4 citations · 9 across the 14 of their papers we have counts for
16 papers
Homogenization and Long Time Behavior of Wasserstein gradient flow for McKean-Vlasov Equation
Yuan Gao, Nung Kwan Yip
We consider a McKean-Vlasov equation incorporating spatial fast oscillatory behavior into both the energetic and kinematic components of the model. The former is given in terms of…
Anisotropic mean curvature flow with contact angle and Neumann boundary conditions in arbitrary dimensions
Can Cui, Nung Kwan Yip
Over a bounded strictly convex domain in with smooth boundary, we establish a priori gradient estimate for an anisotropic mean curvature flow with prescribed contact…
Two dimensional anisotropic mean curvature flow with contact angle condition
Can Cui, Nung Kwan Yip
In this paper, we study surfaces which evolve by anisotropic mean curvature flow with contact angle boundary condition over a strictly convex domain in . We establish…
Far Field Asymptotics of Nematic Flows Around a Small Spherical Particle
Dmitry Golovaty, Nung Kwan Yip
Given a small spherical particle, we consider flow of a nematic liquid crystal in the corresponding exterior domain. Our focus is on precise far field asymptotic behavior of the fl…
Homogenization of Wasserstein gradient flows
Yuan Gao, Nung Kwan Yip
We prove the convergence of a Wasserstein gradient flow of a free energy in inhomogeneous media. Both the energy and media can depend on the spatial variable in a fast oscillatory…
Numerical Stability for Differential Equations with Memory
Guihong Wang, Yuqing Li, Tao Luo +3
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step meth…
Dynamics and steady state of squirmer motion in liquid crystal
Leonid Berlyand, Hai Chi, Mykhailo Potomkin +1
We analyze a nonlinear PDE system describing the motion of a microswimmer in a nematic liquid crystal environment. For the microswimmer's motility, the squirmer model is used in wh…
Bunching instability and asymptotic properties in epitaxial growth with elasticity effects: continuum model
Tao Luo, Yang Xiang, Nung Kwan Yip
We study the continuum epitaxial model for elastic interacting atomic steps on vicinal surfaces proposed by Xiang and E (Xiang, SIAM J. Appl. Math. 63:241-258, 2002; Xiang and E, P…
Stability of Self-similar Solutions to Geometric Flows
Hengrong Du, Nung Kwan Yip
We show that self-similar solutions for the mean curvature flow, surface diffusion and Willmore flow of entire graphs are stable upon perturbations of initial data with small Lipsc…
A Retrospective Approximation Approach for Smooth Stochastic Optimization
David Newton, Raghu Bollapragada, Raghu Pasupathy +1
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective and a stochastic first-order ora…
Towards an Understanding of Residual Networks Using Neural Tangent Hierarchy (NTH)
Yuqing Li, Tao Luo, Nung Kwan Yip
Gradient descent yields zero training loss in polynomial time for deep neural networks despite non-convex nature of the objective function. The behavior of network in the infinite…
Energy Scaling and Asymptotic Properties of One-Dimensional Discrete System with Generalized Lennard--Jones Interaction
Tao Luo, Yang Xiang, Nung Kwan Yip
It is well known that elastic effects can cause surface instability. In this paper, we analyze a one-dimensional discrete system which can reveal pattern formation mechanism resemb…
Infinite server queues in a random fast oscillatory environment
Harsha Honnappa, Yiran Liu, Samy Tindel +1
In this paper, we consider a infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluct…
Convergence of Diffusion Generated Motion to Motion by Mean Curvature
Drew Swartz, Nung Kwan Yip
We provide a new proof of convergence to motion by mean curvature (MMC) for the Merriman-Bence-Osher (MBO) thresholding algorithm. The proof is elementary and does not rely on maxi…
Convergence of Space-Time Discrete Threshold Dynamics to Anisotropic Motion by Mean Curvature
Oleksandr Misiats, Nung Kwan Yip
We analyze the continuum limit of a thresholding algorithm for motion by mean curvature of one dimensional interfaces in various space-time discrete regimes. The algorithm can be v…
Existence and uniqueness of invariant measures for stochastic reaction-diffusion equations in unbounded domains
Oleksandr Misiats, Oleksandr Stanzhytsyi, Nung Kwan Yip
In this paper we investigate the long-time behavior of stochastic reaction-diffusion equations of the type , where is an elliptic operator, …