尼斯大学

We show that a generic analytic strongly convex billiard is "maximally chaotic" in the sense that, for every rational number p/q∈ℚ∩ (0,1), all intersections between the stable and unstable manifolds of maximizing periodic orbits with rotation number p/q are transverse.

In this paper, we construct a new class of uniformly rotating vortex sheets arising as perturbations of the circular configuration within the Kelvin–Helmholtz model for two incompressible fluids of equal density, with surface tension effects taken into account. Despite the fundamental importance of the problem, few results are available on the long-time dynamics, due to the strong instability inherent in the Kelvin–Helmholtz mechanism. We carry out a detailed bifurcation analysis and construct families of nontrivial rotating solutions that bifurcate from the circular state when either the rotational speed or the surface tension coefficient is varied. The stationary branches obtained by varying the mean vorticity follow from the same analysis through the scaling symmetry of the equations.

Quasars hosting greater than or similar to 10(9) M-circle dot black holes at z > 6 challenge growth scenarios that start from light seeds and assume accretion within already formed galaxies. Motivated by the James Webb Space Telescope (JWST) discovery of Little Red Dots (LRDs), which suggests that similar to 10(6) M-circle dot black holes can be active in compact, pre-galactic environments, we revisit early black hole growth with a minimal cosmology-based framework. We model the accretion history as the smaller of the Bondi inflow rate and the Eddington-limited rate, where the Bondi rate is set by the supply of overdense primordial gas whose density declines with cosmic expansion, and the Eddington rate captures regulation by radiative feedback. By fitting the observed masses and luminosities of J0313-1806(z = 7.64) and J0100+2802 (z = 6.30) with Bayesian inference, we infer initial conditions that favor massive seed black holes with initial mass M-0 similar to 10(6) M-circle dot, formed at z similar to 20-30 in environments with baryonic overdensity factors f(rho) greater than or similar to 50 relative to the cosmic mean. The resulting growth histories include a prolonged supply-limited stage, and they reproduce the observed quasar masses without requiring sustained Eddington accretion or any super-Eddington episodes. The inferred seed mass scale is consistent with black holes produced by the collapse of quantum-degenerate fermion dark matter cores, providing a physically defined pathway to massive seeds at the redshifts implied by LRD phenomenology.

We study a problem of minimal surfaces with free boundary written in the form of a non convex minimization problem. Our aim is to characterize optimal solutions by finding a suitable calibration field. A natural upper bound of the infimum is given by a variant of the Cheeger problem that we solve explicitly proving the optimality thanks to the construction of a cut-locus potential. The comparison with the original problem is then discussed in detail.