Interaction of point sources and vortices for incompressible planar fluids

We consider a new system of differential equations which is at the same time gradient and locally Hamiltonian. It is obtained by just replacing a factor in the equations of interaction for N point vortices, and it is interpreted as an interaction of N point sources. Because of the local Hamiltonian structure and the symmetries it obeys, it does possess some of the first integrals that appear in the N vortex problem. We will show that binary collisions are easily blown up in this case since the equations of motion are of first order. This method may be easily generalized to the blow up of higher order collisions. We then generalize the model further to interactions of sources and vortices.Comment: 9 page

Blow up of mechanical systems with a homogeneous energy

By using the ideas introduced by McGehee in the study of thesingularities in some problems of Celestial Mechanics, we study the singularities at the origin and at the infinity for some classical mechanical systems with homogeneous kinetic and potential energy functions. For these systems the origin and the infinity of the configuration coordinates is usually a singularity or a nullity of the Hamiltonian function and the vector field. This work generalizes a previous one by the first and the third authors, where the kinetic energy did not depend on the configuration coordinates

On the periodic orbits of the circular double Sitnikov problem

We introduce a restricted four body problem in a 2+2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the planewhere the primaries evolve, so almost every solution is a collision orbit. We extend the solutions beyond collisions with a symplectic regularization and study the set of energy surfaces that contain periodic orbits.Comment: 4 pages. Accepted in C. R. Acad. Sci. de Paris, Serie I. This is not the final versio

Early Adolescents’ Food Selection After Evaluating the Healthiness of Remote Peers’ Food Choices

This study investigates whether asking early adolescents to evaluate the food choices of remote peers improves their own food selection. Participants were students from fifth (N = 219, Mage = 9.30 years) and sixth grades (N = 248, Mage = 10.28 years) of varying nationalities living in the United Arab Emirates (race and ethnicity were not collected). Students saw peers\u27 healthy or unhealthy food choices before picking their own food. In some conditions, students also critically evaluated the healthiness of the peers\u27 choices. Evaluation of peer choices led to healthier decisions (d = .53) to the point that it offsets the negative impact of observing unhealthy peer choices. This effect is larger for sixth graders compared to fifth graders

Revisiting Strategic versus Non-Strategic Cooperation

We use a novel experimental design to disentangle strategically- and non-strategically-motivated cooperation. By using contingent responses in a repeated sequential prisoners’ dilemma with a known probabilistic end, we differentiate end-game behavior from continuation behavior within individuals while controlling for expectations. This design allows us to determine the extent to which strategically-cooperating individuals are responsible for the so-called endgame effect. Experiments with two different subject pools indicate that the most common motive for cooperation in repeated games is strategic and that the extent to which endgame effects are driven by strategically-cooperating individuals depends on the profitability of cooperation.