Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally-resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. For unbounded suspensions and suspensions sedimented against a single no-slip boundary, we rely on existing analytical expressions for the Rotne-Prager tensor combined with a fast multipole method or a direct summation on a Graphical Processing Unit to obtain an simple yet efficient and scalable implementation. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently-developed rigid-body immersed boundary method to suspensions of freely-moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid body equations converges in a bounded number of iterations regardless of the system size. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201

Topological Aspect of high-TcT_c Superconductivity, Fractional Quantum Hall Effect and Berry Phase

We have analysed here the equivalence of RVB states with $\nu=1/2$ FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the 3-dimensional spinons and holons are characterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with $\nu=1/2$.Comment: 12 pages latex fil

Magnetization in electron- and Mn- doped SrTiO3

Mn-doped SrTiO_3.0, when synthesized free of impurities, is a paramagnetic insulator with interesting dielectric properties. Since delocalized charge carriers are known to promote ferromagnetism in a large number of systems via diverse mechanisms, we have looked for the possibility of any intrinsic, spontaneous magnetization by simultaneous doping of Mn ions and electrons into SrTiO_3 via oxygen vacancies, thereby forming SrTi_(1-x)Mn_xO_(3-d), to the extent of making the doped system metallic. We find an absence of any enhancement of the magnetization in the metallic sample when compared with a similarly prepared Mn doped, however, insulating sample. Our results, thus, are not in agreement with a recent observation of a weak ferromagnetism in metallic Mn doped SrTiO_3 system.Comment: 10 pages and 4 figure