Determining the shape of defects in non-absorbing inhomogeneous media from far-field measurements

International audienceWe consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases

Feasibility of Using Ultra-High Field (7 T) MRI for Clinical Surgical Targeting

The advantages of ultra-high magnetic field (7 Tesla) MRI for basic science research and neuroscience applications have proven invaluable. Structural and functional MR images of the human brain acquired at 7 T exhibit rich information content with potential utility for clinical applications. However, (1) substantial increases in susceptibility artifacts, and (2) geometrical distortions at 7 T would be detrimental for stereotactic surgeries such as deep brain stimulation (DBS), which typically use 1.5 T images for surgical planning. Here, we explore whether these issues can be addressed, making feasible the use of 7 T MRI to guide surgical planning. Twelve patients with Parkinson's disease, candidates for DBS, were scanned on a standard clinical 1.5 T MRI and a 7 T MRI scanner. Qualitative and quantitative assessments of global and regional distortion were evaluated based on anatomical landmarks and transformation matrix values. Our analyses show that distances between identical landmarks on 1.5 T vs. 7 T, in the mid-brain region, were less than one voxel, indicating a successful co-registration between the 1.5 T and 7 T images under these specific imaging parameter sets. On regional analysis, the central part of the brain showed minimal distortion, while inferior and frontal areas exhibited larger distortion due to proximity to air-filled cavities. We conclude that 7 T MR images of the central brain regions have comparable distortions to that observed on a 1.5 T MRI, and that clinical applications targeting structures such as the STN, are feasible with information-rich 7 T imaging

Dynamic stiffness formulation for circular rings

International audienceThis paper describes a procedure for calculating the dynamic stiffness matrix of a circular ring. The basisof the dynamic stiffness method resides in determining the dynamic stiffness matrix of such structuralelements. The solution of the elementary problem is derived using Hamilton’s principle and a Fourier seriesexpansion of the solution. Concentrated and distributed loads are applied to the ring along severaldirections in order to determine the response of the system. The performances of the method are evaluatedusing comparisons with the harmonic responses of a circular ring obtained using the finite elementmethod

The linear sampling method in inverse electromagnetic scattering theory

We survey the linear sampling method for solving the inverse scattering problem for time-harmonic electromagnetic waves at fixed frequency. We consider scattering by an obstacle as well as scattering by an inhomogeneous medium both in R2 and R3. Included in our discussion is the use of regularization methods for ill-posed problems and numerical examples in both two and three dimensions

Efficient solution of a wave equation with fractional-order dissipative terms

AbstractWe consider a wave equation with fractional-order dissipative terms modeling visco-thermal losses on the lateral walls of a duct, namely the Webster–Lokshin model. Diffusive representations of fractional derivatives are used, first to prove existence and uniqueness results, then to design a numerical scheme which avoids the storage of the entire history of past data. Two schemes are proposed depending on the choice of a quadrature rule in the Laplace domain. The first one mimics the continuous energy balance but suffers from a loss of accuracy in long time simulation. The second one provides uniform control of the accuracy. However, even though the latter is more efficient and numerically stable under the standard CFL condition, no discrete energy balance has been yet found for it. Numerical results of comparisons with a closed-form solution are provided

A Contribution to the Design of Robust Profile Modifications in Spur and Helical Gears by Combining Analytical Results and Numerical Simulations

This paper addresses the definition of robust profile modifications in spur and helical gears. An original methodology is introduced which relies on closed-form analytical results on transmission errors combined with a gradient descent algorithm and a Gauss quadrature (GQ) based full factorial method. The results compare very well with those delivered by using classic Monte Carlo simulations with a considerable gain in computational time. The influence of the probability distribution law for the design parameters (depth and extent of modification) is analyzed along with the contribution of gear quality grade and load variation. Some optimum robust linear relief is presented which minimizes transmission error fluctuations over a broad range of loads even in the presence of significant geometrical tolerances.</jats:p

Dynamic stiffness formulation and response analysis of stiffened shells

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