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In this work, we prove a threshold theorem for the 2D Navier-Stokes equations posed on the periodic channel, $$\mathbb{T} \times [-1,1]$$, supplemented with Navier boundary conditions $$\omega|_{y = \pm 1} = 0$$. Initial datum is taken to be a perturbation of Couette in the following sense: the shear component of the perturbation is assumed small (in an appropriate Sobolev space) but importantly is independent of $$\nu$$. On the other hand, the nonzero modes are assumed size $$O(\nu^{\frac12})$$ in an anisotropic Sobolev space. For such datum, we prove nonlinear enhanced dissipation and inviscid damping for the resulting solution. The principal innovation is to capture quantitatively the \textit{inviscid damping}, for which we introduce a new Singular Integral Operator which is a physical space analogue of the usual Fourier multipliers which are used to prove damping. We then include this SIO in the context of a nonlinear hypocoercivity framework. 

International Ocean Discovery Program (IODP) Expedition 399 collected new cores from the Atlantis Massif (30°N; Mid-Atlantic Ridge), an oceanic core complex that hosts the Lost City hydrothermal field (LCHF). Studies of the Atlantis Massif and the LCHF have transformed our understanding of tectonic, magmatic, hydrothermal, and microbial processes at slow-spreading ridges. The Atlantis Massif was the site of four previous expeditions (Integrated Ocean Drilling Program Expeditions 304, 305, and 340T and IODP Expedition 357) and numerous dredging and submersible expeditions. The deepest IODP hole in young (<2 My) oceanic lithosphere, Hole U1309D, was drilled ~5 km north of the LCHF and reached 1415 meters below seafloor (mbsf) through a series of primitive gabbroic rocks. A series of 17 shallow (<16.4 mbsf) holes were also drilled at 9 sites across the south wall of the massif during Expedition 357, recovering heterogeneous rock types including hydrothermally altered peridotites, gabbroic, and basaltic rocks. The hydrologic regime differs between the two locations, with a low-permeability conductive regime in Hole U1309D and a high- (and possibly deep-reaching) permeability regime along the southern wall. Expedition 399 targeted Hole U1309D and the southern wall area to collect new data on ancient processes during deformation and alteration of detachment fault rocks. The recovered rocks and fluids are providing new insights into past and ongoing water-rock interactions, processes of mantle partial melting and gabbro emplacement, deformation over a range of temperatures, abiotic organic synthesis reactions, and the extent and diversity of life in the subseafloor in an actively serpentinizing system. We sampled fluids and measured temperature in Hole U1309D before deepening it to 1498 mbsf. The thermal structure was very similar to that measured during Expedition 340T, and lithologies were comparable to those found previously in Hole U1309D. A significant zone of cataclasis and alteration was found at 1451–1474 mbsf. A new Hole U1601C (proposed Site AMDH-02A) was drilled on the southern ridge close to Expedition 357 Hole M0069A, where both deformed and undeformed serpentinites had previously been recovered. Rapid drilling rates achieved a total depth of 1267.8 mbsf through predominantly ultramafic (68%) and gabbroic (32%) rocks, far surpassing the previous drilling record in a peridotite-dominated system of 201 m. Recovery was excellent overall (71%) but particularly high in peridotite-dominated sections where recovery regularly exceeded 90%. The recovery of sizable sections of largely intact material will provide robust constraints on the architecture and composition of the oceanic mantle lithosphere. The deepest portions of the newly drilled borehole may be beyond the known limits of life, providing the means to assess the role of biological activity across the transition from a biotic to an abiotic regime. Borehole fluids from both holes were collected using both the Kuster Flow-Through Sampler and the new Multi-Temperature Fluid Sampler. Wireline logging in Hole U1601C provided information on downhole density and resistivity, imaged structural features, and documented fracture orientations. A reentry system was installed in Hole U1601C, and both it and Hole U1309D were left open for future deep drilling, fluid sampling, and potential borehole observatories. 

The interaction between radio jets and quasar host galaxies plays a paramount role in quasar and galaxy co-evolution. However, very little is known at present about this interaction at very high−z. Here, we present new Atacama Large Millimeter/submillimeter Array (ALMA) observations in Bands 7 and 3 of six radio-loud (RL) quasar host galaxies atz > 5. We recovered [C II] 158 μm line and underlying dust continuum emission at > 2σfor five sources, while we obtained upper limits for the CO(6-5) emission line and continuum for the remaining source. At the spatial resolution of our observations (∼1″​​_.0–1″​​_.4), we did not recover any perturbed or extended morphologies or kinematics, which are known signatures of potential mergers. These galaxies already host large quantities of gas (∼10¹⁰M_⊙), with [C II] luminosities ofL_[C II] ∼ 10^8 − 9 L_⊙and [C II]-based star formation rates of 30 − 400 M_⊙yr⁻¹. In building their radio/submillimeter (radio/submm) spectral energy distributions (SEDs), we found that in at least four cases, the 1 mm continuum intensity arises from a combination of synchrotron and dust emission. The initial estimation of synchrotron contribution at 300 GHz in these cases is of ≳10%. Assuming a scenario where the continuum emission is solely due to cold dust as an upper limit, we obtained infrared (IR) luminosities ofL_IR ∼ 10^{11 − 12} L_⊙. We compared the properties of the sources inspected here with a large collection of radio-quiet sources from the literature, as well as a sample of RL quasars from previous studies at comparable redshifts. We recovered a mild potential decrease inL_[C II]for the RL sources, which might be due to a suppression of the cool gas emission due to the radio jets. We did not find any [C II] emitting companion galaxy candidate around the five RL quasars observed in Band 7. Given the depth of our dataset, this result is still consistent with what has been observed around radio-quiet quasars. Future higher spatial-resolution observations, over a broader frequency range, of high−zRL quasars hosts will allow us to further improve our understanding of the physics of these sources.