A Compact Eulerian Representation of Axisymmetric Inviscid Vortex Sheet Dynamics

A classical problem in fluid mechanics is the motion of an axisymmetric vortex sheet evolving under the action of surface tension, surrounded by an inviscid fluid. Lagrangian descriptions of these dynamics are well-known, involving complex nonlocal expressions for the radial and longitudinal velocities in terms of elliptic integrals. Here we use these prior results to arrive at a remarkably compact and exact Eulerian evolution equation for the sheet radius $r(z,t)$ in an explicit flux form associated with the conservation of enclosed volume. The flux appears as an integral involving the pairwise mutual induction formula for vortex loop pairs first derived by Helmholtz and Maxwell. We show how the well-known linear stability results for cylindrical vortex sheets in the presence of surface tension and streaming flows [A.M. Sterling and C.A. Sleicher, $J.~Fluid~Mech.$ ${\bf 68}$, 477 (1975)] can be obtained directly from this formulation. Furthermore, the inviscid limit of the empirical model of Eggers and Dupont [$J.~Fluid~Mech.$ $\textbf{262}$ 205 (1994); $SIAM~J.~Appl.~Math.$ ${\bf 60}$, 1997 (2000)], which has served as the basis for understanding singularity formation in droplet pinchoff, is derived within the present formalism as the leading order term in an asymptotic analysis for long slender axisymmetric vortex sheets, and should provide the starting point for a rigorous analysis of singularity formation.This work was supported in part by Established Career Fellowship EP/M017982/1 from the EPSRC (REG & AIP). REG and AIP are grateful to the I.H.E.S., and especially Patrick Gourdon, for hospitality during an extended visit supported by the Schlumberger Visiting Professorship (REG)

Elastohydrodynamic synchronization of adjacent beating flagella

It is now well established that nearby beating pairs of eukaryotic flagella or cilia typically synchronize in phase. A substantial body of evidence supports the hypothesis that hydrodynamic coupling between the active filaments, combined with waveform compliance, provides a robust mechanism for synchrony. This elastohydrodynamic mechanism has been incorporated into bead-spring models in which the beating flagella are represented by microspheres tethered by radial springs as they are driven about orbits by internal forces. While these low-dimensional models reproduce the phenomenon of synchrony, their parameters are not readily relatable to those of the filaments they represent. More realistic models, which reflect the underlying elasticity of the axonemes and the active force generation, take the form of fourth-order nonlinear partial differential equations (PDEs). While computational studies have shown the occurrence of synchrony, the effects of hydrodynamic coupling between nearby filaments governed by such continuum models have been examined theoretically only in the regime of interflagellar distances d large compared to flagellar length $\textit{L}$. Yet in many biological situations $\textit{d/L}$≪1. Here we present an asymptotic analysis of the hydrodynamic coupling between two extended filaments in the regime $\textit{d/L}$≪1 and find that the form of the coupling is independent of the microscopic details of the internal forces that govern the motion of the individual filaments. The analysis is analogous to that yielding the localized induction approximation for vortex filament motion, extended to the case of mutual induction. In order to understand how the elastohydrodynamic coupling mechanism leads to synchrony of extended objects, we introduce a heuristic model of flagellar beating. The model takes the form of a single fourth-order nonlinear PDE whose form is derived from symmetry considerations, the physics of elasticity, and the overdamped nature of the dynamics. Analytical and numerical studies of this model illustrate how synchrony between a pair of filaments is achieved through the asymptotic coupling.This work was supported by Wellcome Trust Senior Investigator Award 097855MA (R.E.G. and A.I.P.) and by a Marie Curie Career Integration Grant (E.L.)

