363 research outputs found
A discrete contact model for crowd motion
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 spontaneous velocity onto
the set of admissible velocities (i.e. velocities which do not violate the
non-overlapping constraint). We describe here the underlying mathematical
framework, and we explain how recent results by J.F. Edmond and L. Thibault on
the sweeping process by uniformly prox-regular sets can be adapted to handle
this situation in terms of well-posedness. We propose a numerical scheme for
this contact dynamics model, based on a prediction-correction algorithm.
Numerical illustrations are finally presented and discussed.Comment: 22 page
A 2-adic approach of the human respiratory tree
We propose here a general framework to address the question of trace
operators on a dyadic tree. This work is motivated by the modeling of the human
bronchial tree which, thanks to its regularity, can be extrapolated in a
natural way to an infinite resistive tree. The space of pressure fields at
bifurcation nodes of this infinite tree can be endowed with a Sobolev space
structure, with a semi-norm which measures the instantaneous rate of dissipated
energy. We aim at describing the behaviour of finite energy pressure fields
near the end. The core of the present approach is an identification of the set
of ends with the ring Z_2 of 2-adic integers. Sobolev spaces over Z_2 can be
defined in a very natural way by means of Fourier transform, which allows us to
establish precised trace theorems which are formally quite similar to those in
standard Sobolev spaces, with a Sobolev regularity which depends on the growth
rate of resistances, i.e. on geometrical properties of the tree. Furthermore,
we exhibit an explicit expression of the "ventilation operator", which maps
pressure fields at the end of the tree onto fluxes, in the form of a
convolution by a Riesz kernel based on the 2-adic distance.Comment: 22 page
A congestion model for cell migration
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 two
situations: a single active species moves in a passive matrix (cell migration)
with a given desired velocity, and a closed-loop Keller-Segel type model, where
the desired velocity is the gradient of a self-emitted chemoattractant. We
propose a theoretical framework for the open-loop model (desired velocities are
defined as gradients of given functions) based on a formulation in the form of
a gradient flow in the Wasserstein space. We propose a numerical strategy to
discretize the model, and illustrate its behaviour in the case of a prescribed
velocity, and for the saturated Keller-Segel model
Modeling of the oxygen transfer in the respiratory process
International audienceIn this article, we propose an integrated model for oxygen transfer into the blood, coupled with a lumped mechanical model for the ventilation process. We aim at investigating oxygen transfer into the blood at rest or exercise. The first task consists in describing nonlinear effects of the oxygen transfer under normal conditions. We also include the possible diffusion limitation in oxygen transfer observed in extreme regimes involving parameters such as alveolar and venous blood oxygen partial pressures, capillary volume, diffusing capacity of the membrane, oxygen binding by hemoglobin and transit time of the red blood cells in the capillaries. The second task consists in discussing the oxygen concentration heterogeneity along the path length in the acinu
SnO2 coated Ni particles prepared by fluidized bed chemical vapor deposition
A Fluidized Bed Metal–Organic Chemical Vapor Deposition (FB-MOCVD) process was developed for the growth of tin oxide thin films on large hollow Ni particles. Tetraethyl tin was used as tin source and dry air both as fluidization gas and oxidant reagent. The SnO2 films were grown in a FBCVD reactor under reduced pressure (13.3 kPa) in the temperature range of 633–663 K. A series of specific experiments was carried out to optimize the design of the reactor and to determine the range of experimental parameters (flow rate, pressure, temperature) leading to good fluidization of the large hollow Ni particles used as base material. The SnO2 films deposited on particles exhibited a dense nodular surface morphology similar to that previously observed on flat substrates. The relative thickness of the films was determined by EDS analyses and the real values were measured by SEM on cross-sections of particles. The SnO2 films exhibit satisfactory thickness uniformity from one particle to another in the same batch and from run to run. XRD studies revealed that the films exhibited good crystallinity with the cassiterite structure. Traces of NiO were found at the SnO2/Ni interface. Finally, the SnO2 CVD coated-Ni particles were used as anodes in an electrochemical cell. The potential limit of oxygen evolution measured was that of the SnO2 layer despite the initial porosity of the hollow Ni particles inherent to their preparation. This work is the first step towards the preparation of high specific surface area electrodes
Multiscale modelling of the respiratory tract
International audienceWe 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 the special case where the spring stiffness is equal to zero, we obtain an existence result globally in time provided that the data are small enough. The behaviour of the global model is illustrated by three-dimensional simulations
A macroscopic crowd motion model of gradient flow type
A simple model to handle the flow of people in emergency evacuation
situations is considered: at every point x, the velocity U(x) that individuals
at x would like to realize is given. Yet, the incompressibility constraint
prevents this velocity field to be realized and the actual velocity is the
projection of the desired one onto the set of admissible velocities. Instead of
looking at a microscopic setting (where individuals are represented by rigid
discs), here the macroscopic approach is investigated, where the unknwon is the
evolution of the density . If a gradient structure is given, say U is the
opposite of the gradient of D where D is, for instance, the distance to the
exit door, the problem is presented as a Gradient Flow in the Wasserstein space
of probability measures. The functional which gives the Gradient Flow is
neither finitely valued (since it takes into account the constraints on the
density), nor geodesically convex, which requires for an ad-hoc study of the
convergence of a discrete scheme
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