Research interests
My current research interests are focused at the interface between biology, mathematics, fluid dynamics and numerical methods. More specifically, my research involves modeling, analyzing and simulating the dynamics of domain formation in vesicle biomembranes in a viscous fluid. I have developed efficient and accurate numerical algorithms using a boundary integral approach for the multicomponent vesicle in a fluid model. Also I have developed a new interface capturing algorithm between particle and level set method.
Recent research topic1:
Moving interfce problem with elliptic equation and modifided particle level set method which have wide ranging application including, computational fluid dynamics, computational solid mechanics and other open curve problem. This new numerical scheme only uses massless particles on the interface to capture the evolution of the interface and this is much easy to implement and has pretty good 2nd order convergence results.
Recent research topic2:
I have developed and investigated a thermodynamically consistent model of two-dimensional multicomponent vesicles in an incompressible viscous fluid with my colleagues. The model is derived using an energy variation approach that accounts for variation among the surface phases and the associated the excess energy (line energy) between juxtaposed surface phases, bending energy, spontaneous curvature, local inextensibility and fluid flow via the Stokes equations. In particular, we derived the generalized Laplace - Young boundary condition for the normal stress jump across the vesicle membrane. The equations are high-order (fourth order) nonlinear and nonlocal due to the incompressibility of the fluid and the local inextensibility of the vesicle membrane so that it is highly challenging to perform dynamical simulations of all effects. To solve the equations numerically, I developed a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. The small scale decomposition is used to develop efficient, explicit time integration schemes for both the evolution of the membrane and the surface phases. In addition, the equation for the Lagrange multiplier introduced to enforce local inextensibility is reformulated.
This work has resulted in one first author publications with another in preparation.
I also extended the algorithm to 3D axisymmetric vesicles. To do this, I have also collaborated with Shuwang Li and Xiaofan Li, from IIT in Chicago, IL. I compared our results with experimental vesicle morphologies. By using same parameter settings, we obtain a good agreement between the experimental and theoretical results. A paper describing these results has been published and another has been submitted and is being in review.
