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    Application of a high density ratio lattice-Boltzmann model for the droplet impingement on flat and spherical surfaces

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    In the current study, a 3-dimensional lattice Boltzmann model which can tolerate high density ratios is employed to simulate the impingement of a liquid droplet onto a flat and a spherical target. The four phases of droplet impact on a flat surface, namely, the kinematic, spreading, relaxation and equilibrium phase, have been obtained for a range of Weber and Reynolds numbers. The predicted maximum spread factor is in good agreement with experimental data published in the literature. For the impact of the liquid droplet onto a spherical target, the temporal variation of the film thickness on the target surface is investigated. The three different temporal phases of the film dynamics, namely, the initial drop deformation phase, the inertia dominated phase and the viscosity dominated phase are reproduced and studied. The effect of the droplet Reynolds number and the target-to-drop size ratio on the film flow dynamics is investigated

    Local diffusion theory of localized waves in open media

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    We report a first-principles study of static transport of localized waves in quasi-one-dimensional open media. We found that such transport, dominated by disorder-induced resonant transmissions, displays novel diffusive behavior. Our analytical predictions are entirely confirmed by numerical simulations. We showed that the prevailing self-consistent localization theory [van Tiggelen, {\it et. al.}, Phys. Rev. Lett. \textbf{84}, 4333 (2000)] is valid only if disorder-induced resonant transmissions are negligible. Our findings open a new direction in the study of Anderson localization in open media.Comment: 4 pages, 2 figure
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