Wrinkling of microcapsules in shear flow

Elastic capsules can exhibit short wavelength wrinkling in external shear flow. We analyse this instability of the capsule shape and use the length scale separation between the capsule radius and the wrinkling wavelength to derive analytical results both for the threshold value of the shear rate and for the critical wave-length of the wrinkling. These results can be used to deduce elastic parameters from experiments.Comment: 4 pages, 2 figures, submitted to PR

Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method

The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J. M. Rallison, The Time-Dependent Deformation of a Capsule Freely Suspended in a Linear Shear Flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak et al., Strain Energy Function of Red Blood Cell Membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.Comment: 23 pages, 14 figures, 3 table

Reprocessing the Hipparcos data for evolved stars III Revised Hipparcos period-luminosity relationship for galactic long-period variable stars

We analyze the K band luminosities of a sample of galactic long-period variables using parallaxes measured by the Hipparcos mission. The parallaxes are in most cases re-computed from the Hipparcos Intermediate Astrometric Data using improved astrometric fits and chromaticity corrections. The K band magnitudes are taken from the literature and from measurements by COBE, and are corrected for interstellar and circumstellar extinction. The sample contains stars of several spectral types: M, S and C, and of several variability classes: Mira, semiregular SRa, and SRb. We find that the distribution of stars in the period-luminosity plane is independent of circumstellar chemistry, but that the different variability types have different P-L distributions. Both the Mira variables and the SRb variables have reasonably well-defined period-luminosity relationships, but with very different slopes. The SRa variables are distributed between the two classes, suggesting that they are a mixture of Miras and SRb, rather than a separate class of stars. New period-luminosity relationships are derived based on our revised Hipparcos parallaxes. The Miras show a similar period-luminosity relationship to that found for Large Magellanic Cloud Miras by Feast et al. (1989). The maximum absolute K magnitude of the sample is about -8.2 for both Miras and semi-regular stars, only a little fainter than the expected AGB limit. We show that the stars with the longest periods (P>400d) have high mass loss rates and are almost all Mira variables.Comment: Comments welcome. Submitted to A&A 11 pages, 7 figs, 3 table

Motion of a spherical capsule in branched tube flow with finite inertia

We computationally study the transient motion of an initially spherical capsule flowing through a right-angled tube bifurcation, composed of tubes having the same diameter. The capsule motion and deformation is simulated using a three-dimensional immersed-boundary lattice Boltzmann method. The capsule is modelled as a liquid droplet enclosed by a hyperelastic membrane following the Skalak’s law (Skalak et al., Biophys. J., vol. 13(3), 1973, pp. 245–264). The fluids inside and outside the capsule are assumed to have identical viscosity and density. We mainly focus on path selection of the capsule at the bifurcation as a function of the parameters of the problem: the flow split ratio, the background flow Reynolds number Re , the capsule-to-tube size ratio a/R and the capillary number Ca , which compares the viscous fluid force acting on the capsule to the membrane elastic force. For fixed physical properties of the capsule and of the tube flow, the ratio Ca/Re is constant. Two size ratios are considered: a/R=0.2 and 0.4. At low Re , the capsule favours the branch which receives most flow. Inertia significantly affects the background flow in the branched tube. As a consequence, at equal flow split, a capsule tends to flow straight into the main branch as Re is increased. Under significant inertial effects, the capsule can flow into the downstream main tube even when it receives much less flow than the side branch. Increasing Ca promotes cross-stream migration of the capsule towards the side branch. The results are summarized in a phase diagram, showing the critical flow split ratio for which the capsule flows into the side branch as a function of size ratio, Re and Ca/Re . We also provide a simplified model of the path selection of a slightly deformed capsule and explore its limits of validity. We finally discuss the experimental feasibility of the flow system and its applicability to capsule sorting

Stationary shapes of deformable particles moving at low Reynolds numbers

Lecture Notes of the Summer School ``Microswimmers -- From Single Particle Motion to Collective Behaviour'', organised by the DFG Priority Programme SPP 1726 (Forschungszentrum J{\"{u}}lich, 2015).Comment: Pages C7.1-16 of G. Gompper et al. (ed.), Microswimmers - From Single Particle Motion to Collective Behaviour, Lecture Notes of the DFG SPP 1726 Summer School 2015, Forschungszentrum J\"ulich GmbH, Schriften des Forschungszentrums J\"ulich, Reihe Key Technologies, Vol 110, ISBN 978-3-95806-083-

Variability in Proto-Planetary Nebulae: I. Light Curve Studies of 12 Carbon-Rich Objects

We have carried out long-term (14 years) V and R photometric monitoring of 12 carbon-rich proto-planetary nebulae. The light and color curves display variability in all of them. The light curves are complex and suggest multiple periods, changing periods, and/or changing amplitudes, which are attributed to pulsation. A dominant period has been determined for each and found to be in the range of ~150 d for the coolest (G8) to 35-40 d for the warmest (F3). A clear, linear inverse relationship has been found in the sample between the pulsation period and the effective temperature and also an inverse linear relationship between the amplitude of light variation and the effective temperature. These are consistent with the expectation for a pulsating post-AGB star evolving toward higher temperature at constant luminosity. The published spectral energy distributions and mid-infrared images show these objects to have cool (200 K), detached dust shells and published models imply that intensive mass loss ended a few thousand years ago. The detection of periods as long as 150 d in these requires a revision in the published post-AGB evolution models that couple the pulsation period to the mass loss rate and that assume that intensive mass loss ended when the pulsation period had decreased to 100 d. This revision will have the effect of extending the time scale for the early phases of post-AGB evolution. It appears that real time evolution in the pulsation periods of individual objects may be detectable on the time scale of two decades

