Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci

This paper presents new analytical formulae for flow in a channel with one or both walls patterned with a longitudinal array of ridges and arbitrarily protruding menisci. Derived from a matched asymptotic expansion, they extend results by Crowdy (J. Fluid Mech., vol. 791, 2016, R7) for shear flow, and thus make no restriction on the protrusion into or out of the liquid. The slip length formula is compared against full numerical solutions and, despite the assumption of small ridge period in its derivation, is found to have a very large range of validity; relative errors are small even for periods large enough for the protruding menisci to degrade the flow and touch the opposing wall.Comment: 13 pages; supplementary material included in ancillary file

The relationship between cell size and cell fate in Volvox carteri

In Volvox carteri development, visibly asymmetric cleavage divisions set apart large embryonic cells that will become asexual reproductive cells (gonidia) from smaller cells that will produce terminally differentiated somatic cells. Three mechanisms have been proposed to explain how asymmetric division leads to cell specification in Volvox: (a) by a direct effect of cell size (or a property derived from it) on cell specification, (b) by segregation of a cytoplasmic factor resembling germ plasm into large cells, and (c) by a combined effect of differences in cytoplasmic quality and cytoplasmic quantity. In this study a variety of V. carteri embryos with genetically and experimentally altered patterns of development were examined in an attempt to distinguish among these hypotheses. No evidence was found for regionally specialized cytoplasm that is essential for gonidial specification. In all cases studied, cells with a diameter > approximately 8 microns at the end of cleavage--no matter where or how these cells had been produced in the embryo--developed as gonidia. Instructive observations in this regard were obtained by three different experimental interventions. (a) When heat shock was used to interrupt cleavage prematurely, so that presumptive somatic cells were left much larger than they normally would be at the end of cleavage, most cells differentiated as gonidia. This result was obtained both with wild-type embryos that had already divided asymmetrically (and should have segregated any cytoplasmic determinants involved in cell specification) and with embryos of a mutant that normally produces only somatic cells. (b) When individual wild-type blastomeres were isolated at the 16-cell stage, both the anterior blastomeres that normally produce two gonidia each and the posterior blastomeres that normally produce no gonidia underwent modified cleavage patterns and each produced an average of one large cell that developed as a gonidium. (c) When large cells were created microsurgically in a region of the embryo that normally makes only somatic cells, these large cells became gonidia. These data argue strongly for a central role of cell size in germ/soma specification in Volvox carteri, but leave open the question of how differences in cell size are actually transduced into differences in gene expression

A Vavilovian approach to discovering crop-associated microbes with potential to enhance plant immunity

Through active associations with a diverse community of largely non-pathogenic microbes, a plant may be thought of as possessing an “extended genotype,” an interactive cross-organismal genome with potential, exploitable implications for plant immunity. The successful enrichment of plant microbiomes with beneficial species has led to numerous commercial applications, and the hunt for new biocontrol organisms continues. Increasingly flexible and affordable sequencing technologies, supported by increasingly comprehensive taxonomic databases, make the characterization of non-model crop-associated microbiomes a widely accessible research method toward this end; and such studies are becoming more frequent. A summary of this emerging literature reveals, however, the need for a more systematic research lens in the face of what is already a metagenomics data deluge. Considering the processes and consequences of crop evolution and domestication, we assert that the judicious integration of in situ crop wild relatives into phytobiome research efforts presents a singularly powerful tool for separating signal from noise, thereby facilitating a more efficient means of identifying candidate plant-associated microbes with the potential for enhancing the immunity and fitness of crop species

Triton: A hot potato

The effect of sunlight on the surface of Triton was studied. Widely disparate models of the active geysers observed during Voyager 2 flyby were proposed, with a solar energy source almost their only feature. Yet Triton derives more of its heat from internal sources (energy released by the radioactive decay) than any other icy satellite. The effect of this relatively large internal heat on the observable behavior of volatiles on Triton's surface is investigated. The following subject areas are covered: the Global Energy Budget; insulation polar caps; effect on frost stability; mantle convection; and cryovolcanism

The role of nonuniform internal heating in Triton's energy budget

Triton's large heliocentric distance and high albedo, combined with its unusually large silicate mass fraction, make internal heating more important in its energy budget than in that of any other icy satellite. Brown et al. have recently estimated that the average radiogenic heat flux (which is probably between 3.3 and 6.6 mW/sq m depending on core size and composition) may equal 5 to 20 pct. of the average absorbed insolation. On a global scale, this additional energy input appreciably increases the thermal emissivity required to be consistent with the observed surface temperature. Brown et al. also speculated that spatial variations of the internal flux may change the local sublimation deposition balance enough to lead to observable modifications of the distribution of volatiles on Triton's surface. An attempt is made to estimate the magnitude of internal heat flux variations due to the insulating effect of the polar caps, to mantle convection, and to cryovolcanism; the importance is evaluated of these variations in modifying the volatile distribution

Experimental study of a vortex subjected to imposed strain

An experimental project was undertaken to investigate the character of vortex breakdown with particular regard to the waveguide theories of vortex breakdown. A rectangular wing based on the NACA 0012 airfoil was used to produce a trailing vortex which convected downstream without undergoing breakdown. Dye marked the vortex location. A disturbance was then introduced onto the vortex using a small moving wire to 'cut' the vortex. The development of upstream and downstream propagating disturbance waves was observed and the propagation velocities measured. The downstream traveling wave produced a structure similar in appearance to a vortex breakdown. The upstream wave produced a moving, swirling, turbulent region that was not a vortex breakdown. The waves moving in either direction have the same swirl velocity profiles but quite different axial velocity profiles. The upstream disturbance (turbulence) moved into a flow with an axial velocity profile that had a wake-like defect in the core region. The downstream moving vortex breakdown moved into a flow with a jet-like overshoot in the core region. The fact that no breakdown was observed for the wake-like defect and breakdown was observed for the jet-like overshoot is not consistent with computational fluid dynamics (CFD) calculations. Although there are not a lot of examples, CFD results show breakdown for both types of profiles. The longitudinal and swirl velocity profiles were documented by Laser Doppler Velocimeter (LDV) measurement. Wave velocities, swirl angles, and swirl parameters are reported

Analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains

This paper presents the first analysis of a space--time hybridizable discontinuous Galerkin method for the advection--diffusion problem on time-dependent domains. The analysis is based on non-standard local trace and inverse inequalities that are anisotropic in the spatial and time steps. We prove well-posedness of the discrete problem and provide a priori error estimates in a mesh-dependent norm. Convergence theory is validated by a numerical example solving the advection--diffusion problem on a time-dependent domain for approximations of various polynomial degree