We propose here a decomposition of the respiratory tree into three stages which correspond to dif... more We propose here a decomposition of the respiratory tree into three stages which correspond to different mechanical models. The resulting system is described by the Navier-Stokes equation coupled with an ODE (a simple spring model) representing the motion of the thoracic cage. We prove that this problem has at least one solution locally in time for any data and, in
We propose here a decomposition of the respiratory tree into three stages which correspond to dif... more We propose here a decomposition of the respiratory tree into three stages which correspond to different mechanical models. The resulting system is described by the Navier-Stokes equation coupled with an ODE (a simple spring model) representing the motion of the diaphragm muscl. We prove that this problem has at least one solution locally in time for any data and, in
The aim of this paper is to develop a crowd motion model designed to handle highly packed situati... more The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people; The actual velocity is then computed as the projection of the
Mathematical Models and Methods in Applied Sciences, 2015
ABSTRACT Following the approach initially proposed in Maury and Venel,30,31 we consider here crow... more ABSTRACT Following the approach initially proposed in Maury and Venel,30,31 we consider here crowd motion from the standpoint of granular media, and we investigate how theoretical and numerical tools in nonsmooth analysis can help better understanding some paradoxical features. We shall be especially interested in evacuation processes, jams, and we will detail how the granular nature of the flow helps to understand two well-known phenomena, the so-called "Faster is Slower" effect, and "Stop-and-Go" waves.
This paper deals with a class of macroscopic models for cell migration in a saturated medium for ... more This paper deals with a class of macroscopic models for cell migration in a saturated medium for two-species mixtures. Those species tend to achieve some motion according to a desired velocity, and congestion forces them to adapt their velocity. This adaptation is modelled by a correction velocity which is chosen minimal in a least-square sense. We are especially interested in
ESAIM: PROCEEDINGS, July 2007, Vol.18, 143-152 Jean-Frédéric Gerbeau & Stéphane Labbé, Editor... more ESAIM: PROCEEDINGS, July 2007, Vol.18, 143-152 Jean-Frédéric Gerbeau & Stéphane Labbé, Editors UN MOD`ELE DE MOUVEMENTS DE FOULE Bertrand MAURY1 and Juliette VENEL1 Abstract. ... Leur vitesse réelle est donc différente et prend en compte ces contraintes. ...
We present a method to simulate the motion of a rigid body in a fluid governed by the Navier-Stok... more We present a method to simulate the motion of a rigid body in a fluid governed by the Navier-Stokes equations. Numerical simulations of such a problem can be carried out in many different ways, which we may classify into two main classes. The first one relies on a moving mesh which fits the moving part of the boundary (see em
ABSTRACT In this note, we present a smooth extension method for the simulation of the motion of i... more ABSTRACT In this note, we present a smooth extension method for the simulation of the motion of immersed rigid bodies. It is a method of the fictitious domain type, which uses Cartesian meshes and recovers the optimal order of the error by finding a smooth extension of the exact solution defined in the domain with holes. We first present the method with a Poisson problem and show next how it can be adapted to the case of immersed rigid bodies. Finally, the method is validated in both the scalar and the vector cases.
We propose here a decomposition of the respiratory tree into three stages which correspond to dif... more We propose here a decomposition of the respiratory tree into three stages which correspond to different mechanical models. The resulting system is described by the Navier-Stokes equation coupled with an ODE (a simple spring model) representing the motion of the thoracic cage. We prove that this problem has at least one solution locally in time for any data and, in
We propose here a decomposition of the respiratory tree into three stages which correspond to dif... more We propose here a decomposition of the respiratory tree into three stages which correspond to different mechanical models. The resulting system is described by the Navier-Stokes equation coupled with an ODE (a simple spring model) representing the motion of the diaphragm muscl. We prove that this problem has at least one solution locally in time for any data and, in
The aim of this paper is to develop a crowd motion model designed to handle highly packed situati... more The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people; The actual velocity is then computed as the projection of the
Mathematical Models and Methods in Applied Sciences, 2015
ABSTRACT Following the approach initially proposed in Maury and Venel,30,31 we consider here crow... more ABSTRACT Following the approach initially proposed in Maury and Venel,30,31 we consider here crowd motion from the standpoint of granular media, and we investigate how theoretical and numerical tools in nonsmooth analysis can help better understanding some paradoxical features. We shall be especially interested in evacuation processes, jams, and we will detail how the granular nature of the flow helps to understand two well-known phenomena, the so-called "Faster is Slower" effect, and "Stop-and-Go" waves.
This paper deals with a class of macroscopic models for cell migration in a saturated medium for ... more This paper deals with a class of macroscopic models for cell migration in a saturated medium for two-species mixtures. Those species tend to achieve some motion according to a desired velocity, and congestion forces them to adapt their velocity. This adaptation is modelled by a correction velocity which is chosen minimal in a least-square sense. We are especially interested in
ESAIM: PROCEEDINGS, July 2007, Vol.18, 143-152 Jean-Frédéric Gerbeau & Stéphane Labbé, Editor... more ESAIM: PROCEEDINGS, July 2007, Vol.18, 143-152 Jean-Frédéric Gerbeau & Stéphane Labbé, Editors UN MOD`ELE DE MOUVEMENTS DE FOULE Bertrand MAURY1 and Juliette VENEL1 Abstract. ... Leur vitesse réelle est donc différente et prend en compte ces contraintes. ...
We present a method to simulate the motion of a rigid body in a fluid governed by the Navier-Stok... more We present a method to simulate the motion of a rigid body in a fluid governed by the Navier-Stokes equations. Numerical simulations of such a problem can be carried out in many different ways, which we may classify into two main classes. The first one relies on a moving mesh which fits the moving part of the boundary (see em
ABSTRACT In this note, we present a smooth extension method for the simulation of the motion of i... more ABSTRACT In this note, we present a smooth extension method for the simulation of the motion of immersed rigid bodies. It is a method of the fictitious domain type, which uses Cartesian meshes and recovers the optimal order of the error by finding a smooth extension of the exact solution defined in the domain with holes. We first present the method with a Poisson problem and show next how it can be adapted to the case of immersed rigid bodies. Finally, the method is validated in both the scalar and the vector cases.
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Papers by Bertrand Maury