74 research outputs found

    Toroidal drops in viscous flow

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    Toroidal drops are known since the experiments by Plateau (1854) in rotating fluids. Such shapes and other non-spherical configurations have become of interest in various technological areas, and recently also as potential carriers of drugs (Champion et al., 2007) or building blocks for more complex assemblies (Velev et al., 2000). Such geometry is obtained, for example, when a drop, falling free in a viscous fluid, experiences a finite surface deformation which develops into a toroidal form (Kojima et al., 1984; Baumann et al., 1992; Sostarecz & Belmonte 2003). In this presentation we shall revisit the stable compression of spherical drops in bi-axial viscous extension, within a finite range of the capillary number, Ca, and show that loss of stability can lead to formation of toroidal shapes. We demonstrate numerically that there is a limited range of Ca in which toroidal stationary solutions exist, and that such drops in this flow are inherently unstable (Zabarankin et al., 2013). However, there is a potential of shape stabilization if the drops are comprised of a mild yield stress material. References BAUMANN, N., JOSEPH, D. D., MOHR, P. & RENARDY, Y. 1992 Vortex rings of one fluid in another in free fall. Phys. Fluids A 4 (3), 567–580. CHAMPION, J. A., KATARE, Y. K. & MITRAGOTRI, S. 2007 Particle shape: A new design parameter for micro- and nanoscale drug delivery carriers. J. Contr. Release 121 (1–2), 3–9. KOJIMA, M., HINCH, E. J. & ACRIVOS, A. 1984 The formation and expansion of a toroidal drop moving in a viscous fluid. Phys. Fluids 27 (1), 19–32. PLATEAU, J. 1857 I. Experimental and theoretical researches on the figures of equilibrium of a liquid mass withdrawn from the action of gravity.–Third series. Philosophical Magazine Series 4 14 (90), 1–22. SOSTARECZ, M. C. & BELMONTE, A. 2003 Motion and shape of a viscoelastic drop falling through a viscous fluid. J. Fluid Mech. 497, 235–252. VELEV, O. D., LENHOFF, A. M. & KALER, E. W. 2000 A class of microstructured particles through colloidal crystallization. Science 287 (5461), 2240–2243. ZABARANKIN, M., SMAGIN, I., LAVRENTEVA, O. M. & NIR, A. 2013 Viscous drop in compressional Stokes flow. J. Fluid Mech. 720, 169–191

    Small Deformation Analysis for Stationary Toroidal Drops in a Compressional Flow

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    Statistical decision problems: selected concepts and portfolio safeguard case studies

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    Optimization of convergence rate and stability margin of information flow in cooperative systems

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    The interplay between the convergence rate and stability margin (e.g. ability to reject disturbances) for a discrete-time information flow filter in cooperative systems is analyzed. For a given communication graph, the convergence rate is defined as the absolute value of the largest nonunit characteristic root of a matrix associated with the filter. The maximal convergence rate, obtained by “tuning” the control gains, is highly correlated to the number of distinct eigenvalues of the graph Laplacian (it is 1 for the complete graph). A stability margin is introduced for multiple-input–multiple-output (MIMO) systems and is then maximized with respect to the control gains subject to a constraint on the convergence rate. The optimal stability margin as a function of the convergence rate is bounded above for any order of the filter, and the bound is attained for the complete graph. For the zero-order filter and all strongly connected communication graphs, the optimal stability margin is found analytically, whereas for the first-order filter and undirected communication graphs, it is evaluated numerically. The results demonstrate the ability to distinguish graph topologies that dominate others in their ability to reject disturbances and converge rapidly to a consensus

    Inverse portfolio problem with coherent risk measures

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    In general, a portfolio problem minimizes risk (or negative utility) of a portfolio of financial assets with respect to portfolio weights subject to a budget constraint. The inverse portfolio problem then arises when an investor assumes that his/her risk preferences have a numerical representation in the form of a certain class of functionals, e.g. in the form of expected utility, coherent risk measure or mean-deviation functional, and aims to identify such a functional, whose minimization results in a portfolio, e.g. a market index, that he/she is most satisfied with. In this work, the portfolio risk is determined by a coherent risk measure, and the rate of return of investor’s preferred portfolio is assumed to be known. The inverse portfolio problem then recovers investor’s coherent risk measure either through finding a convex set of feasible probability measures (risk envelope) or in the form of either mixed CVaR or negative Yaari’s dual utility. It is solved in single-period and multi-period formulations and is demonstrated in a case study with the FTSE 100 index

    Multiresolution and Adaptive Path Planning for Maneuver of Micro-Air-Vehicles in Urban Environments

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    Convex functional analysis

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