Date of Award

Summer 2017

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Yuan N. Young

Second Advisor

Shidong Jiang

Third Advisor

Jonathan H.C. Luke

Fourth Advisor

Michael Siegel

Fifth Advisor

Zhangli Peng


The coarse-grained molecular dynamics (CGMD) or Brownian dynamics (BD) simulation is a particle-based approach that has been applied to a wide range of biological problems that involve interactions with surrounding fluid molecules or the so-called hydrodynamic interactions (HIs). From simple biological systems such as a single DNA macromolecule to large and complicated systems, for instances, vesicles and red blood cells (RBCs), the numerical results have shown outstanding agreements with experiments and continuum modeling by adopting Stokesian dynamics and explicit solvent model. Finally, when combined with fast algorithms such as the fast multipole method (FMM) which has nearly optimal complexity in the total number of CG particles, the resulting method is parallelizable, scalable to large systems, and stable for large time step size, thus making the long-time large-scale BD simulation within practical reach. This will be useful for the study of a large collection of molecules or cells immersed in the fluids.

Included in

Mathematics Commons