10 citations · 28 across the 7 of their papers we have counts for
10 papers
On the triple junction problem with general surface tension coefficients
Nicholas D. Alikakos, Zhiyuan Geng
We investigate the Allen-Cahn system \begin{equation*} Δu-W_u(u)=0,\quad u:\mathbb{R}^2\rightarrow\mathbb{R}^2, \end{equation*} where is a pote…
On the triple junction problem on the plane without symmetry hypotheses
Nicholas D. Alikakos, Zhiyuan Geng
We investigate the Allen-Cahn system \begin{equation*} Δu-W_u(u)=0,\quad u:\mathbb{R}^2\rightarrow\mathbb{R}^2, \end{equation*} where is a pote…
Uniform profile near the point defect of Landau-de Gennes model
Zhiyuan Geng, Arghir Zarnescu
For the Landau-de Gennes functional on 3D domains, \begin{equation*} I_{\varepsilon}(Q,Ω):=\int_Ω\left\{\frac{1}{2}|\nabla Q|^2+\frac{1}{\varepsilon^2}\left( -\frac{a^2}{2}\mathrm{…
A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows
Zhiyuan Geng, Rafael Granero-Belinchón
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of…
Identifying the Relationship between Seasonal Variation in Residential Load and Socioeconomic Characteristics
Zhenyu Wang, Hao Wang
Smart meter data analysis can provide insights into residential electricity consumption behaviors. Seasonal variation in consumption is not well understood but yet important to uti…
Two dimensional liquid crystal droplet problem with tangential boundary condition
Zhiyuan Geng, Fanghua Lin
This paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a…