Corrigendum to the paper “Ovoidal packings of PG(3,q) for even q”

We point out that the proof of Theorem 3.3 of Bagchi and Sastry (2013) contains a serious flaw. Accordingly, this theorem needs to be modified. In consequence, we also have to retract Corollary 3.4, Corollary 3.6 and Theorem 3.8 of Bagchi and Sastry (2013).     

Lateral migration of a capsule in a plane Poiseuille flow in a channel

Three-dimensional numerical simulation is presented on the motion of a deformable capsule undergoing large deformation in a plane Poiseuille flow in a channel at small inertia. The capsule is modeled as a liquid drop surrounded by an elastic membrane which follows neo-Hookean law. The numerical methodology is based on a mixed finite-difference/Fourier transform method for the flow solver and a front-tracking method for the deformable interface. The methodology can address large deformation of a capsule over a wide range of capsule-to-medium viscosity ratio. An extensive validation of the methodology is presented on capsule deformation in linear shear flow and compared with the boundary-element/integral simulations. Motion of a capsule in wall-bounded parabolic flow is simulated over an extended period of time to consider both transient and steady-state motion. Lateral migration of the capsule towards the centerline of the channel is observed. Results are presented over a range of capillary number, viscosity ratio, capsule-to-channel size ratio, and lateral location. After an initial transient phase during which the capsule deforms very quickly, the flow of the capsule is observed to be a quasi-steady process irrespective of capillary number (Ca)$(\mathit{Ca})$, capsule-to-channel size ratio (a/H)$(a/H)$, and viscosity ratio (λ)$(\lambda )$. Migration velocity and capsule deformation are observed to increase with increasing Ca$\mathit{Ca}$ and a/H$a/H$, but decrease with increasing λ$\lambda$, and increasing distance from the wall. Numerical results on the capsule migration are compared with the analytical results for liquid drops, and capsules with Hookean membrane which are valid in the limit of small deformation. Unlike the prediction for liquid drops, capsules are observed to migrate toward the centerline for 0.2?λ?5$0.2?\lambda ?5$ range considered here. The migration velocity is observed to depend linearly on (a/H)³$(a/H{)}^3$, in agreement with the small-deformation theory, but non-linearly on Ca$\mathit{Ca}$ and the distance from the wall, in violation of the theory. Using the present numerical results and the analytical results, we present a correlation that can reasonably predict migration velocity of a capsule for moderate values of a/H$a/H$ and Ca$\mathit{Ca}$.