Wettability-independent droplet transport by \emph{Bendotaxis}

We demonstrate \textit{bendotaxis}, a novel mechanism for droplet self-transport at small scales. A combination of bending and capillarity in a thin channel causes a pressure gradient that, in turn, results in the spontaneous movement of a liquid droplet. Surprisingly, the direction of this motion is always the same, regardless of the wettability of the channel. We use a combination of experiments at a macroscopic scale and a simple mathematical model to study this motion, focussing in particular on the time scale associated with the motion. We suggest that \emph{bendotaxis} may be a useful means of transporting droplets in technological applications, for example in developing self-cleaning surfaces, and discuss the implications of our results for such applications.Comment: 5 pages, 4 figures. Supplementary Information available on reques

Tipping point in ice-sheet grounding-zone melting due to ocean water intrusion

Marine ice sheets are highly sensitive to submarine melting in their grounding zones, where they transition between grounded and floating ice. Recently published studies of the complex hydrography of grounding zones suggest that warm ocean water can intrude large distances beneath the ice sheet, with dramatic consequences for ice dynamics. Here we develop a model to capture the feedback between intruded ocean water, the melting it induces and the resulting changes in ice geometry. We reveal a sensitive dependence of the grounding-zone dynamics on this feedback: as the grounding zone widens in response to melting, both temperature and flow velocity in the region increase, further enhancing melting. We find that increases in ocean temperature can lead to a tipping point being passed, beyond which ocean water intrudes in an unbounded manner beneath the ice sheet, via a process of runaway melting. Additionally, this tipping point may not be easily detected with early warning indicators. Although completely unbounded intrusions are not expected in practice, this suggests a mechanism for dramatic changes in grounding-zone behaviour, which are not currently included in ice-sheet models. We consider the susceptibility of present-day Antarctic grounding zones to this process, finding that both warm and cold water cavity ice shelves may be vulnerable. Our results point towards a stronger sensitivity of ice-sheet melting, and thus higher sea-level-rise contribution in a warming climate, than has been previously understood

Bendocapillary Instability of Liquid in a Flexible-Walled Channel

We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a periodic pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we develop a mathematical model of this instability. We describe equilibria of the system, and use a combination of numerical methods and asymptotic analysis in the limit of small channel wall deflections, to elucidate the key features of this instability. We find that configurations are unstable to perturbations of sufficiently small wavenumber regardless of parameter values, that the growth rate of the instability is highly sensitive to the volume of liquid in the channel, and that both wetting and non-wetting configurations are susceptible to the instability in the same channel. Insight into novel interfacial instabilities opens the possibility for their control and thus exploitation in processes such as microfabrication

General Relativistic 1+3 Orthonormal Frame Approach Revisited

The equations of the 1+3 orthonormal frame approach are explicitly presented and discussed. Natural choices of local coordinates are mentioned. A dimensionless formulation is subsequently given. It is demonstrated how one can obtain a number of interesting problems by specializing the general equations. In particular, equation systems for ``silent'' dust cosmological models also containing magnetic Maxwell fields, locally rotationally symmetric spacetime geometries and spatially homogeneous cosmological models are presented. We show that while the 3-Cotton--York tensor is zero for Szekeres dust models, it is nonzero for a generic representative within the ``silent'' class.Comment: 41 pages, uufiles encoded postscript file, submitted to Phys. Rev.

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Employment status and work-related difficulties in stomach cancer survivors compared with the general population

Little was known about work situation and work-related difficulties, including housework after stomach cancer diagnosis. We aimed to compare employment status and work-related difficulties between stomach cancer survivors and the general population. We enrolled 408 stomach cancer survivors from two hospitals 28 months after diagnosis and 994 representative volunteers from the general population from 15 geographic districts. Working was defined as being employed (including self-employed) and nonworking as being retired or a homemaker. Nonworking was significantly higher among stomach cancer survivors (46.6%) than in the general population (36.5%). Compared with the general population, the survivors had more fatigue in performing both housework (adjusted odds ratio (aOR)=2.08; 95% confidence interval (95% CI)=1.01–4.29) and gainful work (aOR=4.02; 2.55–6.33). More cancer survivors had reduced working hours (aOR=1.42; 95% CI=4.60–28.35) and reduced work-related ability (aOR=6.11; 95% CI=3.64–10.27) than did the general population. The association of nonworking with older age and being female was significantly more positive for survivors than for the general population. Among survivors, poorer Eastern Cooperation Oncology Group Performance Status and receiving total gastrectomy were positively associated with nonworking. Stomach cancer survivors experienced more difficulties in both housework and gainful employment than did the general population. Our findings on stomach cancer survivors' work-related difficulties and the predictors of nonworking will help physicians guide patients towards more realistic postsurgical employment plans

