Centre de Physique Théorique


Février 2018

Vendredi 2 février 14:00-15:00, Amphi 5 du CPT

Vortex and mass dynamics over surfaces : Maxwell laws, geometry and surface topology

Stefanella Boatto

In basic courses of mechanics a first approach to central forces and, in particular, to the gravitational force, is made through Newton’s laws and the expression of the Newtonian gravitational force.
It should be pointed out that, in the expression of the force, the 1/r^2 dependence was deduced from Hooke, based on many years of experiments (as a reference see, among others, Arnold’s book ”Huygens and Barrow, Newton and Hooke”). In such an approach the gravitational potential U (r) (F (x) = −grad(U) ) is derived from the knowledge of the force. How to find the expression of the gravitational force when studying the mass dynamics in other geometries ? For examples on surfaces ? We have the problem of not being able to perform two-dimensional experiments to measure the force between two bodies and therefore we must find the answer to the following :

1) How to define a central force in an arbitrary geometry ?
2) Given the distribution of matter on a given surface what is the fundamental equation for deducing the corresponding gravitational potential ?

We propose a formulation of the dynamics directly in the intrinsic geometry of the surface and that uses fundamental solutions of the equation of the gravitational field. We show how the equations of gravitational dynamics are closely linked to those of electric charges and to the dynamics of point vortices. Furthermore, we shall show how known laws, such as Kepler’s laws and some mechanics axioms (Newton’s Laws), may depend on the geometry of the space, i.e. they are not universal properties. Among other things, we show that in the plane the 2-body problem does not obeys to the known Kepler laws. For masses on an infinite cylinder we are able to observe topological effects in the dynamics.

Mercredi 7 février 14:00-15:00, Amphi 5 du CPT

Regularized formulations for hyper-singular boundary integral operators

Tao Yin, (Université de Grenoble, Laboratoire Jean Kuntzmann)


In this talk, the Galerkin boundary element method is concerned for solving the three dimensional exterior elastic and thermoelastic wave scattering problems. New analytically accurate regularized formulations are derived for the hyper-singular boundary integral operators (BIOs) associated with the time-harmonic Navier equation and Biot system of linearized thermoelasticity. Using the derived regularized formulations, all the integrals involved in the weak forms of the hyper-singular BIOs are at most weakly-singular. In numerical implementations, all weakly-singular integrals are evaluated semi-analytically under a special local coordinate system. The accuracy of the regularized formulations is demonstrated using several numerical examples.

Mercredi 14 février 14:00-15:00, Amphi 5 du CPT

Concentrations spectrales pour des Hamiltoniens magnétiques en dimension 2

Vincent Bruneau (IMB, Université de Bordeaux)


Nous nous intéressons à l’opérateur de Schrödinger avec champ magnétique constant en dimension 2 perturbé par un potentiel électrique. Après un rappel des résultats dans le plan tout entier et sur une bande, nous étudierons les phénomènes d’accumulation spectrale dans le cas du demi-plan avec condition de Dirichlet ou de Neumann. Cette partie sur le demi-plan, est tirée d’un travail en collaboration avec Pablo Miranda (Santiago, Chili).

Mercredi 21 février 16:00-17:00, Amphi 5 du CPT

Séminaire de Physique Statistique & Matière Condensée

Alexandre Nicolas (LPTMS, Orsay)

Titre : Bottleneck flows of pedestrian crowds and granular media

Résumé :

Several collective effects in human crowds can be accounted for without entering the complexity of the decision-making process or the detailed interactions between people. In this talk, I will focus on the evacuation of a pedestrian crowd through a narrow door. On the basis of experiments conducted by us and others [1-2], I will show that the dynamics are mostly governed by the density of people in front of the door, irrespective of the individual behaviours, at least at moderate crowd pressure, and I will point to some similarities with granular hopper flows, in particular with respect to the time gaps between successive exits. Then, I will present a model that reproduces many observed features in the dynamics and highlight the mechanisms at their origin.

[1] Garcimartín, A., Zuriguel, I., Pastor, J. M., Martín-Gómez, C., & Parisi, D. R. (2014). Experimental evidence of the “Faster Is Slower” effect. Transportation Research Procedia, 2, 760-767.
[2] Nicolas, Alexandre, Sebastián Bouzat, and Marcelo N. Kuperman. "Pedestrian flows through a narrow doorway : Effect of individual behaviours on the global flow and microscopic dynamics." Transportation Research Part B : Methodological 99 (2017).

Vendredi 23 février 14:00-15:00, Amphi 5 du CPT


Gergely Endrodi