Mathematics Colloquia and Seminars

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A general version of the immersed boundary (gIB) method combined with the unconstrained Kirchhoff rod theory has been developed to study the hydrodynamic interaction of filamentous structures such as bacterial flagella and DNA sequences. The Kirchhoff rod describes a filamentous structure as a “three-dimensional space curve” together with an orthonormal triad (material frame) at each point of the rod. The gIB method solves the fluid-structure interaction problems and treats more general elasticity models that include both positional and rotational degrees of freedom. The positional degrees of freedom of the immersed structure move according to the local linear velocity of the fluid, whereas the rotational degrees of freedom move according to the local angular velocity. We apply this method to some biological problems, in particular, to understand the swimming mechanism of a bacterium E. coli and to study the DNA dynamics.