# Calendar

## February 2018

### 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.

### Regularized formulations for hyper-singular boundary integral operators

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

### Concentrations spectrales pour des Hamiltoniens magnétiques en dimension 2

#### Vincent Bruneau (IMB, Université de Bordeaux)

### 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).

### Pion stars from lattice QCD

#### Gergely Endrodi

A novel type of compact star is proposed that consists of a Bose-Einstein

condensate of charged pions and a gas of electrons. The equation of state and

the mass-radius relation of such objects can be determined from first-principle

lattice QCD simulations. It is demonstrated that pion star matter exhibits

gravitationally bound configurations and is metastable against electroweak

decays. The ingredients of the lattice simulations as well as of the

construction of the stars will be discussed in detail.