Mass loss rates of a sample of irregular and semiregular M-type AGB-variables

We have determined mass loss rates and gas expansion velocities for a sample of 69 M-type irregular (IRV; 22 objects) and semiregular (SRV; 47 objects) AGB-variables using a radiative transfer code to model their circumstellar CO radio line emission. We believe that this sample is representative for the mass losing stars of this type. The (molecular hydrogen) mass loss rate distribution has a median value of 2.0E-7 solar masses per year. M-type IRVs and SRVs with a mass loss rate in excess of 5E-7 solar masses per year must be very rare, and among these mass losing stars the number of sources with mass loss rates below a few 10E-8 solar masses per year must be small. We find no significant difference between the IRVs and the SRVs in terms of their mass loss characteristics. Among the SRVs the mass loss rate shows no dependence on the period. Likewise the mass loss rate shows no correlation with the stellar temperature. The gas expansion velocity distribution has a median of 7.0 km/s. The mass loss rate and the gas expansion velocity correlate well, a result in line with theoretical predictions for an optically thin, dust-driven wind. In general, the model produces line profiles which acceptably fit the observed ones. We have compared the results of this M-star sample with a similar C-star sample analysed in the same way. The mass loss rate characteristics are very similar for the two samples. On the contrary, the gas expansion velocity distributions are clearly different. In particular, the number of low-velocity sources is much higher in the M-star sample. We found no example of the sharply double-peaked CO line profile, which is evidence of a large, detached CO-shell, among the M-stars. About 10% of the C-stars show this phenomenon.Comment: 16 pages, 11 figures, accepted by A&

Peculiarities and variations in the optical spectrum of the post-AGB star V448Lac=IRAS22223+4327

Repeated observations with high spectral resolution acquired in 1998-2008 are used to study the temporal behavior of the spectral line profiles and velocity field in the atmosphere and circumstellar envelope of the post-AGB star V448Lac. Asymmetry of the profiles of the strongest absorption lines with low-level excitation potentials less 1eV and time variations of these profiles have been detected, most prominently the profiles of the resonance lines of BaII, YII, LaII, SiII. The peculiarity of these profiles can be explained using a superposition of stellar absorption line and shell emission lines. Emission in the (0;1) 5635A Swan band of the C2 molecule has been detected in the spectrum of V448Lac for the first time. The core of the Halpha line displays radial velocity variations with an amplitude ~8 km/s. Radial velocity variations displayed by weakest metallic lines with lower amplitudes, 1-2 km/s, may be due to atmospheric pulsations. Differential line shifts, 0 -- 8 km/s, have been detected on various dates. The position of the molecular spectrum is stationary in time, indicating a constant expansion velocity of the circumstellar shell, Vexp=15.2 km/s, as derived from the C2 and NaI lines.Comment: 19 pages, 8 figures, 1 tabl

Методическая работа в дошкольной образовательной организации как условие развития профессионально-педагогической культуры педагогов

Тема работы актуальна. В ВКР представлена методическая работа с педагогами ДОУ, по формирования профессионально-педагогической культуры. Работа имеет практическую значимост

Post-AGB stars with hot circumstellar dust: binarity of the low-amplitude pulsators

While the first binary post-AGB stars were serendipitously discovered, the distinct characteristics of their Spectral Energy Distribution (SED) allowed us to launch a more systematic search for binaries. We selected post-AGB objects which show a broad dust excess often starting already at H or K, pointing to the presence of a gravitationally bound dusty disc in the system. We started a very extensive multi-wavelength study of those systems and here we report on our radial velocity and photometric monitoring results for six stars of early F type, which are pulsators of small amplitude. To determine the radial velocity of low signal-to-noise time-series, we constructed dedicated auto-correlation masks. The radial velocity variations were subjected to detailed analysis to differentiate between pulsational variability and variability due to orbital motion. Finally orbital minimalisation was performed to constrain the orbital elements. All of the six objects are binaries, with orbital periods ranging from 120 to 1800 days. Five systems have non-circular orbits. The mass functions range from 0.004 to 0.57 solar mass and the companions are likely unevolved objects of (very) low initial mass. We argue that these binaries must have been subject to severe binary interaction when the primary was a cool supergiant. Although the origin of the circumstellar disc is not well understood, the disc is generally believed to be formed during this strong interaction phase. The eccentric orbits of these highly evolved objects remain poorly understood. With the measured orbits and mass functions we conclude that the circumbinary discs seem to have a major impact on the evolution of a significant fraction of binary systems.Comment: 13 pages, 15 figures, accepted for Astronomy and Astrophysic