2021/09/19 by Yue Chan, Chan, Yue, Daoju Cai +9
Engineering · Mathematics · #Applied Physics (physics.app-ph) #Classical Physics (physics.class-ph) #FOS: Physical sciences #Fluid Dynamics and Heat Transfer #Gas Dynamics and Kinetic Theory #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.2109.09059
openalex publication_date 2021/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Manually tailored wrinkled graphene sheets hold great promise in fabricating smart solid-state devices. In this paper, we employ an energy method to transform the original third-order partial differential equation (pde), i.e. Eq. (1) into the first-order pde, i.e. Eq. (8) for the thermophoretic motion of substrate-supported graphene sheets, which can be solved in terms of semi-group and transcendental solutions. Unlike soliton solutions derived using other more sophisticated techniques [9, 23], the present transcendental solution can be easily solved numerically and provides physical insights. Most importantly, we verify that the formation of various forms for wrinkling wave solutions can be determined by the evolution of equilibrium points for Eq. (1). This sheds a light on modifying the heat sources in order to control the configuration of wrinkle waves that has not been previously addressed.