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boundary  brain  data obtained  data  eeg data  eeg  equation  factorization method  method  obstacle  problem  scattering  stochastic equation 
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Preview: IMA Journal of Applied Mathematics - Advance Access

IMA Journal of Applied Mathematics Advance Access





Published: Tue, 20 Feb 2018 00:00:00 GMT

Last Build Date: Tue, 20 Feb 2018 06:48:39 GMT

 



The factorization method for the inverse obstacle scattering problem with oblique derivative boundary condition

Tue, 20 Feb 2018 00:00:00 GMT

Abstract
We consider a direct and inverse problem for the scattering of an obstacle with a generalized oblique derivative and impedance boundary condition due to the incident plane wave, which arises in some scattering phenomenons such as the scattering of tidal waves by islands under suitable assumptions. The solvability of the direct scattering problem is proven by using the boundary integral equation method. A special technique is proposed in order to show the formulated boundary integral operator is Fredholm with index 0. Then the factorization method is established to reconstruct the shape of the obstacle. We note that the tangential derivative on the obstacle boundary leads to the difficulties on mathematical analysis. Finally, we present some numerical examples in 2D to show the feasibility and effectiveness of the factorization method.



Quantifying errors during the source localization process in electroencephalography for confocal systems

Fri, 19 Jan 2018 00:00:00 GMT

Abstract
Electroencephalography (EEG) is an important clinical tool detecting the electrical activity of the brain. The present work aims to analyse the sensitivity of analytical algorithms that are used to interpret the EEG data obtained from an actual subject, with respect to data obtained from an average head–brain system. We consider the case where the EEG data are misinterpreted as if they referred to a brain with different size than the actual brain under consideration. We employ a homogeneous triaxial ellipsoid to model the head brain system, which offers the best fit realistic approach that permits classical analysis. Utilizing the ellipsoidal coordinate system, two confocal ellipsoids, i.e. their foci remain fixed, are implemented in order to analytically calculate the approximation errors and bounds that occur when solving the EEG problem with respect to an ellipsoidal volume conductor of different size. Our results indicate a high error rate when comparing different sized brains.



Strong solvability of regularized stochastic Landau–Lifshitz–Gilbert equation

Fri, 19 Jan 2018 00:00:00 GMT

Abstract
We examine a stochastic Landau–Lifshitz–Gilbert equation based on an exchange energy functional containing second-order derivatives of the unknown field. Such regularizations are featured in advanced micromagnetic models recently introduced in connection with nanoscale topological solitons. We show that, in contrast to the classical stochastic Landau–Lifshitz–Gilbert equation based on the Dirichlet energy alone, the regularized equation is solvable in the stochastically strong sense. As a consequence it preserves the topology of the initial data, almost surely.