Long Time Evolution of Phase Oscillator Systems

It is shown, under weak conditions, that the dynamical evolution of an important class of large systems of globally coupled, heterogeneous frequency, phase oscillators is, in an appropriate physical sense, time-asymptotically attracted toward a reduced manifold of system states. This manifold, which is invariant under the system evolution, was previously known and used to facilitate the discovery of attractors and bifurcations of such systems. The result of this paper establishes that attractors for the order parameter dynamics obtained by restriction to this reduced manifold are, in fact, the only such attractors of the full system. Thus all long time dynamical behavior of the order parameters of these systems can be obtained by restriction to the reduced manifold.Comment: Improved discussion of Eqs. (28)- (30) Corrected typos. Made notation consisten

Radioactive nuclei from cosmochronology to habitability

In addition to long-lived radioactive nuclei like U and Th isotopes, which have been used to measure the age of the Galaxy, also radioactive nuclei with half-lives between 0.1 and 100 million years (short-lived radionuclides, SLRs) were present in the early Solar System (ESS), as indicated by high-precision meteoritic analysis. We review the most recent meteoritic data and describe the nuclear reaction processes responsible for the creation of SLRs in different types of stars and supernovae. We show how the evolution of radionuclide abundances in the Milky Way Galaxy can be calculated based on their stellar production. By comparing predictions for the evolution of galactic abundances to the meteoritic data we can build up a time line for the nucleosynthetic events that predated the birth of the Sun, and investigate the lifetime of the stellar nursery where the Sun was born. We then review the scenarios for the circumstances and the environment of the birth of the Sun within such a stellar nursery that have been invoked to explain the abundances in the ESS of the SLRs with the shortest lives - of the order of million years or less. Finally, we describe how the heat generated by radioactive decay and in particular by the abundant 26Al in the ESS had important consequences for the thermo-mechanical and chemical evolution of planetesimals, and discuss possible implications on the habitability of terrestrial-like planets. We conclude with a set of open questions and future directions related to our understanding of the nucleosynthetic processes responsible for the production of SLRs in stars, their evolution in the Galaxy, the birth of the Sun, and the connection with the habitability of extra-solar planets.Comment: Review published in Progress in Particle and Nuclear Physics. The article is being published Open Access, access to the full article is not restricted in any way. Please download the final version of the paper at https://doi.org/10.1016/j.ppnp.2018.05.00

The Role of Turbulence in Neutrino-Driven Core-Collapse Supernova Explosions

The neutrino-heated "gain layer" immediately behind the stalled shock in a core-collapse supernova is unstable to high-Reynolds-number turbulent convection. We carry out and analyze a new set of 19 high-resolution three-dimensional (3D) simulations with a three-species neutrino leakage/heating scheme and compare with spherically-symmetric (1D) and axisymmetric (2D) simulations carried out with the same methods. We study the postbounce supernova evolution in a $15$-$M_\odot$ progenitor star and vary the local neutrino heating rate, the magnitude and spatial dependence of asphericity from convective burning in the Si/O shell, and spatial resolution. Our simulations suggest that there is a direct correlation between the strength of turbulence in the gain layer and the susceptability to explosion. 2D and 3D simulations explode at much lower neutrino heating rates than 1D simulations. This is commonly explained by the fact that nonradial dynamics allows accreting material to stay longer in the gain layer. We show that this explanation is incomplete. Our results indicate that the effective turbulent ram pressure exerted on the shock plays a crucial role by allowing multi-D models to explode at a lower postshock thermal pressure and thus with less neutrino heating than 1D models. We connect the turbulent ram pressure with turbulent energy at large scales and in this way explain why 2D simulations are erroneously exploding more easily than 3D simulations.Comment: 13 pages, 8 figures, accepted by Ap

Claudins in the Renal Collecting Duct

The renal collecting duct fine-tunes urinary composition, and thereby, coordinates key physiological processes, such as volume/blood pressure regulation, electrolyte-free water reabsorption, and acid-base homeostasis. The collecting duct epithelium is comprised of a tight epithelial barrier resulting in a strict separation of intraluminal urine and the interstitium. Tight junctions are key players in enforcing this barrier and in regulating paracellular transport of solutes across the epithelium. The features of tight junctions across different epithelia are strongly determined by their molecular composition. Claudins are particularly important structural components of tight junctions because they confer barrier and transport properties. In the collecting duct, a specific set of claudins (Cldn-3, Cldn-4, Cldn-7, Cldn-8) is expressed, and each of these claudins has been implicated in mediating aspects of the specific properties of its tight junction. The functional disruption of individual claudins or of the overall barrier function results in defects of blood pressure and water homeostasis. In this concise review, we provide an overview of the current knowledge on the role of the collecting duct epithelial barrier and of claudins in collecting duct function and pathophysiology