove several local and global well-posedness results and study some of its qualitative properties. We also provide numerics

    Pervasiveness of the pp-Laplace operator under localization of fractional gg-Laplace operators

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    In this work we analyze the behavior of truncated functionals as \begin{equation*} \int_{\mathbb{R}^N}\int_{B(x,\delta)} G\left(\frac{|u(x)-u(y)|}{|x-y|^{s}}\right)\frac{dydx}{|x-y|^N}\qquad\text{for }\delta\to0^+. \end{equation*} Here the function GG is an Orlicz function that in addition is assumed to be a regularly varying function at 00. A prototype of such function is given by G(t)=tp(1+∣log⁡(t)∣)G(t)=t^p(1+|\log(t)|) with p≥2p\geq2. These kind of functionals arise naturally in {\it peridynamics}, where long-range interactions are neglected and only those exerted at distance smaller than δ>0\delta>0 are taken into account, i.e., the {\it horizon} δ>0\delta>0 represents the range of interactions or nonlocality.\\ This work is inspired by the celebrated result by Bourgain, Brezis and Mironescu, who analyzed the limit s→1−s\to1^- with G(t)=tpG(t)=t^p. In particular, we prove that, under appropriate conditions, \begin{equation*} \lim\limits_{\delta\to0^+}\frac{p(1-s)}{G(\delta^{1-s})}\int_{\mathbb{R}^N}\int_{B(x,\delta)}G\left(\frac{|u(x)-u(y)|}{|x-y|^{s}}\right)\frac{dydx}{|x-y|^N}=K_{N,p}\int_{\mathbb{R}^N}|\nabla u(x)|^p dx, \end{equation*} for p=index(G)p=index(G) and an explicit constant KN,p>0K_{N,p}>0. Moreover, the converse is also true, if the above localization limit exist as δ→0+\delta\to0^+, the Orlicz function GG is a regularly varying function with index(G)=pindex(G)=p

    Fractional Schr\"odinger systems coupled by Hardy-Sobolev critical terms

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    In this work we analyze a class of nonlinear fractional elliptic systems involving Hardy--type potentials and coupled by critical Hardy-Sobolev--type nonlinearities in RN\mathbb{R}^N. Due to the lack of compactness at the critical exponent the variational approach requires a careful analysis of the Palais-Smale sequences. In order to overcome this loss of compactness, by means of a concentration--compactness argument the compactness of PS sequences is derived. This, combined with a energy characterization of the semi-trivial solutions, allow us to conclude the existence of positive ground and bound state solutions en terms of coupling parameter ν>0\nu>0 and the involved exponents α,β\alpha,\beta.Comment: arXiv admin note: text overlap with arXiv:2211.1704

    Design of optical metamaterial waveguide structures

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    Subwavelength gratings (SWGs) are periodic structures with a pitch (Λ) smaller than the wavelength of the propagating wave (λ), so that diffraction effects are suppressed. These structures thus behave as artificial metamaterials where the refractive index and the dispersion profile can be controlled with a proper design of the geometry of the structure. SWG waveguides have found extensive applications in the field of integrated optics, such as efficient fiber-chip couplers, broadband multimode interference (MMI) couplers, polarization beam splitters or evanescent field sensors, among others. From the point of view of nano-fabrication, the subwavelength condition (Λ << λ) is much easier to meet for long, mid-infrared wavelengths than for the comparatively short near-infrared wavelengths. Since most of the integrated devices based on SWGs have been proposed for the near-infrared, the true potential of subwavelength structures has not yet been completely exploited. In this talk we summarize some valuable guidelines for the design of high performance SWG integrated devices. We will start describing some practical aspects of the design, such as the range of application of semi-analytical methods, the rigorous electromagnetic simulation of Floquet modes, the relevance of substrate leakage losses and the effects of the random jitter, inherent to any fabrication process, on the performance of SWG structures. Finally, we will show the possibilities of the design of SWG structures with two different state-of-the-art applications: i) ultra-broadband MMI beam splitters with an operation bandwidth greater than 300nm for telecom wavelengths and ii) a set of suspended waveguides with SWG lateral cladding for mid-infrared applications, including low loss waveguides, MMI couplers and Mach-Zehnder interferometers.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

    Pedagogía terapéutica en Educación Infantil. Análisis y tratamiento de un caso de Trastorno Específico del Lenguaje

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    Puesto que este Trabajo de Fin de Grado, está dedicado a la Pedagogía Terapéutica, y en la edad en la que se da el caso de observación, uno de los aspectos más importantes es el desarrollo de la capacidad expresiva y de producción, este trabajo en concreto irá dirigido hacia el TEL, Trastorno Específico del Lenguaje, analizándose en él un caso observado en el Prácticum III, del cual se ha podido disponer de informes anteriores, entrevistas con las familias, así como la propia experiencia de contacto, en las aulas tanto de Pedagogía Terapéutica como de Audición y Lenguaje, con el caso en cuestión. El trabajo estará casi exclusivamente dedicado al campo de la expresión, que podría dificultar la comunicación verbal, pudiendo llegar a retrasar, de manera significativa los aprendizajes, convirtiéndose así en tema prioritario, sobre todo en Audición y Lenguaje
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