Арап элифбесинде нешир этильген къырымтатар грамматикаларнынъ тенъештирме талили

Статья посвящена сопоставительному анализу имени существительного и глагола в арабографических грамматиках крымскотатарского языка.Стаття присвячена порівняльному аналізу іменника і дієслова в арабографічних граматиках кримськотатарської мови.The article annotation is devoted to the comparative analysis of the noun and the verb in arabographis grammars of the Crimean Tatar language

Beam-forming errors in Murchison Widefield Array phased array antennas and their effects on Epoch of Reionization science

Accurate antenna beam models are critical for radio observations aiming to isolate the redshifted 21 cm spectral line emission from the Dark Ages and the Epoch of Reionization (EOR) and unlock the scientific potential of 21 cm cosmology. Past work has focused on characterizing mean antenna beam models using either satellite signals or astronomical sources as calibrators, but antenna-to-antenna variation due to imperfect instrumentation has remained unexplored. We characterize this variation for the Murchison Widefield Array (MWA) through laboratory measurements and simulations, finding typical deviations of the order of ±10%–20% near the edges of the main lobe and in the sidelobes. We consider the ramifications of these results for image- and power spectrum-based science. In particular, we simulate visibilities measured by a 100 m baseline and find that using an otherwise perfect foreground model, unmodeled beam-forming errors severely limit foreground subtraction accuracy within the region of Fourier space contaminated by foreground emission (the "wedge"). This region likely contains much of the cosmological signal and accessing it will require measurement of per-antenna beam patterns. However, unmodeled beam-forming errors do not contaminate the Fourier space region expected to be free of foreground contamination (the "EOR window"), showing that foreground avoidance remains a viable strategy

Measuring HERA's Primary Beam in Situ: Methodology and First Results

The central challenge in 21 cm cosmology is isolating the cosmological signal from bright foregrounds. Many separation techniques rely on the accurate knowledge of the sky and the instrumental response, including the antenna primary beam. For drift-scan telescopes, such as the Hydrogen Epoch of Reionization Array (HERA), that do not move, primary beam characterization is particularly challenging because standard beam-calibration routines do not apply (Cornwell et al.) and current techniques require accurate source catalogs at the telescope resolution. We present an extension of the method from Pober et al. where they use beam symmetries to create a network of overlapping source tracks that break the degeneracy between source flux density and beam response and allow their simultaneous estimation. We fit the beam response of our instrument using early HERA observations and find that our results agree well with electromagnetic simulations down to a -20 dB level in power relative to peak gain for sources with high signal-to-noise ratio. In addition, we construct a source catalog with 90 sources down to a flux density of 1.4 Jy at 151 MHz.The central challenge in 21 cm cosmology is isolating the cosmological signal from bright foregrounds. Many separation techniques rely on the accurate knowledge of the sky and the instrumental response, including the antenna primary beam. For drift-scan telescopes, such as the Hydrogen Epoch of Reionization Array (HERA), that do not move, primary beam characterization is particularly challenging because standard beam-calibration routines do not apply (Cornwell et al.) and current techniques require accurate source catalogs at the telescope resolution. We present an extension of the method from Pober et al. where they use beam symmetries to create a network of overlapping source tracks that break the degeneracy between source flux density and beam response and allow their simultaneous estimation. We fit the beam response of our instrument using early HERA observations and find that our results agree well with electromagnetic simulations down to a -20 dB level in power relative to peak gain for sources with high signal-to-noise ratio. In addition, we construct a source catalog with 90 sources down to a flux density of 1.4 Jy at 151 MHz