Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces

We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and collate useful vector calculus identities for these coordinates. These results and provided code enable consistent accounting of geometric effects in the derivation of boundary layer asymptotics for a wide range of physical systems.Comment: 24 pages, 3 figures, Mathematica code available at https://github.com/ericwhester/signed-distance-cod

On the stability of isothermal shocks in black hole accretion disks

Most black holes possess accretion disks. Models of such disks inform observations and constrain the properties of the black holes and their surrounding medium. Here, we study isothermal shocks in a thin black hole accretion flow. Modelling infinitesimal molecular viscosity allows the use of multiple-scales matched asymptotic methods. We thus derive the first explicit calculations of isothermal shock stability. We find that the inner shock is always unstable, and the outer shock is always stable. The growth/decay rates of perturbations depend only on an effective potential and the incoming--outgoing flow difference at the shock location. We give a prescription of accretion regimes in terms of angular momentum and black hole radius. Accounting for angular momentum dissipation implies unstable outer shocks in much of parameter space, even for realistic viscous Reynolds numbers of the order $\approx 10^{20}$.Comment: 26 page

Bistability in Rayleigh-B\'enard convection with a melting boundary

A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and solid phases appears. Depending on the initial conditions, freezing or melting occurs until the interface eventually converges towards a stationary state. This evolution is studied numerically in a two-dimensional configuration using a phase-field method coupled with the Navier-Stokes equations. Varying the control parameters of the model, we exhibit two types of equilibria: diffusive and convective. In the latter case, Rayleigh-B\'enard convection in the liquid phase shapes the solid-liquid front, and a macroscopic topography is observed. A simple way of predicting these equilibrium positions is discussed and then compared with the numerical simulations. In some parameter regimes, we show that multiple equilibria can coexist depending on the initial conditions. We also demonstrate that, in this bi-stable regime, transitioning from the diffusive to the convective equilibrium is inherently a nonlinear mechanism involving finite-amplitude perturbations

Magneto-Stokes Flow in a Shallow Free-Surface Annulus

We analyse a magnetohydrodynamic flow inspired by the kinematic reversibility of viscous Taylor-Couette flows. The system considered here shares the cylindrical-annular geometry of the Taylor-Couette cell, but uses applied electromagnetic forces to drive "magneto-Stokes" flow in a shallow, free-surface layer of electrolyte. An analytical solution is presented and validated with coupled laboratory and numerical experiments. The dominant balance of Lorentz forcing and basal viscous drag reproduces the kinematic reversibility observed by G.I. Taylor with precise electromagnetic control. Induced fluid deformation may be undone by simply reversing the polarity of electric current through the system. We illustrate this analogy with theory and experiment, and we draw a further connection to potential flow using the Hele-Shaw approximation. The stability and controllability of the magneto-Stokes system make it an attractive tool for investigating shear flows in a variety of settings from industrial to astrophysical. In addition, the set-up's simplicity and robustness make magneto-Stokes flow a good candidate for PIV calibration and for educational demonstrations of magnetohydrodynamics, boundary layers, and flow transition

Fluid dynamics alters liquid-liquid phase separation in confined aqueous two-phase systems

Liquid-liquid phase separation is key to understanding aqueous two-phase systems (ATPS) arising throughout cell biology, medical science, and the pharmaceutical industry. Controlling the detailed morphology of phase-separating compound droplets leads to new technologies for efficient single-cell analysis, targeted drug delivery, and effective cell scaffolds for wound healing. We present a computational model of liquid-liquid phase separation relevant to recent laboratory experiments with gelatin-polyethylene glycol mixtures. We include buoyancy and surface-tension-driven finite viscosity fluid dynamics with thermally induced phase separation. We show that the fluid dynamics greatly alters the evolution and equilibria of the phase separation problem. Notably, buoyancy plays a critical role in driving the ATPS to energy-minimizing crescent-shaped morphologies and shear flows can generate a tenfold speedup in particle formation. Neglecting fluid dynamics produces incorrect minimum-energy droplet shapes. The model allows for optimization of current manufacturing procedures for structured microparticles and improves understanding of ATPS evolution in confined and flowing settings important in biology and biotechnology.Comment: 9 pages, 8 figures, 3 supplementary movies, to appear in Proceedings of the National Academy of Sciences, accompanying code and parameters to generate data available at https://github.com/ericwhester/multiphase-fluids-cod

Pre-main sequence stars in the Cepheus flare region

We present results of optical spectroscopic and BVR_CI_C photometric observations of 77 pre-main sequence (PMS) stars in the Cepheus flare region. A total of 64 of these are newly confirmed PMS stars, originally selected from various published candidate lists. We estimate effective temperatures and luminosities for the PMS stars, and comparing the results with pre-main sequence evolutionary models we estimate stellar masses of 0.2-2.4M_sun and stellar ages of 0.1-15 Myr. Among the PMS stars, we identify 15 visual binaries with separations of 2-10 arcsec. From archival IRAS, 2MASS, and Spitzer data, we construct their spectral energy distributions and classify 5% of the stars as Class I, 10% as Flat SED, 60% as Class II, and 3% as Class III young stellar objects (YSOs). We identify 12 CTTS and 2 WTTS as members of NGC 7023, with mean age of 1.6 Myr. The 13 PMS stars associated with L1228 belong to three small aggregates: RNO 129, L1228A, and L1228S. The age distribution of the 17 PMS stars associated with L1251 suggests that star formation has propagated with the expansion of the Cepheus flare shell. We detect sparse aggregates of 6-7 Myr old PMS stars around the dark clouds L1177 and L1219, at a distance of 400 pc. Three T Tauri stars appear to be associated with the Herbig Ae star SV Cep at a distance of 600 pc. Our results confirm that the molecular complex in the Cepheus flare region contains clouds of various distances and star forming histories.Comment: 61 pages, 27 figures, 8 tables; accepted for publication by ApJ

The Uses of Stance in Media Production: Embodied Sociolinguistics and Beyond

While many conversation analysts, and scholars in related fields, have used video-recordings to study interaction, this study is one of a small but growing number that investigates video-recordings of the joint activities of media professionals working with, and on, video. It examines practices of media production that are, in their involvement with the visual and verbal qualities of video, both beyond talk and deeply shaped by talk. The article draws upon video recordings of the making of a feature-length documentary. In particular, it analyses a complex course of action where an editing team are reviewing their interview of the subject of the documentary, their footage is being intercut with existing reality TV footage of that same interviewee. The central contributions that the article makes are, firstly, to the sociolinguistics of mediatisation, through the identification of the workplace concerns of the members of the editing team, secondly showing how editing is accomplished, moment-by-moment, through the use of particular forms of embodied action and, finally, how the media themselves feature in the ordering of action. While this is professional work it sheds light on the video-mediated practices in contemporary culture, especially those found in social media where video makers carefully consider their editing of the perspective toward themselves and others