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Search Results: 1 - 10 of 2094 matches for " Franz Chouly "
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On convergence of the penalty method for unilateral contact problems
Franz Chouly,Hild Patrick
Mathematics , 2012, DOI: 10.1016/j.apnum.2012.10.003
Abstract: We present a convergence analysis of the penalty method applied to unilateral contact problems in two and three space dimensions. We first consider, under various regularity assumptions on the exact solution to the unilateral contact problem, the convergence of the continuous penalty solution as the penalty parameter $\varepsilon$ vanishes. Then, the analysis of the finite element discretized penalty method is carried out. Denoting by $h$ the discretization parameter, we show that the error terms we consider give the same estimates as in the case of the constrained problem when the penalty parameter is such that $\varepsilon = h$.
A Nitsche-based domain decomposition method for hypersingular integral equations
Franz Chouly,Norbert Heuer
Mathematics , 2011,
Abstract: We introduce and analyze a Nitsche-based domain decomposition method for the solution of hypersingular integral equations. This method allows for discretizations with non-matching grids without the necessity of a Lagrangian multiplier, as opposed to the traditional mortar method. We prove its almost quasi-optimal convergence and underline the theory by a numerical experiment.
A local projection stabilized method for fictitious domains
Gabriel Raúl Barrenechea,Franz Chouly
Mathematics , 2011,
Abstract: In this work a local projection stabilization method is proposed to solve a fictitious domain problem. The method adds a suitable fluctuation term to the formulation thus rendering the natural space for the Lagrange multiplier stable. Stability and convergence are proved and these results are illustrated by a numerical experiment.
Evaluating soft tissue simulation in maxillofacial surgery using pre and post-operative CT scan
Matthieu Chabanas,Christophe Marecaux,Franz Chouly,Franck Boutault,Yohan Payan
Physics , 2006,
Abstract: One of the most important issue in soft tissue modeling is to assess the quality of the simulations. A validation protocol is presented based on two CT scans of the patient acquired before and after cranio-maxillofacial surgery. The actual bones repositioning realized during the intervention are accurately measured and reproduced. A evaluation of the soft tissue deformation is then computed using a finite element model of the face. The simulations are therefore compared, qualitatively and quantitatively, with the actual outcome of the surgery. This protocol enable to rigorously evaluate different modeling methods, and to assess the clinical relevance of soft tissue simulation in maxillofacial surgery.
Modelling the human pharyngeal airway: validation of numerical simulations using in vitro experiments
Franz Chouly,Annemie Van Hirtum,Pierre-Yves Lagrée,Xavier Pelorson,Yohan Payan
Physics , 2008, DOI: 10.1007/s11517-008-0412-1
Abstract: In the presented study, a numerical model which predicts the flow-induced collapse within the pharyngeal airway is validated using in vitro measurements. Theoretical simplifications were considered to limit the computation time. Systematic comparisons between simulations and measurements were performed on an in vitro replica, which reflects asymmetries of the geometry and of the tissue properties at the base of the tongue and in pathological conditions (strong initial obstruction). First, partial obstruction is observed and predicted. Moreover, the prediction accuracy of the numerical model is of 4.2% concerning the deformation (mean quadratic error on the constriction area). It shows the ability of the assumptions and method to predict accurately and quickly a fluid-structure interaction.
Reproduction of hypopnea phenomenon using a physical and numerical model
Franz Chouly,Annemie Van Hirtum,Pierre-Yves Lagrée,Xavier Pelorson,Yohan Payan
Physics , 2006,
Abstract: Obstructive sleep apnea syndrome is now considered as a major health care topic. An in-vitro setup which reproduces and simplifies upper airway geometry has been the basis to study the fluid/walls interaction that leads to an apnea. It consists of a rigid pipe (the pharynx) in contact with a deformable latex cylinder filled with water (the tongue). Air flows out of the rigid pipe and induces pressure forces on the cylinder. We present a numerical model of this setup: a finite element model of the latex cylinder is in interaction with a fluid model. Simulation of an hypopnea (partial collapsus of the airway) has been possible and in agreement with observations from the in-vitro setup. The same phenomenon has been simulated on a soft palate model obtained from a patient sagittal radiography. These first results encourage us to improve the model so as it could reproduce the complete apnea phenomenon, and be used for a planification purpose in sleep apnea surgery.
Maxillofacial computer aided surgery: a 5 years experience and future
Christophe Marecaux,Matthieu Chabanas,Vincent Luboz,Annaig Pedrono,Franz Chouly,Pascal Swider,Yohan Payan,Franck Boutault
Physics , 2006,
Abstract: This paper gives a review of the experience provided by our group in terms of computer aided maxillo-facial surgery.
A Method for Quantifying the Emotional Intensity and Duration of a Startle Reaction with Customized Fractal Dimensions of EEG Signals  [PDF]
Franz Konstantin Fuss
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.74033
Abstract: The assessment of emotions with fractal dimensions of EEG signals has been attempted before, but the quantification of the intensity and duration of sudden and short emotions remains a challenge. This paper suggests a method for this purpose, by using a new fractal dimension algorithm and by adjusting the amplitude of the EEG signal in order to obtain maximal separation of high and low fractal dimensions. The emotion was induced by embedding a scary image at 20 seconds in landscape videos of 60 seconds length. The new method did not only detect the onset of the emotion correctly, but also revealed its duration and intensity. The intensity is based on the magnitude and impulse of the fractal dimension signal. It is also shown that Higuchi’s method does not always detect emotion spikes correctly; on the contrary, the region of the expected emotional response can be represented by fractal dimensions smaller than the rest of the signal, whereas the new method directly reveals distinct spikes. The duration of these spikes was 10 - 11 seconds. The magnitude of these spikes varied across the EEG channels. The build-up and cool-down of the emotions can occur with steep and flat gradients.
Introducing Cinematic Rendering: A Novel Technique for Post-Processing Medical Imaging Data  [PDF]
Franz A. Fellner
Journal of Biomedical Science and Engineering (JBiSE) , 2016, DOI: 10.4236/jbise.2016.93013
Abstract: Since the 1980s, various techniques have been used in the field of medicine for the post-processing of medical imaging data from computed tomography (CT) and magnetic resonance (MR). They include multiplanar reformations (MPR), maximum intensity projection (MIP) and Volume Rendering (VR). This paper presents the prototype of a new means of post-processing radiological examinations such as CT and MR, a technique that, for the first time, provides photorealistic visualizations of the human body. This new procedure was inspired by the quality of images achieved by animation software such as programs used in the entertainment industry, particularly to produce animated films. Thus, the name: Cinematic Rendering. It is already foreseeable that this new method of depiction will quickly be incorporated into the set of instruments employed in socalled virtual anatomy (teaching anatomy through the use of radiological depictions of the human body via X-ray, CT and MR in addition to the use of computer animation programs designed especially for human anatomy). Its potential for medical applications will have to be evaluated by future scientific investigations.
The Equilibrium of Fractional Derivative and Second Derivative: The Mechanics of a Power-Law Visco-Elastic Solid  [PDF]
Franz Konstantin Fuss
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.716156
Abstract: This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line; transition—centre of mass reciprocation without crossing the zero line; overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401; two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578; and one phase— overdamping—exists exclusively if 0.578 < η < 1.
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