Antiphase Synchronization in a Flagellar-Dominance Mutant of Chlamydomonas

This is the final version. Available on open access from American Physical Society via the DOI in this record. Groups of beating flagella or cilia often synchronize so that neighboring filaments have identical frequencies and phases. A prime example is provided by the unicellular biflagellate Chlamydomonas reinhardtii, which typically displays synchronous in-phase beating in a low-Reynolds number version of breaststroke swimming. We report the discovery that ptx1, a flagellar-dominance mutant of C. reinhardtii, can exhibit synchronization in precise antiphase, as in the freestyle swimming stroke. High-speed imaging shows that ptx1 flagella switch stochastically between in-phase and antiphase states, and that the latter has a distinct waveform and significantly higher frequency, both of which are strikingly similar to those found during phase slips that stochastically interrupt in-phase beating of the wild-type. Possible mechanisms underlying these observations are discussed.Spanish Ministerio de Ciencia y InnovaciónEngineering and Physical Sciences Research Council (EPSRC)Biotechnology and Biological Sciences Research Council (BBSRC)European Research CouncilWellcome Trus

Solar wind interaction with comet 67P: impacts of corotating interaction regions

International audienceWe present observations from the Rosetta Plasma Consortium of the effects of stormy solar wind on comet 67P/Churyumov-Gerasimenko. Four corotating interaction regions (CIRs), where the first event has possibly merged with a coronal mass ejection, are traced from Earth via Mars (using Mars Express and Mars Atmosphere and Volatile EvolutioN mission) to comet 67P from October to December 2014. When the comet is 3.1–2.7 AU from the Sun and the neutral outgassing rate ∼1025–1026 s−1, the CIRs significantly influence the cometary plasma environment at altitudes down to 10–30 km. The ionospheric low-energy (∼5 eV) plasma density increases significantly in all events, by a factor of >2 in events 1 and 2 but less in events 3 and 4. The spacecraft potential drops below −20 V upon impact when the flux of electrons increases. The increased density is likely caused by compression of the plasma environment, increased particle impact ionization, and possibly charge exchange processes and acceleration of mass-loaded plasma back to the comet ionosphere. During all events, the fluxes of suprathermal (∼10–100 eV) electrons increase significantly, suggesting that the heating mechanism of these electrons is coupled to the solar wind energy input. At impact the magnetic field strength in the coma increases by a factor of 2–5 as more interplanetary magnetic field piles up around the comet. During two CIR impact events, we observe possible plasma boundaries forming, or moving past Rosetta, as the strong solar wind compresses the cometary plasma environment. We also discuss the possibility of seeing some signatures of the ionospheric response to tail disconnection events

The foundations of statistical mechanics from entanglement: Individual states vs. averages

We consider an alternative approach to the foundations of statistical mechanics, in which subjective randomness, ensemble-averaging or time-averaging are not required. Instead, the universe (i.e. the system together with a sufficiently large environment) is in a quantum pure state subject to a global constraint, and thermalisation results from entanglement between system and environment. We formulate and prove a "General Canonical Principle", which states that the system will be thermalised for almost all pure states of the universe, and provide rigorous quantitative bounds using Levy's Lemma.Comment: 12 pages, v3 title changed, v2 minor change

