Visiting Assistant Professor, Applied Mathematics and Statistics
- PhD, Tulane University
- MS, Tulane University
- BA/BS, The Evergreen State College
- I am interested broadly in numerical methods and biofluids with particular emphasis on Stokes flow.
Current Research Projects
- Singly-periodic Stokes Flow with a Wall: There are many real world phenomena of interest that involve viscous fluid near a wall or surface such as the beating of cilia and blood flow through small capillaries. There are often situations that involve many repeated structures, like carpets of cilia and flow past obstacles. It can be computationally expensive to the extent of being prohibitive to model a large number of these structures individually. One approach to try and still capture the influence of many structures is to assume that they are periodically repeated. In this project I obtained the exact flow due to an infinite array of regularized Stokeslet in 2 dimensions. Using the method of images this result was extended to enforce zero flow along a wall. A few applications were looked at, such as simulating an infinite array of cilia (as well as flow past periodic objects near a wall.
- Simulating Cilia in 3 Dimensions: Cilium play a diverse and important role in biology, from facilitating the transport of the ovum through the Fallopian tubes to the movement of mucus and particles in the lungs and mechanotransduction. The biological structure of cilium has been fairly well documented (the so called “9+2” axoneme structure), but it is still unkown how the individual parts interact to form a cohesive and regular beat. This projects looking at modeling cilia where the beat shape arises organically from attempting to simulate the internal mechanisms. This approach means that the motion of the cilium itself is coupled with the fluid and properties that depend on hydrodynamic coupling such as how the beat frequency depends on the spacing between cilia and the synchronization of cilia beat patterns can be investigated.
- Forest Mannan, Ricardo Cortez. An Explicit Formula for 2D Regularized Stokeslets Flow with Periodicity in one Direction and Bounded by a Plane Wall, (accepted). Preprint
- Forest Mannan, Ricardo Cortez. An Integrative Computational Model of Ciliary Beating in 3D , (in preparation).