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An efficient scheme is presented for the numerical calculation of hydrodynamic interactions of many spheres in Stokes flow. The spheres may have various sizes, and are freely moving or arranged in rigid arrays. Both the friction and mobility matrix are found from the solution of a set of coupled equations. The Stokesian dynamics of many spheres and the(More)
A mechanical model of swimming and flying in an incompressible viscous fluid in the absence of gravity is studied on the basis of assumed equations of motion. The system is modeled as an assembly of rigid spheres subject to elastic direct interactions and to periodic actuating forces which sum to zero. Hydrodynamic interactions are taken into account in the(More)
A matrix formulation is derived for the calculation of the swimming speed and the power required for swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent. The spheres may have arbitrary radii and may interact with elastic forces. The analysis is based on the Stokes mobility matrix of the set of spheres, defined in low(More)
Translational and rotational swimming at small Reynolds number of a planar assembly of identical spheres immersed in an incompressible viscous fluid is studied on the basis of a set of equations of motion for the individual spheres. The motion of the spheres is caused by actuating forces and forces derived from a direct interaction potential, as well as(More)
The swimming of a deformable planar slab in a viscous incompressible fluid is studied on the basis of the Navier-Stokes equations. A continuum of plane wave displacements, symmetric on both sides of the slab and characterized by a polarization angle, allows optimization of the swimming efficiency with respect to polarization. The mean swimming velocity and(More)
The swimming of an assembly of rigid spheres immersed in a viscous fluid of infinite extent is studied in low-Reynolds-number hydrodynamics. The instantaneous swimming velocity and rate of dissipation are expressed in terms of the time-dependent displacements of sphere centers about their collective motion. For small-amplitude swimming with periodically(More)
Escape by diffusion in one dimension from a parabolic well across a parabolic barrier is investigated for a range of barrier heights. The probability of occupation of the well decays at long times inversely with the square root of time due to repeated return to the well after excursion in the outer space. The amplitude of the long-time tail increases as the(More)
The rotational diffusion equation for a dipole in the presence of a rotating field is solved by expansion of the orientational distribution function in terms of spherical harmonics. For the stationary solution, the distribution function rotates bodily in angular space. The magnitude of the average dipole moment and the lag angle are studied as functions of(More)
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