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We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element…
Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and…
Magnetic resonance velocimetry (MRV) is a non-invasive experimental technique widely used in medicine and engineering to measure the velocity field of a fluid. These measurements are dense but have a low signal-to-noise ratio (SNR). The…
Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…
In this paper we establish weighted $L^{q}$-$L^{p}$-maximal regularity for linear vector-valued parabolic initial-boundary value problems with inhomogeneous boundary conditions of static type. The weights we consider are power weights in…
Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the conductivity is indeed…
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…
Modeling physical phenomena like heat transport and diffusion is crucially dependent on the numerical solution of partial differential equations (PDEs). A PDE solver finds the solution given coefficients and a boundary condition, whereas an…
This work introduces a computational framework for applying absolute electrical impedance tomography to head imaging without accurate information on the head shape or the electrode positions. A library of fifty heads is employed to build a…
We study the conditions of integrability when the boundary terms are considered in the variation of the geometric contribution of the Einstein-Hilbert action. We explore the emergent physical dynamics that is obtained when we make a…
For the two dimensional Schr\"odinger equation in a bounded domain, we prove uniqueness of determination of potentials in $W^1_p(\Omega),\,\, p>2$ in the case where we apply all possible Neumann data supported on an arbitrarily non-empty…
Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that has earned significant attention for its potential in real-time monitoring of various physiological parameters. Despite its promise, the sensitivity and…
The minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a "kinetic undercooling" type boundary condition in a Laplacian growth problem of…
We consider the problem of minimizing variational integrals defined on \cc{nonlinear} Sobolev spaces of competitors taking values into the sphere. The main novelty is that the underlying energy features a non-uniformly elliptic integrand…
In this paper we study an inverse boundary value problem for Maxwell's equations. The goal is to reconstruct perturbations in the refractive index of the medium inside an object from the knowledge of the tangential trace of an electric…
In this paper we consider the electromagnetic scattering problem by an obstacle characterised by a Generalized Impedance Boundary Condition in the harmonic regime. These boundary conditions are well known to provide accurate models for thin…
We consider a quasilinear nonhomogeneous, anisotropic Maxwell system in a bounded smooth domain of $\mathbb{R}^{3}$ with a strictly positive conductivity subject to the boundary conditions of a perfect conductor. Under appropriate…
We consider non-equilibrium transport in disordered conductors. We calculate the interaction correction to the current for a short wire connected to electron reservoirs by resistive interfaces. In the absence of charging effects we find a…
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…
The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current.…