Perturbation theory for the effective diffusion constant in a medium of random scatterer

We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random media. The random media contains point scatterers of density $\rho$ uniformly distributed through out the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalisation group approach based on thinning out the scatterers, this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme its predictions are confronted with results obtained by numerical simulation.Comment: 22 pages, 6 figures, IOP (J. Phys. A. style

L'equilibre architectural de la face: un concept cephalometrique 3D. [The architectural balance of the face: a 3D cephalometric concept]

The use of the c2000 software led us to develop a new 3D cephalometric construction, based on the selection on the axial CT Scans of 8 anatomical landmarks and of teeth, all of which were situated along the trigeminal neuro matriciel facial growth axes. The analysis of this construction is based on the use of an original mathematical tool in biology: the axes of inertia. Using the selection of both mental foramen, both infra and supra orbital foramen and the head of both malleus, the C 2000 software creates a geometrical construction called: "the maxillo-facial frame", as well as, a 3D cephalometric analysis: angles, distances, areas, volumes center of gravity and axes of inertia. Using the selection of teeth, the C 2000 software calculates the axes of inertia of each tooth or of groups of teeth. The use of the axes of inertia allow us to create of a hierarchy of anatomical levels the teeth, the half arches, the arches, both arches and the maxillo-facial frame. In addition, for each of these anatomical levels, the axes of inertia create a 3D landmark which allows the calculation of the orientation of each of these elements in relation to the others. The study of 28 orthomorphic people using this analysis revealed the existence of a maxillo-facial balance that is unique for each individual

Guidelines of the French Society of ENT (SFORL): Drug-induced sleep endoscopy in adult obstructive sleep apnea syndrome

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