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We present a theory for pitch, a matrix property that is linked to the coupling of rotational and translational motion of rigid bodies at low Reynolds numbers. The pitch matrix is a geometric property of objects in contact with a surrounding fluid, and it can be decomposed into three principal axes of pitch and their associated moments of pitch. The moments of pitch predict the translational motion in a direction parallel to each pitch axis when the object is rotated around that axis and can be used to explain translational drift, particularly for rotating helices. We also provide a symmetrized boundary element model for blocks of the resistance tensor, allowing calculation of the pitch matrix for arbitrary rigid bodies. We analyze a range of chiral objects, including chiral molecules and helices. Chiral objects with a Cn symmetry axis with n > 2 show additional symmetries in their pitch matrices. We also show that some achiral objects have non-vanishing pitch matrices, and we use this result to explain recent observations of achiral microswimmers. We also discuss the small but non-zero pitch of Lord Kelvin’s isotropic helicoid. 

Abstract Observing exoplanets through transmission spectroscopy supplies detailed information about their atmospheric composition, physics and chemistry. Before the James Webb Space Telescope (JWST), these observations were limited to a narrow wavelength range across the near-ultraviolet to near-infrared, alongside broadband photometry at longer wavelengths. To understand more complex properties of exoplanet atmospheres, improved wavelength coverage and resolution are necessary to robustly quantify the influence of a broader range of absorbing molecular species. Here we present a combined analysis of JWST transmission spectroscopy across four different instrumental modes spanning 0.5–5.2 μm using Early Release Science observations of the Saturn-mass exoplanet WASP-39 b. Our uniform analysis constrains the orbital and stellar parameters within subpercentage precision, including matching the precision obtained by the most precise asteroseismology measurements of stellar density to date, and it further confirms the presence of Na, K, H₂O, CO, CO₂and SO₂as atmospheric absorbers. Through this process, we have improved the agreement between the transmission spectra of all modes, except for the NIRSpec PRISM, which is affected by partial saturation of the detector. This work provides strong evidence that uniform light curve analysis is an important aspect to ensuring reliability when comparing the high-precision transmission spectra provided by JWST. 

ABSTRACT In this paper, we present high-resolution spectroscopic transit observations from ESPRESSO of the super-Neptune WASP-166 b. In addition to spectroscopic ESPRESSO data, we analyse photometric data from TESS of six WASP-166 b transits along with simultaneous NGTS observations of the ESPRESSO runs. These observations were used to fit for the planetary parameters as well as assessing the level of stellar activity (e.g. spot crossings, flares) present during the ESPRESSO observations. We utilize the reloaded Rossiter McLaughlin (RRM) technique to spatially resolve the stellar surface, characterizing the centre-to-limb convection-induced variations, and to refine the star–planet obliquity. We find WASP-166 b has a projected obliquity of $$\lambda = -15.52^{+2.85}_{-2.76}\, ^{\circ }$$ and vsin (i) = 4.97 ± 0.09 km s−1 which is consistent with the literature. We were able to characterize centre-to-limb convective variations as a result of granulation on the surface of the star on the order of a few km s−1 for the first time. We modelled the centre-to-limb convective variations using a linear, quadratic, and cubic model with the cubic being preferred. In addition, by modelling the differential rotation and centre-to-limb convective variations simultaneously, we were able to retrieve a potential antisolar differential rotational shear (α ∼ −0.5) and stellar inclination (i* either 42.03$$^{+9.13}_{-9.60}\, ^{\circ }$$ or 133.64$$^{+8.42}_{-7.98}\, ^{\circ }$$ if the star is pointing towards or away from us). Finally, we investigate how the shape of the cross-correlation functions change as a function of limb angle and compare our results to magnetohydrodynamic simulations. 

Twenty-five United Nations member states in the wider Caribbean region ratified the Cartagena Convention, which covers the marine environment of the Gulf of Mexico, the Caribbean Sea and some parts of the Atlantic Ocean. The Land-Based Sources and Activities protocol (LBS Protocol) of that convention addresses nutrient pollution from sewage discharges, agricultural runoff and other sources. Unfortunately, most Caribbean people use conventional onsite wastewater treatment systems (OWTs), especially septic systems. These systems fail to remove nitrogen effectively, posing a challenge for near shore environments. Passive biological nitrogen removal (BNR) processes have been developed for OWTs that rely on simple packed bed bioreactors, with little energy or chemical inputs and low operations and maintenance (O&M) requirements. This paper provides a case study from Florida on the partnerships and pathways for research to develop an innovative technology, Hybrid Adsorption and Biological Treatment System (HABiTS), for nitrogen reduction in OWTs. HABiTS combine ion exchange materials and BNR to remove nitrogen from septic tank effluent and buffer transient loadings. HABiTS, employs natural zeolite material (e.g. clinoptilolite) and expanded clay in the first stage to achieve both ammonium ion exchange and nitrification. The second stage of HABiTS utilizes tire chips, elemental sulphur pellets and oyster shells for adsorption of nitrate as well as sulphur oxidizing denitrification. Under transient load applications, the nitrogen in excess of the biodegradation capacity during high loading events was partially retained within the ion exchange and adsorption materials and readily available later for the microorganisms during lower loading events. Results from a bench scale bioreactor study with marine wastewater, which is relevant to where seawater is used for toilet flushing, are also presented. Pilot scale tests on the OWT of an engaged stakeholder dependent on the marine environment, would contribute to broader discussions for paradigm shifts for nutrient removal from wastewater. 

Planets with radii between that of the Earth and Neptune (hereafter referred to as `sub-Neptunes') are found in close-in orbits around more than half of all Sun-like stars1,2. However, their composition, formation and evolution remain poorly understood3. The study of multiplanetary systems offers an opportunity to investigate the outcomes of planet formation and evolution while controlling for initial conditions and environment. Those in resonance (with their orbital periods related by a ratio of small integers) are particularly valuable because they imply a system architecture practically unchanged since its birth. Here we present the observations of six transiting planets around the bright nearby star HD 110067. We find that the planets follow a chain of resonant orbits. A dynamical study of the innermost planet triplet allowed the prediction and later confirmation of the orbits of the rest of the planets in the system. The six planets are found to be sub-Neptunes with radii ranging from 1.94R⊕ to 2.85R⊕. Three of the planets have measured masses, yielding low bulk densities that suggest the presence of large hydrogen-dominated atmospheres.