Effects of microwave sintering in aging resistance of zirconia-based ceramics

[EN] Innovative techniques for materials processing that result in shorter times and lower energy consumption than conventional methods, such as microwave sintering, are currently under investigation in order to obtain fully-consolidated ceramic materials. Microwave sintering has important effects on the resulting properties of zirconia-based ceramics, which, in turn, affectits performance and durability, as in the case of their susceptibility to low temperature hydrothermal degradation (LTD), an ageing phenomenon that deteriorates their mechanical performance. The purpose of this work consists on assessing the effects of microwave sintering on the microstructure and mechanical performance of zirconia composites by comparing itto conventional sintering. Resistance to LTD of 3Y-TZP-only materials has also been evaluated. The results obtained in this work suggest that microwave sintering can reduce processing times and sintering temperatures when compared to conventional sintering while still obtaining dense zirconia-based ceramics and complying with the expected mechanical properties. At the same time, an increase in the resistance to LTD is also observed.This work has been supported by the Spanish Ministry of Economy and Competitiveness MINECO (project MAT2015-67586-C3-R). The authors acknowledge to CAPES Programa Ciencias sem Fronteiras (Brazil) for the concession of a PVE project No. A086/2013. A. Presenda acknowledges the Generalitat Valenciana for his Santiago Grisolia scholarship (GRISOLIA/2013/035). A. Borrell acknowledges the MINECO for her Juan de la Cierva-Incorporacion contract (IJCI-2014-19839).Presenda-Barrera, A.; Salvador Moya, MD.; Penaranda-Foix, FL.; Catalá Civera, JM.; Pallone, E.; Ferreira, J.; Borrell Tomás, MA. (2017). Effects of microwave sintering in aging resistance of zirconia-based ceramics. Chemical Engineering and Processing Process Intensification. 112:404-412. https://doi.org/10.1016/j.cep.2017.03.002S40441211

IACT observations of gamma-ray bursts: prospects for the Cherenkov Telescope Array

Gamma rays at rest frame energies as high as 90 GeV have been reported from gamma-ray bursts (GRBs) by the Fermi Large Area Telescope (LAT). There is considerable hope that a confirmed GRB detection will be possible with the upcoming Cherenkov Telescope Array (CTA), which will have a larger effective area and better low-energy sensitivity than current-generation imaging atmospheric Cherenkov telescopes (IACTs). To estimate the likelihood of such a detection, we have developed a phenomenological model for GRB emission between 1 GeV and 1 TeV that is motivated by the high-energy GRB detections of Fermi-LAT, and allows us to extrapolate the statistics of GRBs seen by lower energy instruments such as the Swift-BAT and BATSE on the Compton Gamma-ray Observatory. We show a number of statistics for detected GRBs, and describe how the detectability of GRBs with CTA could vary based on a number of parameters, such as the typical observation delay between the burst onset and the start of ground observations. We also consider the possibility of using GBM on Fermi as a finder of GRBs for rapid ground follow-up. While the uncertainty of GBM localization is problematic, the small field-of-view for IACTs can potentially be overcome by scanning over the GBM error region. Overall, our results indicate that CTA should be able to detect one GRB every 20 to 30 months with our baseline instrument model, assuming consistently rapid pursuit of GRB alerts, and provided that spectral breaks below 100 GeV are not a common feature of the bright GRB population. With a more optimistic instrument model, the detection rate can be as high as 1 to 2 GRBs per year.Comment: 28 pages, 24 figures, 4 tables, submitted to Experimental Astronom

Logistic random effects regression models: a comparison of statistical packages for binary and ordinal outcomes

<p>Abstract</p> <p>Background</p> <p>Logistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models.</p> <p>Methods</p> <p>We used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC.</p> <p>Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted.</p> <p>Results</p> <p>The packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient.</p> <p>Conclusions</p> <p>On relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain.</p

Long Astral Microtubules and RACK-1 Stabilize Polarity Domains during Maintenance Phase in Caenorhabditis elegans Embryos

Cell polarity is a very well conserved process important for cell differentiation, cell migration, and embryonic development. After the establishment of distinct cortical domains, polarity cues have to be stabilized and maintained within a fluid and dynamic membrane to achieve proper cell asymmetry. Microtubules have long been thought to deliver the signals required to polarize a cell. While previous studies suggest that microtubules play a key role in the establishment of polarity, the requirement of microtubules during maintenance phase remains unclear. In this study, we show that depletion of Caenorhabditis elegans RACK-1, which leads to short astral microtubules during prometaphase, specifically affects maintenance of cortical PAR domains and Dynamin localization. We then investigated the consequence of knocking down other factors that also abolish astral microtubule elongation during polarity maintenance phase. We found a correlation between short astral microtubules and the instability of PAR-6 and PAR-2 domains during maintenance phase. Our data support a necessary role for astral microtubules in the maintenance phase of cell polarity