Shape deformation analysis is concerned with determining a deformation of a given shape into another one, which is optimal for a certain cost. We provide the main ideas for a new general approach to shape deformation analysis, using the framework of optimal control theory. This point of view can be made independent from the parametrization of the shape, and allows to model...
The paper presents the last few years of research at ICUBE, Team MECAFLU in the “Instabilité, Turbulence, Diphasique”group on the simulations of fluid-structure interactions applied to falling bodies using the NSMB solver. The first part of the study was devoted to the numerical study of a sphere falling in a vertical tube filled with a Poiseuille flow. Then the NSMB software has...
High-order Discontinuous Galerkin Methods (DGM) are now routinely used for simulation of wave propagation, especially for geophysical applications. However, to fully take full advantage of the high-order space discretization, it is relevant to use a high-order time discretization. Hence, DGM are currently coupled with ADER schemes, which leads to high-order explicit time schemes...
Heart Rate Variability (HRV) carries a wealth of information about the physiological state and the behaviour of a living individual. Indeed, the heart rate variation is intrinsically linked to the autonomic nervous system: the parasympathetic and orthosympathetic systems. Thus, any imbalance in these two opposite systems results in a variation of the cardiac frequency modulation...
Specific traffic flow conditions, such as the presence of toll gates, construction sites or moving bottlenecks caused by slow moving vehicles, can be realistically modeled by conservation laws with local unilateral constraints on the flux. We give an overview of the related analytical and numerical results.Certaines spécificités de la circulation routière, comme la présence de...
In this review, we present an example of a system of collectively moving agents which exhibit spontaneous self-organization: this example consist of a model of ant-trail formation. We use this example to illustrate what are the challenges in the mathematical modeling of these systems and to outline some possible methodological tracks.Dans cet article de revue, nous présentons un...
In this paper, the author addresses the issue of designing a theoretically well-motivated and computationally efficient method ensuring topology preservation on image-registration-related deformation fields. The model is motivated by a mathematical characterization of topology preservation for a deformation field mapping two subsets of Z2, namely, positivity of the four...
In this paper, we consider the so-called local induction approximation (LIA): $$ \Xt = \Xs\wedge\Xss, $$ X t = X s ∧ X ss , where ∧ is the usual cross product, and s denotes the arc-length parametrization. We study its evolution, taking planar regular polygons of M sides as initial data. Assuming uniqueness and bearing in mind the invariances and symmetries of the problem, we are...
In 1973, Helfrich suggested a simple model to describe the shapes of vesicles: a free bending energy involving geometric quantities like curvature. However, the mathematical questions concerning the existence and the regularity of minimizers to such shape optimization problems still remain open. In this article, we consider a class of admissible shapes in which the existence of...
This work deals with the construction of a low-order absorbing boundary condition (ABC) for 2D elliptic TTI media, preserving the system stability. The construction is based on comparing and then connecting the slowness curves for isotropic and elliptic TTI waves. Numerical experiments illustrate the performance of the new ABC. They are performed by integrating the ABC in a DG...
In this paper is described the general aspect of a numerical method for piecewise deterministic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov equation with respect to a test function space is proved. Next we prove the existence and uniqueness of a positive solution to the finite volume...
In this work, we present a numerical analysis of a method which combines a deterministic and a probabilistic approaches to quantify the migration of a contaminant, under the presence of uncertainty on the permeability of the porous medium. More precisely, we consider the flow equation in a random porous medium coupled with the advection-diffusion equation. Quantities of interest...
This paper describes a method for analyzing the structure and documenting a fairly large chunk of source code for image analysis with a literate programming tool called Lepton. We propose a step-by-step approach to deconstructing the source code and indicate where Lepton’s specific features are most useful.Ce manuscrit présente le logiciel Lepton et comment l’utiliser pour...
Protein aggregation leading to the formation of amyloid fibrils is involved in several neurodegenerative diseases such as prion diseases. To clarify how these fibrils are able to incorporate additional units, prion fibril aggregation and disaggregation kinetics were experimentally studied using Static Light Scattering (SLS). Values that are functions of ∑i ≥ 1i2 Ci, with ci being...
We consider a generalized version of the Hughes’ macroscopic model of pedestrian motion. It consists of a conservation law on the pedestrian mass with an eikonal equation giving the direction of the flux depending of the density. The model displays a non-classical dynamics at the splitting point. Known convergence results for finite volume schemes do not apply in this setting...
Bioluminescence Tomography (BLT) is a recently developed noninvasive imaging tool that allows a direct study of the molecular activity in small animal models. While the forward problem is reduced to a diffusion equation since the scattering phenomena are dominated by the absorption ones in biological tissues, the reconstruction of the distribution of the BLT source is an inverse...
The topology optimization of systems subject to a fluid flow shows a wide potential for designing optimal and innovative structures. The present works apply the concepts of shape optimization and shape derivative to laminar flows (Navier-Stokes) coupled with heat transfers. In addition to the direct model introduction, a special attention is given to the bi-objective optimization...
We introduce an analytical approximation to efficiently price forward start options on equity in time-dependent local volatility models as the forward start date, the maturity or the volatility coefficient are small. We use a conditional expectation argument to represent the price as an expectation of a Black-Scholes formula computed with a stochastic implied volatility depending...
We overview a series of recent works related to some multiscale problems motivated by practical problems in Mechanics. The common denominator of all these works is that they address multiscale problems where the geometry of the microstructures is not periodic. Random modelling, as well as other types of nonperiodic modelling, can then be used to account for the imperfections of...
The goal of this paper is to give recent results in risk theory presented at the Conference ”Journée MAS 2012” which took place in Clermont Ferrand. After a brief state of the art on ruin theory, we explore some particular aspects and recent results. One presents matrix exponential approximations of the ruin probability. Then we present asymptotics of the ruin probability based...
In this paper, we review some recent results obtained in the context of Bayesian non and semiparametric models in terms of posterior concentration, Bernstein-von Mises theorems and tests. Then two specific cases are studied in more details. The first concerns tests for monotonicity and the second some asymptotic properties of empirical Bayes procedures.Cet article est un article...
These notes correspond to a three hours lecture given during the workshop “Metastability and Stochastic Processes”held in Marne-la-Vallée in September 21st-23rd 2011. I would like to warmly thank the organizers Tony Lelièvre and Arnaud Guillin for a very nice organization and for obliging me first to give the lecture, second to write these notes. I also want to acknowledge all...
We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases such as the TCP model or a model of switched vector fields, better results can be proved, especially as regards long time behaviour. We...
In these notes, we first give a brief overwiew of martingales methods, from Paul Lévy (1935) untill now, to explain why these methods have become a central tool in probability, statistics and ergodic theory. Next, we present some recent results for/or based on martingales: exponential bounds for super-martingales, concentration inequalities for Lipschitz functionals of dynamical...
In this overview paper, we consider the scoring approach applied to the ranking problem from a nonparametric perspective. We first focus on the problem of ROC curve optimization in terms of description of optimal elements. Then, we introduce summaries of this function-valued description of performance which are related to well-known statistics that are of higher order compared to...