PHYSICS OF FLUIDS 21, 063301 2009 The inertial lift on a spherical particle settling in a horizontal viscous flow through a vertical slot Evgeny S. Asmolov1,2,a and Andrei A. Osiptsov1 1 2 Department of Geomechanics, Schlumberger Moscow Research ... Zhukovsky, Moscow Region 140180, Russia Received 10 September 2008; accepted 29 April 2009; published online 4 June 2009 The inertial lift force exerted on a small rigid sphere settling due to gravity in a horizontal ...

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... We start with a simple case of the control system x = f (x, u), x M 2, u S1, on a two-dimensional manifold M whose tangent plane at each point is equipped with the set of admissible velocities Im , and assume that this set is a closed smooth curve. ... A supporting plane of a curve I = {r(t)} is a co-oriented plane whose open positive half-space does not contain points of I , and the plane itself contains points of I . ... Three points on a line form the support of a supporting plane. ...

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J Stat Phys (2008) 130: 599­616 DOI 10.1007/s10955-007-9442-6 Birth of a New Class of Period-Doubling Scaling Behavior as a Result of Bifurcation in the Renormalization Equation S.P. Kuznetsov · A.A. Mailybaev · I.R. Sataev Received: 2 December 2006 / Accepted: 19 September 2007 / Published online: 24 October 2007 © Springer Science+Business Media, LLC 2007 Abstract It is found that a fixed point of the renormalization group ... J Stat Phys (2008) 130: 599­616 605 Fig. ... Phys. Rev. Lett. ...

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