7,652 research outputs found

    Recovery of a space-dependent vector source in thermoelastic systems

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    In this contribution, an inverse problem of determining a space-dependent vector source in a thermoelastic system of type-I, type-II and type-III is studied using information from a supplementary measurement at a fixed time. These thermoelastic systems consist of two equations that are coupled: a parabolic equation for the temperature [GRAPHICS] and a vectorial hyperbolic equation for the displacement [GRAPHICS] . In this latter one, the source is unknown, but solely space dependent. A spacewise-dependent additional measurement at the final time ensures that the inverse problem corresponding with each type of thermoelasticity has a unique solution when a damping term [GRAPHICS] (with [GRAPHICS] componentwise strictly monotone increasing) is present in the hyperbolic equation. Despite the ill-posed nature of these inverse problems, a stable iterative algorithm is proposed to recover the unknown source in the case that [GRAPHICS] is also linear. This method is based on a sequence of well-posed direct problems, which are numerically solved at each iteration, step by step, using the finite element method. The instability of the inverse source problem is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results support the theoretically obtained results

    Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity-Part I: Modeling and Inverse Problems

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    In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs' Green function to derive a novel parametrization of the acquired images. This parametrization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a non-negative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology.Comment: published, 15 page

    New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model

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    In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.Comment: 8 Pages, The Journal Thermal Science, 201
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