A simple transcendental travelling wave solution and stability study for the thermophoretic motion with variable heat transmission factors on substrate-supported grapheme sheet
| Autor: | Chan, Yue, Cai, Daoju, Cai, Kaisheng, Lee, Shern-Long, Lin, Rumiao, Ren, Yong |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 8 pages, 5 figures, conference |
| Databáze: | arXiv |
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