7,652 research outputs found
Recovery of a space-dependent vector source in thermoelastic systems
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
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and a vectorial hyperbolic equation for the displacement
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. 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
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(with
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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
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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 SparsityPart I: Modeling and Inverse Problems
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
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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