Related papers: The Monotonicity Principle for Magnetic Induction …
We propose a multi-scale deep energy model that is strongly convex in the local neighbourhood around the data manifold to represent its probability density, with application in inverse problems. In particular, we represent the negative…
A reexamination of the Clausius-Mossotti relation in which material with both electric and magnetic responses yields surprising results. Materials with indices near zero and with real parts less than zero, that is the real part of both the…
We consider randomly forced resistive magnetic relaxation equations (MRE) with resistivity $\kappa>0$ and a force proportional to $\sqrt{\kappa}\ $ on the flat $d$-torus $\mathbb{T}^{d}$ for $d\geq 2$. We show the path-wise global…
We review the fundamental properties of the quantum relative entropy for finite-dimensional Hilbert spaces. In particular, we focus on several inequalities that are related to the second law of thermodynamics, where the positivity and the…
Instead of computing magneticallly induced (MI) current densities (CD) via the wave function and their quatum mechanical definition one can also use the differential form of the Amp\`ere-Maxwell law to obtain them from spatial derivatives…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
We obtain the conductance of a system of electrons connected to leads, within time-dependent density-functional theory, using a direct relation between the conductance and the density response function. Corrections to the non-interacting…
We consider inverse problems for $p$-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying $\sigma_1 \geq \sigma_2$ and having the same nonlinear Dirichlet-to-Neumann map…
The objective of electrical impedance tomography is to reconstruct the internal conductivity of a physical body based on measurements of current and potential at a finite number of electrodes attached to its boundary. Although the…
Microscopic theories of magnetoresistance have traditionally focused on momentum relaxation and the plasma frequency of itinerant electrons. Here, we uncover a distinct mechanism in which magnetoresistance originates from quantum…
The realization of optical non-reciprocity is crucial for many device applications, and also of fundamental importance for manipulating and protecting the photons with desired time-reversal symmetry. Recently, various new mechanisms of…
Simulations of the magnetorotational instability (MRI) in a homogeneous shearing box have shown that the asymptotic strength of the magnetic field declines steeply with increasing resolution. Here I model the MRI driven dynamo as a large…
This work reformulates the complete electrode model of electrical impedance tomography in order to enable more efficient numerical solution. The model traditionally assumes constant contact conductances on all electrodes, which leads to a…
We restore part of the thermodynamic formalism for some renormalized measures that are known to be non-Gibbsian. We first point out that a recent theory due to Pfister implies that for block-transformed measures free energies and relative…
This work presents a new constructive uniqueness proof for Calder\'on's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise…
A magnetizable piezoelectric beam model, free at both ends, is considered. Piezoelectric materials have a strong interaction of electromagnetic and acoustic waves, whose wave propagation speeds differ substantially. The corresponding…
This paper presents an improved technique for solving the inverse problem in magnetic induction tomography (MIT) by considering skin and proximity effects in coils. MIT is a non-contact, noninvasive, and low-cost imaging modality for…
We present calculations that reconstruct electronic current densities in two stacked layers at known depths, using magnetic field data. Solving this inverse problem requires knowledge of the magnetic field in two planes -- one above both…
In Electrical Impedance Tomography (EIT) one wants to image the conductivity distribution of a body from current and voltage measurements carried out on its boundary. In this paper we consider the underlying mathematical model, the inverse…
This work focuses on the robust optimization of a permanent magnet (PM) synchronous machine while considering a driving cycle. The robustification is obtained by considering uncertainties of different origins. Firstly, there are geometrical…