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Motility induced changes in viscosity of suspensions of swimming microbes in extensional flows  [PDF]
Amarin G. McDonnell,Tilvawala C. Gopesh,Jennifer Lo,Moira O'Bryan,Leslie Y. Yeo,James R. Friend,Ranganathan Prabhakar
Physics , 2015,
Abstract: Suspensions of motile cells are model systems for understanding the unique mechanical properties of living materials which often consist of ensembles of self-propelled particles. We present here a quantitative comparison of theory against experiment for the rheology of such suspensions. The influence of motility on viscosities of cell suspensions is studied using a novel acoustically-driven microfluidic capillary-breakup extensional rheometer. Motility increases the extensional viscosity of suspensions of algal pullers, but decreases it in the case of bacterial or sperm pushers. A recent model [Saintillan, Phys. Rev. E, 2010, 81:56307] for dilute active suspensions is extended to obtain predictions for higher concentrations, after independently obtaining parameters such as swimming speeds and diffusivities. We show that details of body and flagellar shape can significantly determine macroscale rheological behaviour.
Enhancement of coil--stretch hysteresis by self-concentration in extensional flows, and its implications for capillary thinning of liquid bridges of dilute polymer solutions  [PDF]
Ranganathan Prabhakar
Physics , 2014,
Abstract: The coil-stretch transition in extensional flows of viscoelastic dilute polymer solutions is known to be associated with a strong hysteresis in molecular conformations and rheo-optical properties. At infinite dilution, hysteresis is caused by the large difference in frictional drag coefficient between undeformed isotropic polymer coils and highly stretched conformations. At the low extension rates in the hysteresis regime, stretched molecules pervade larger volumes than equilibrium coils since the flow is too weak to suppress transverse fluctuations. The onset of intermolecular overlap occurs for such stretched conformations at polymer concentrations much smaller than c*, the conventional critical overlap concentration for equilibrium coils. Therefore, for a range of concentrations c < c*, intramolecular hydrodynamic interactions may be significantly screened in stretched conformations. Scaling arguments based on "blob" concepts are used here to argue that the stretched state drag coefficient can grow strongly with concentration in the dilute regime. A dumbbell model with conformation-dependent drag model is used to predict a concomitant strong enhancement of coil-stretch hysteresis with increasing concentration in the dilute regime. This extensional flow induced self-concentration leads to a maximum in hysteretic effects around c*, which progressively diminish in the semi-dilute regime where screening in isotropic coils reduces the difference in drag coefficient between stretched and coiled states. It is shown that the concentration dependence observed by Clasen et al. (2006) of capillary-thinning dynamics in liquid bridges of polymer solutions provides direct evidence of coil-stretch hysteresis enhancement by self-concentration.
Liquid-gas-solid flows with lattice Boltzmann: Simulation of floating bodies  [PDF]
Simon Bogner,Ulrich Rüde
Computer Science , 2012, DOI: 10.1016/j.camwa.2012.09.012
Abstract: This paper presents a model for the simulation of liquid-gas-solid flows by means of the lattice Boltzmann method. The approach is built upon previous works for the simulation of liquid-solid particle suspensions on the one hand, and on a liquid-gas free surface model on the other. We show how the two approaches can be unified by a novel set of dynamic cell conversion rules. For evaluation, we concentrate on the rotational stability of non-spherical rigid bodies floating on a plane water surface - a classical hydrostatic problem known from naval architecture. We show the consistency of our method in this kind of flows and obtain convergence towards the ideal solution for the measured heeling stability of a floating box.
Rheological Behaviors Investigation of Multiple-Emulsion Globules in Extensional Flows

王靖涛,徐根苗,Kelkil E A,许慎
- , 2018, DOI: 10.11784/tdxbz201703098
Abstract: 为了探究复乳液内部子液滴的大小和位置分布对其流变行为的影响, 采用二维波谱边界元素法数值模拟了延展流中同心复乳液和非对称复乳液的流变行为.通过改变子液滴的大小和位置得到复乳液不同的流变行为, 并深入分析其变形和移动机理.研究结果表明:在不同的毛细管数下, 同心复乳液内部子液滴的存在对复乳液的变形有正反双重作用; 双子液滴的不对称分布导致非对称复乳液两侧界面变形和曲率不对称, 界面曲率差驱使母液滴在延展流中发生移动.
