1,450 research outputs found
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
Mathematical existence results for the Doi-Edwards polymer model
In this paper, we present some mathematical results on the Doi-Edwards model
describing the dynamics of flexible polymers in melts and concentrated
solutions. This model, developed in the late 1970s, has been used and tested
extensively in modeling and simulation of polymer flows. From a mathematical
point of view, the Doi-Edwards model consists in a strong coupling between the
Navier-Stokes equations and a highly nonlinear constitutive law.
The aim of this article is to provide a rigorous proof of the well-posedness
of the Doi-Edwards model, namely it has a unique regular solution. We also
prove, which is generally much more difficult for flows of viscoelastic type,
that the solution is global in time in the two dimensional case, without any
restriction on the smallness of the data.Comment: 48 page
Global existence results for some viscoelastic models with an integral constitutive law
We provide a proof of global regularity of solutions of some models of
viscoelastic flow with an integral constitutive law, in the two spatial
dimensions and in a periodic domain. Models that are included in these results
are classical models for flow memory: for instance some K-BKZ models, the PSM
model or the Wagner model. The proof is based on the fact that these models
naturally give a -bound on the stress and that they allow to control
the spatial gradient of the stress. The main result does not cover the case of
the Oldroyd-B model
Convergence to the Reynolds approximation with a double effect of roughness
We prove that the lubrication approximation is perturbed by a non-regular
roughness of the boundary. We show how the flow may be accelerated using
adequate rugosity profiles on the bottom. We explicit the possible effects of
some abrupt changes in the profile. The limit system is mathematically
justified through a variant of the notion of two-scale convergence. Finally, we
present some numerical results, illustrating the limit system in the
three-dimensional case
Low-Thrust Lyapunov to Lyapunov and Halo to Halo with -Minimization
In this work, we develop a new method to design energy minimum low-thrust
missions (L2-minimization). In the Circular Restricted Three Body Problem, the
knowledge of invariant manifolds helps us initialize an indirect method solving
a transfer mission between periodic Lyapunov orbits. Indeed, using the PMP, the
optimal control problem is solved using Newton-like algorithms finding the zero
of a shooting function. To compute a Lyapunov to Lyapunov mission, we first
compute an admissible trajectory using a heteroclinic orbit between the two
periodic orbits. It is then used to initialize a multiple shooting method in
order to release the constraint. We finally optimize the terminal points on the
periodic orbits. Moreover, we use continuation methods on position and on
thrust, in order to gain robustness. A more general Halo to Halo mission, with
different energies, is computed in the last section without heteroclinic orbits
but using invariant manifolds to initialize shooting methods with a similar
approach
Viscoroute 2.0: a tool for the simulation of moving load effects on asphalt pavement
As shown by strains measured on full scale experimental aircraft structures,
traffic of slow-moving multiple loads leads to asymmetric transverse strains
that can be higher than longitudinal strains at the bottom of asphalt pavement
layers. To analyze this effect, a model and a software called ViscoRoute have
been developed. In these tools, the structure is represented by a multilayered
half-space, the thermo-viscoelastic behaviour of asphalt layers is accounted by
the Huet-Sayegh rheological law and loads are assumed to move at constant
speed. First, the paper presents a comparison of results obtained with
ViscoRoute to results stemming from the specialized literature. For thick
asphalt pavement and several configurations of moving loads, other ViscoRoute
simulations confirm that it is necessary to incorporate viscoelastic effects in
the modelling to well predict the pavement behaviour and to anticipate possible
damages in the structure.Comment: 27 pages
Roughness effect on the Neumann boundary condition
36 pagesInternational audienceWe study the effect of a periodic roughness on a Neumann boundary condition. We show that, as in the case of a Dirichlet boundary condition, it is possible to approach this condition by a more complex law on a domain without rugosity, called wall law. This approach is however different from that usually used in Dirichlet case. In particular, we show that this wall law can be explicitly written using an energy developed in the roughness boundary layer. The first part deals with the case of a Laplace operator in a simple domain but many more general results are next given: when the domain or the operator are more complex, or with Robin-Fourier boundary conditions. Some numerical illustrations are used to obtain magnitudes for the coefficients appearing in the new wall laws. Finally, these wall laws can be interpreted using a fictive boundary without rugosity. That allows to give an application to the water waves equation
Handling congestion in crowd motion modeling
We address here the issue of congestion in the modeling of crowd motion, in
the non-smooth framework: contacts between people are not anticipated and
avoided, they actually occur, and they are explicitly taken into account in the
model. We limit our approach to very basic principles in terms of behavior, to
focus on the particular problems raised by the non-smooth character of the
models. We consider that individuals tend to move according to a desired, or
spontanous, velocity. We account for congestion by assuming that the evolution
realizes at each time an instantaneous balance between individual tendencies
and global constraints (overlapping is forbidden): the actual velocity is
defined as the closest to the desired velocity among all admissible ones, in a
least square sense. We develop those principles in the microscopic and
macroscopic settings, and we present how the framework of Wasserstein distance
between measures allows to recover the sweeping process nature of the problem
on the macroscopic level, which makes it possible to obtain existence results
in spite of the non-smooth character of the evolution process. Micro and macro
approaches are compared, and we investigate the similarities together with deep
differences of those two levels of description
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