Choice of computational method for swimming and pumping with nonslender helical filaments at low Reynolds number

The flows induced by biological and artificial helical filaments are important to many possible applications including microscale swimming and pumping. Microscale helices can span a wide range of geometries, from thin bacterial flagella to thick helical bacterial cell bodies. While the proper choice of numerical method is critical for obtaining accurate results, there is little guidance about which method is optimal for a specified filament geometry. Here, using two physical scenarios-a swimmer with a head and a pump-we establish guidelines for the choice of numerical method based on helical radius, pitch, and filament thickness. For a range of helical geometries that encompass most natural and artificial helices, we create benchmark results using a surface distribution of regularized Stokeslets and then evaluate the accuracy of resistive force theory, slender body theory, and a centerline distribution of regularized Stokeslets. For the centerline distribution of regularized Stokeslets or slender body theory, we tabulate appropriate blob size and Stokeslet spacing or segment length, respectively, for each geometry studied. Finally, taking the computational cost of each method into account, we present the optimal choice of numerical method for each filament geometry as a guideline for future investigations involving filament-induced flows. (C) 2016 AIP Publishing LLC

Maximum likelihood estimation by monte carlo simulation:Toward data-driven stochastic modeling

We propose a gradient-based simulated maximum likelihood estimation to estimate unknown parameters in a stochastic model without assuming that the likelihood function of the observations is available in closed form. A key element is to develop Monte Carlo-based estimators for the density and its derivatives for the output process, using only knowledge about the dynamics of the model. We present the theory of these estimators and demonstrate how our approach can handle various types of model structures. We also support our findings and illustrate the merits of our approach with numerical results

Low-Reynolds number swimming in gels

Many microorganisms swim through gels, materials with nonzero zero-frequency elastic shear modulus, such as mucus. Biological gels are typically heterogeneous, containing both a structural scaffold (network) and a fluid solvent. We analyze the swimming of an infinite sheet undergoing transverse traveling wave deformations in the "two-fluid" model of a gel, which treats the network and solvent as two coupled elastic and viscous continuum phases. We show that geometric nonlinearities must be incorporated to obtain physically meaningful results. We identify a transition between regimes where the network deforms to follow solvent flows and where the network is stationary. Swimming speeds can be enhanced relative to Newtonian fluids when the network is stationary. Compressibility effects can also enhance swimming velocities. Finally, microscopic details of sheet-network interactions influence the boundary conditions between the sheet and network. The nature of these boundary conditions significantly impacts swimming speeds.Comment: 6 pages, 5 figures, submitted to EP

Beating patterns of filaments in viscoelastic fluids

Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end, and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high viscosity of purely viscous or viscoelastic solutions can lead to the experimentally observed beating patterns of sperm flagella, in which motion is concentrated at the distal end of the flagella