In order to explore the impact of inner droplets’ size and position on rheological behaviors of outer droplets,the two-dimensional spectral boundary element method was employed to simulate the rheological behaviors of concentric multiple-emulsion globules and asymmetric multiple-emulsion globules in extensional flows. The different rheological behaviors of multiple-emulsion globules were obtained by changing the size and position of the inner droplets,and the mechanism of deformation and movement was deeply analyzed. The results show that the inner droplet of the concentric multiple-emulsion globules has positive or negative effects on the deformation of the globules under different capillary numbers. The asymmetric layout of the double-emulsion droplets leads to the asymmetric deformation of the globules with different interface curvatures,which causes the oriented shift of the globules
Extensional dimension and completion of maps  [PDF]
H. Murat Tuncali,E. D. Tymchatin,Vesko Valov
Mathematics , 2003,
Abstract: We prove that any closed map between metrizable spaces can be extended to a closed map between completely metrizable spaces with the same extensional dimension.
Periodic boundary conditions for the simulation of uniaxial extensional flow  [PDF]
Thomas A. Hunt
Physics , 2013,
Abstract: It is very common with molecular dynamics and other simulation techniques to apply Lees-Edwards periodic boundary conditions (PBCs) for the simulation of shear flow. However the behavior of a complex liquid can be quite different under extensional flow. Simple deformation of a simulation cell and its periodic images only allows for simulations of these flows with short duration. For the simulation of planar extensional flow it was recognized that the PBCs of Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] could be used to perform simulations of this flow with arbitrary duration. However, a very common extensional flow in industrial applications and experiment is uniaxial extensional flow. Kraynik and Reinelt found that their method could not be directly generalized to this flow because of the lack of a lattice which reproduces itself during uniaxial extension. PBCs are presented in this article which solve this problem, by finding a lattice which is compatible with the flow, finding the reduced basis to the lattice at all times and using this basis when calculating the position and separation of particles. Using these new PBCs we perform nonequilibrium molecular dynamics simulations of a simple liquid and show that the technique gives results which agree with those from simulations using simply deforming PBCs.
Extensional and Intensional Strategies
Tony Bourdier,Horatiu Cirstea,Daniel Dougherty,Hélène Kirchner
Electronic Proceedings in Theoretical Computer Science , 2010, DOI: 10.4204/eptcs.15.1
Abstract: This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an abstract reduction system. We then move to a more intensional definition supporting the abstract view but more operational in the sense that it describes a means for determining such a set. We characterize the class of extensional strategies that can be defined intensionally. We also give some hints towards a logical characterization of intensional strategies and propose a few challenging perspectives.
A Note on "Extensional PERs"  [PDF]
W. P. Stekelenburg
Mathematics , 2009,
Abstract: In the paper "Extensional PERs" by P. Freyd, P. Mulry, G. Rosolini and D. Scott, a category $\mathcal{C}$ of "pointed complete extensional PERs" and computable maps is introduced to provide an instance of an \emph{algebraically compact category} relative to a restricted class of functors. Algebraic compactness is a synthetic condition on a category which ensures solutions of recursive equations involving endofunctors of the category. We extend that result to include all internal functors on $\mathcal{C}$ when $\mathcal{C}$ is viewed as a full internal category of the effective topos. This is done using two general results: one about internal functors in general, and one about internal functors in the effective topos.
Extensional Information Articulation from the Universe  [PDF]
Makoto Yoshitake,Yasufumi Saruwatari
Information , 2012, DOI: 10.3390/info3040644
Abstract: Information must have physical support and this physical universe comprisesphysical interactions. Hence actual information processes should have a description byinteractions alone, i.e., an extensional description. In this paper, such a model of the processof information articulation from the universe is developed by generalizing the extensivemeasurement theory in metrology. Moreover, a model of the attribute creation processis presented to exemplify a step of the informational articulation process. These modelsdemonstrate the valuableness of the extensional view and are expected to enhance theunderstanding of the extensional aspects of fundamentals of information.
Internalization of extensional equality  [PDF]
Andrew Polonsky
Computer Science , 2014,
Abstract: We give a type system in which the universe of types is closed by reflection into it of the logical relation defined externally by induction on the structure of types. This contribution is placed in the context of the search for a natural, syntactic construction of the extensional equality type (Tait [1995], Altenkirch [1999], Coquand [2011], Licata and Harper [2012], Martin-Lof [2013]). The system is presented as an extension of lambda-*, the terminal pure type system in which the universe of all types is a type. The universe inconsistency is then removed by the usual method of stratification into levels. We give a set-theoretic model for the stratified system. We conjecture that Strong Normalization holds as well.
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