https://neckpinch.com/authors/yuchuan-yang/New arXiv papers by Yuchuan Yang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2608.00293/arxiv:2608.00293Fri, 31 Jul 2026 00:00:00 GMTYuchuan Yang, Selim Esedoglu — We develop a new phase-field (diffuse interface) approximation of multiphase curvature motion with triple junction drag - an important sharp interface model for the evolution of microstructure in polycrystalline materials during heat treatment. This sharp interface model arises as gradient flow for the total length of the interfacial network with respect to a certain metric. Accordingly, we derive our diffuse interface approximation - a coupled system of partial differential equations that is a variant of the Allen-Cahn system - from a variational perspective, in the style of minimizing movements: starting from a discrete in time approximation that entails a convex optimization problem to advance from one time step to the next. In the process, we propose a simple integral expression that counts the number of junctions using the order parameter that appears to be new even for the standard multiphase Allen-Cahn system. The convergence of the resulting flow to the desired sharp interface limit is then verified via the method of matched asymptotic expansions. Numerical convergence studies against both known exact solutions as well as highly accurate benchmark solutions obtained via front tracking provide clear further evidence for this convergence. Moreover, the method retains the most desirable feature of diffuse interface methods: Automatic handling of topological changes in the network of interfaces.Other curvature flowsAnisotropic & nonlocal flowsWeak & singular flowsNumerics & visualizationPhase fields & multiphase flows https://neckpinch.com/papers/2509.06125/arxiv:2509.06125Sun, 07 Sep 2025 00:00:00 GMTYuchuan Yang, Selim Esedoglu — We consider a PDE system that describes curvature motion of networks with a dynamic boundary condition known as triple junction drag. This model arises in the study of grain boundary evolution in polycrystalline materials. In this system, the surface tension coefficients depend on the crystallographic orientations of the grains, which are allowed to rotate. We prove existence and uniqueness of solutions to this system in the parabolic Hölder class C^(2+α,1+α/2). Moreover, we extend our existence result to accommodate a wider class of initial networks by relaxing the compatibility conditions on the angles and curvatures at the triple junction. As an important by-product of our result, we demonstrate the possibility of a new type of topological change during the evolution of the network. We also revisit the question of stability of stationary networks and how it is affected by the choice of surface tensions.Other curvature flowsAnisotropic & nonlocal flowsStability & uniquenessBoundaries & non-compactPhase fields & multiphase flows