Linear non-local diffusion problems in metric measure spaces

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator. We then study the solutions of linear evolution non-local diffusion problems, with emphasis on similarities and differences with the standard heat equation in smooth domains. In particular, we prove weak and strong maximum principles and describe the asymptotic behaviour using spectral methods.

Caught in the act: gas and stellar velocity dispersions in a fast Quenching compact star-forming galaxy at z ~ 1.7

We present Keck I MOSFIRE spectroscopy in the Y and H bands of GDN-8231, a massive, compact, star-forming galaxy at a redshift of z ~ 1.7. Its spectrum reveals both Hα and [Nii] emission lines and strong Balmer absorption lines. The Hα and Spitzer MIPS 24 μm fluxes are both weak, thus indicating a low star-formation rate of SFR≲5-10 M_⨀ yr−1. This, added to a relatively young age of ~700 Myr measured from the absorption lines, provides the first direct evidence for a distant galaxy being caught in the act of rapidly shutting down its star formation. Such quenching allows GDN-8231 to become a compact, quiescent galaxy, similar to three other galaxies in our sample, by z ~ 1.5. Moreover, the color profile of GDN-8231 shows a bluer center, consistent with the predictions of recent simulations for an early phase of inside-out quenching. Its line-of-sight velocity dispersion for the gas, σ_LOG^gas = 127 ± 32 km s^−1, is nearly 40% smaller than that of its stars, σ_LOG^* = 215 ± 35 km s^−1. High-resolution hydro-simulations of galaxies explain such apparently colder gas kinematics of up to a factor of ~1.5 with rotating disks being viewed at different inclinations and/or centrally concentrated star-forming regions. A clear prediction is that their compact, quiescent descendants preserve some remnant rotation from their star-forming progenitors.

Temperature chaos in 3D Ising spin glasses is driven by rare events

Temperature chaos has often been reported in the literature as a rare-event–driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a largedeviations functional that allows to discuss the size dependences. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.

On neutron stars in ƒ (R) theories: Small radii, large masses and large energy emitted in a merger

In the context of ƒ (R) gravity theories, we show that the apparent mass of a neutron star as seen from an observer at infinity is numerically calculable but requires careful matching, first at the star’s edge, between interior and exterior solutions, none of them being totally Schwarzschild-like but presenting instead small oscillations of the curvature scalar R; and second at large radii, where the Newtonian potential is used to identify the mass of the neutron star. We find that for the same equation of state, this mass definition is always larger than its general relativistic counterpart. We exemplify this with quadratic R^2 and Hu-Sawicki-like modifications of the standard General Relativity action. Therefore, the finding of two-solar mass neutron stars basically imposes no constraint on stable ƒ (R) theories. However, star radii are in general smaller than in General Relativity, which can give an observational handle on such classes of models at the astrophysical level. Both larger masses and smaller matter radii are due to much of the apparent effective energy residing in the outer metric for scalar-tensor theories. Finally, because the ƒ (R) neutron star masses can be much larger than General Relativity counterparts, the total energy available for radiating gravitational waves could be of order several solar masses, and thus a merger of these stars constitutes an interesting wave source.