Topological character of hydrodynamic screening in suspensions of hard spheres: an example of universal phenomenon

Although in the case of polymer solutions the existence of hydrodynamic screening is considered as established, use of the same methods for suspensions of hard spheres so far have failed to produce similar results. In this work we reconsider this problem. Using superposition of topological, combinatorial and London-style qualitative arguments, we prove the existence of screening in suspensions. We show that the nature of hydrodynamic screening in suspensions is analogous to that known for the Meissner effect in superconductors. The extent of screening depends on volume fraction of hard spheres. The zero volume fraction limit corresponds to the normal state. The case of finite volume fractions-to the mixed state typical for superconductors of the second kind. Such a state is becoming fully "superconducting" at some critical volume fraction for which the (zero frequency) relative viscosity diverges. Our analytical results describing this divergence are in accord with known scaling results obtained by Brady and Bicerano et al which are well supported by experimental data. We provide theoretical explanation of the divergence of relative viscosity in terms of a topological-type transition which mathematically can be made isomorphic to the more familiar Bose-Einstein condensation transition. Because of this, the methods developed in this work are not limited to suspensions only. In concluding section we mention other applications of the developed formalism ranging from turbulence and magnetohydrodynamics to high temperature superconductors, QCD, string models, etc.Comment: 49 page

The First Habitable-zone Earth-sized Planet from TESS. I. Validation of the TOI-700 System

We present the discovery and validation of a three-planet system orbiting the nearby (31.1 pc) M2 dwarf star TOI-700 (TIC 150428135). TOI-700 lies in the TESS continuous viewing zone in the Southern Ecliptic Hemisphere; observations spanning 11 sectors reveal three planets with radii ranging from 1 R⊕ to 2.6 R⊕ and orbital periods ranging from 9.98 to 37.43 days. Ground-based follow-up combined with diagnostic vetting and validation tests enables us to rule out common astrophysical false-positive scenarios and validate the system of planets. The outermost planet, TOI-700 d, has a radius of 1.19 ± 0.11 R⊕ and resides within a conservative estimate of the host star's habitable zone, where it receives a flux from its star that is approximately 86% of Earth's insolation. In contrast to some other low-mass stars that host Earth-sized planets in their habitable zones, TOI-700 exhibits low levels of stellar activity, presenting a valuable opportunity to study potentially rocky planets over a wide range of conditions affecting atmospheric escape. While atmospheric characterization of TOI-700 d with the James Webb Space Telescope (JWST) will be challenging, the larger sub-Neptune, TOI-700 c (R = 2.63 R⊕), will be an excellent target for JWST and future space-based observatories. TESS is scheduled to once again observe the Southern Hemisphere, and it will monitor TOI-700 for an additional 11 sectors in its extended mission. These observations should allow further constraints on the known planet parameters and searches for additional planets and transit timing variations in the system