Professor Lee Dong-sun of Incheon National University's Mathematics Education Department and Professor Kim Hyun-joo of Korea Institute of Energy Technology

Professor Lee Dong-sun of Incheon National University's Mathematics Education Department and Professor Kim Hyun-joo of Korea Institute of Energy Technology announced that they have published a research paper that presents a new model in the field of computational science and numerical simulation by interpreting phase separation in domains where different substances are connected based on time-fractional phase-field equations.

Phase separation is a phenomenon in which different phases are separated within a mixture, generally affected by temperature and material properties. In previous studies, it was not possible to calculate what kind of phase separation occurs on the domain where different substances are connected because the domain in which the phase exists must be homogeneous. In this study, Professor Lee Dong-sun of Incheon National University and co-researcher Professor Kim Hyun-joo studied phase separation and geometric movement on the surface of a polyhedron with different domain characteristics for each side through the Allen-Cahn model, which applied various time-fraction orders, numerically revealed the phase separation phenomenon on the domain where several substances are bound.

In particular, this study produced interesting results on the diffusion and reaction of particles by applying the Allen-Kan model of different time-fraction orders to each side of the polyhedral surface. This study is expected to contribute to providing an important scientific foundation for precise phase property control and semiconductor design in the fields of energy and material engineering.

The findings were published in the online edition of November 19, 2024, in the journal Communications in Nonline Science and Numeral Simulation, which falls within the top 5% of applicable mathematics.

(a)shows the surface of the tetrahedron as a domain. (b) and (c) are the results of phase separation simulations in the homogeneous domain when the differential order for the time of each face is the same as an integer order.

It is a picture that shows only the zero-level set for the phase separation phenomenon that occurs when different time-fraction orders are applied to each side of the tetrahedron. It can be seen that the rate and pattern of phase separation between heterogeneous planes with different time-fraction orders are different, but the continuity at the inter-plane boundary is maintained. This means that a natural phase separation pattern appears even when faces with different material properties are bonded.