A general version of the immersed boundary method and its applications to biology
Abstract
We present a generalized immersed boundary (IB) method combined with the unconstrained Kirchhoff rod theory which has been developed to study the biological fluid mechanics in filamentous structures such as bacterial flagella and DNA sequences.
A thin elastic filament (rod) in the Kirchhoff model that resists bending and twisting can be modeled as a ``three-dimensional space curve'' together with an orthonormal triad (material frame) at each point of the rod. The space curve represents the centerline of the rod and the triad indicates the amount of bend and twist of the elastic rod. This is a well-established theory in the statics and dynamics of thin elastic filaments without fluid. Combining Kirchhoff rod theory with the standard models of viscous incompressible fluids will allow us to study the complicated hydrodynamics of bacterial swimming, DNA supercoiling, and more.