Mollification in strongly Lipschitz domains with application to continuous and discrete De Rham complex

We construct mollification operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are $L^p$ stable for any real number $p\in[1,\infty]$, and commute with the differential operators $\nabla$, $\nabla{\times}$, and $\nabla{\cdot}$. We also construct mollification operators satisfying boundary conditions and use them to characterize the kernel of traces related to the tangential and normal trace of vector fields. We use the mollification operators to build projection operators onto general $H^1$-, $\mathbf{H}(\text{curl})$- and $\mathbf{H}(\text{div})$-conforming finite element spaces, with and without homogeneous boundary conditions. These operators commute with the differential operators $\nabla$, $\nabla{\times}$, and $\nabla{\cdot}$, are $L^p$-stable, and have optimal approximation properties on smooth functions

A converse to Fortin's Lemma in Banach spaces

The converse of Fortin's Lemma in Banach spaces is established in this Note

Prostate biopsies guided by three-dimensional real-time (4-D) transrectal ultrasonography on a phantom: comparative study versus two-dimensional transrectal ultrasound-guided biopsies

OBJECTIVE: This study evaluated the accuracy in localisation and distribution of real-time three-dimensional (4-D) ultrasound-guided biopsies on a prostate phantom. METHODS: A prostate phantom was created. A three-dimensional real-time ultrasound system with a 5.9MHz probe was used, making it possible to see several reconstructed orthogonal viewing planes in real time. Fourteen operators performed biopsies first under 2-D then 4-D transurethral ultrasound (TRUS) guidance (336 biopsies). The biopsy path was modelled using segmentation in a 3-D ultrasonographic volume. Special software was used to visualise the biopsy paths in a reference prostate and assess the sampled area. A comparative study was performed to examine the accuracy of the entry points and target of the needle. Distribution was assessed by measuring the volume sampled and a redundancy ratio of the sampled prostate. RESULTS: A significant increase in accuracy in hitting the target zone was identified using 4-D ultrasonography as compared to 2-D. There was no increase in the sampled volume or improvement in the biopsy distribution with 4-D ultrasonography as compared to 2-D. CONCLUSION: The 4-D TRUS guidance appears to show, on a synthetic model, an improvement in location accuracy and in the ability to reproduce a protocol. The biopsy distribution does not seem improved

A Gaussian beam approach for computing Wigner measures in convex domains

A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset, with initial conditions compactly supported in this set, and Dirichlet or Neumann type boundary condition. The transport of the microlocal energy density along the broken bicharacteristic flow at the high frequency limit is proved through the use of Wigner measures. Our approach consists first in computing explicitly the Wigner measures under an additional control of the initial data allowing to approach the solution by a superposition of first order Gaussian beams. The results are then generalized to standard initial conditions

Prosper: image and robot-guided prostate brachytherapy

Brachytherapy for localized prostate cancer consists in destroying cancer by introducing iodine radioactive seeds into the gland through hollow needles. The planning of the position of the seeds and their introduction into the prostate is based on intra-operative ultrasound (US) imaging. We propose to optimize the global quality of the procedure by: i) using 3D US; ii) enhancing US data with MRI registration; iii) using a specially designed needle-insertion robot, connected to the imaging data. The imaging methods have been successfully tested on patient data while the robot accuracy has been evaluated on a realistic deformable phantom

Effect of torrefaction on grinding energy requirement for thin wood particle production

National audienceThe second generation biofuels exploits the lignocellulosic materials. The main advantage is to not compete with food chain. In the case of thermochemical means (gasification in an entrained flow reactor followed by Fischer-Tropsch synthesis), a grinding step is necessary to inject particles into the burner. The targeted particle size is about 200µm to reach a total conversion and to improve gas quality. Due to the plastic behaviour of the biomass, this step is strongly energy-consuming. Biomass torrefaction (thermal treatment lower than 300°C) is a way to decrease the grinding energy and to standardize materials (composition and moisture). Contrary to natural wood, torrefied wood has a brittle behaviour and a less mechanical strength. The aim of this study is to investigate the interest of torrefaction on wood grinding energy diminution. The torrefactions were carried out on beech and spruce, in an airtight rotating batch kiln under nitrogen. The effect of torrefaction temperature (160-300°C) and duration (5-60min), on weight loss, grinding energy and powder particles size were examined. The grinding energy was calculated by integration of the electric power of the grinder, which was measured by the means of a wattmeter. A grindability criterion, which took into account both grinding energy (E) and the volume fraction (X) of particles lower than the targeted size (200µm), was defined. Results showed a strong interest of torrefaction on the decrease in energy required for fine wood particle grinding. The grindability criterion could be reduced by 93% for treatments beyond 260°C. However, the global energy balance becomes less favourable. It is necessary to reach a compromise between the consumed energy by torrefaction and the decrease in grinding energy. According to the wood species, an optimum could be established around 10% of weight loss and around 85% of the grindability criterion diminution