An Explicit Adaptive Finite Difference Method for the Cahn-Hilliard Equation.

In this study, we propose an explicit adaptive finite difference method (FDM) for the Cahn-Hilliard (CH) equation which describes the process of phase separation. The CH equation has been successfully utilized to model and simulate diverse field applications such as complex interfacial fluid flows and materials science. To numerically solve the CH equation fast and efficiently, we use the FDM and time-adaptive narrow-band domain.

Mathematical modeling and computer simulation of the three-dimensional pattern formation of honeycombs.

We present a mathematical model, a numerical scheme, and computer simulations of the three-dimensional pattern formation of a honeycomb structure by using the immersed boundary method. In our model, we assume that initially the honeycomb cells have a hollow hemisphere mounted by a hollow circular cylinder shape at their birth and there is force acting upon the entire side of the cell. The net force from the individual cells is a key factor in their transformation from a hollow hemisphere mounted by a hollow circular cylinder shape to a rounded rhombohedral surfaces mounted by a hexagonal cylinder shape.

The daily computed weighted averaging basic reproduction number for MERS-CoV in South Korea.

In this paper, we propose the daily computed weighted averaging basic reproduction number for Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, May to July 2015. We use an SIR model with piecewise constant parameters (contact rate) and (removed rate). We use the explicit Euler's method for the solution of the SIR model and a nonlinear least-square fitting procedure for finding the best parameters.

Microphase separation patterns in diblock copolymers on curved surfaces using a nonlocal Cahn-Hilliard equation.

We investigate microphase separation patterns on curved surfaces in three-dimensional space by numerically solving a nonlocal Cahn-Hilliard equation for diblock copolymers. In our model, a curved surface is implicitly represented as the zero level set of a signed distance function. We employ a discrete narrow band grid that neighbors the curved surface.

Mathematical model and numerical simulation of the cell growth in scaffolds.

A scaffold is a three-dimensional matrix that provides a structural base to fill tissue lesion and provides cells with a suitable environment for proliferation and differentiation. Cell-seeded scaffolds can be implanted immediately or be cultured in vitro for a period of time before implantation. To obtain uniform cell growth throughout the entire volume of the scaffolds, an optimal strategy on cell seeding into scaffolds is important.