863 research outputs found

    One-Dimensional Approximation of Viscous Flows

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    Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. In this paper, we derive a set of simple (1+1)-dimensional equations from the Navier-Stokes equations describing thin flows of (non-relativistic and incompressible) viscous fluids. This formulation, a generalization of the theory of drop formation by Eggers and his collaborators, would make it possible to examine the final fate of Rayleigh-Plateau instability, its dimensional dependence, and possible self-similar behaviors before and after the drop formation, in the context of fluid/gravity correspondence.Comment: 17 pages, 3 figures; v2: refs & comments adde

    Contact line motion for partially wetting fluids

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    We study the flow close to an advancing contact line in the limit of small capillary number. To take into account wetting effects, both long and short-ranged contributions to the disjoining pressure are taken into account. In front of the contact line, there is a microscopic film corresponding to a minimum of the interaction potential. We compute the parameters of the contact line solution relevant to the matching to a macroscopic problem, for example a spreading droplet. The result closely resembles previous results obtained with a slip model

    Habitat requirements and ecological niche of two cryptic amphipod species at landscape and local scales

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    Cryptic species are phylogenetically diverged taxa that are morphologically indistinguishable and may differ in their ecological and behavioral requirements. This may have important implications for ecosystem services and conservation of biodiversity. We investigated whether two ecologically important cryptic species of the freshwater amphipod Gammarus fossarum (types A and B) are associated with different habitats. We collected data on their occurrence at both the landscape scale (large watersheds) and at the local scale (river reach) to compare macro- and microscale environmental parameters associated with their presence. Analysis of the landscape scale data showed that occurrence of types A and B differ with respect to watershed and river size and, interestingly, human impact on river ecomorphology. Whereas type B was mainly found in less forested areas with higher human impact, type A showed the opposite occurrence pattern. Analyses of the local scale data suggested that habitats occupied by type A were characterized by larger gravel, larger stones and less macrophytes than habitats occupied by type B. The landscape and local data set showed contradicting patterns with regard to stream size. Overall, the observed differences between the two types of G. fossarum most likely reflect ecological differences between them, but alternative explanations (e.g., historical colonization processes) cannot be completely ruled out. Our study underlines that common cryptic species can differ in their ecology and response to anthropogenic influence. Such differences in habitat requirements among difficult-to-identify taxa present a challenge for biodiversity and ecosystem management. Our results emphasize the importance of conservative and precautionary approaches in maintenance of habitat diversity and environmental heterogeneity

    Air entrainment through free-surface cusps

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    In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose a novel mechanism for this phenomenon, based on the instability of cusp singularities that generically form on free surfaces. The air being drawn into the narrow space inside the cusp destroys its stationary shape when the walls of the cusp come too close. Instead, a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory of this instability is confirmed by experimental observation and quantitative comparison with numerical simulations of the flow equations

    HySIA: Tool for Simulating and Monitoring Hybrid Automata Based on Interval Analysis

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    We present HySIA: a reliable runtime verification tool for nonlinear hybrid automata (HA) and signal temporal logic (STL) properties. HySIA simulates an HA with interval analysis techniques so that a trajectory is enclosed sharply within a set of intervals. Then, HySIA computes whether the simulated trajectory satisfies a given STL property; the computation is performed again with interval analysis to achieve reliability. Simulation and verification using HySIA are demonstrated through several example HA and STL formulas.Comment: Appeared in RV'17; the final publication is available at Springe

    Hydrodynamic theory of de-wetting

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    A prototypical problem in the study of wetting phenomena is that of a solid plunging into or being withdrawn from a liquid bath. In the latter, de-wetting case, a critical speed exists above which a stationary contact line is no longer sustainable and a liquid film is being deposited on the solid. Demonstrating this behavior to be a hydrodynamic instability close to the contact line, we provide the first theoretical explanation of a classical prediction due to Derjaguin and Levi: instability occurs when the outer, static meniscus approaches the shape corresponding to a perfectly wetting fluid

    The Two Fluid Drop Snap-off Problem: Experiments and Theory

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    We address the dynamics of a drop with viscosity λη\lambda \eta breaking up inside another fluid of viscosity η\eta. For λ=1\lambda=1, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement with experiment and previous simulations of Lister and Stone. We also investigate the λ\lambda dependence of the shape and breaking rate.Comment: 4 pages, 3 figure

    Asymptotic theory for a moving droplet driven by a wettability gradient

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    An asymptotic theory is developed for a moving drop driven by a wettability gradient. We distinguish the mesoscale where an exact solution is known for the properly simplified problem. This solution is matched at both -- the advancing and the receding side -- to respective solutions of the problem on the microscale. On the microscale the velocity of movement is used as the small parameter of an asymptotic expansion. Matching gives the droplet shape, velocity of movement as a function of the imposed wettability gradient and droplet volume.Comment: 8 fig
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