5 papers
Turbulent Flame Speed Can Increase under Curvature Smoothing
Hung V. Tran, Jack Xin, Yifeng Yu
Curvature effects are expected to smooth flame-front wrinkles and thereby reduce turbulent flame speed. We construct a smooth three-dimensional periodic shear flow for which introd…
Evaluating AI Grading on Real-World Handwritten College Mathematics: A Large-Scale Study Toward a Benchmark
Zhiqi Yu, Xingping Liu, Haobin Mao +4
Grading in large undergraduate STEM courses often yields minimal feedback due to heavy instructional workloads. We present a large-scale empirical study of AI grading on real, hand…
Does Yakhot's growth law for turbulent burning velocity hold?
Wenjia Jing, Jack Xin, Yifeng Yu
Using formal renormalization theory, Yakhot derived in ([32], 1988) an growth law of the turbulent flame speed with respect to large flow in…
Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz Estimates
Connor Mooney, Zhongjian Wang, Jack Xin +1
We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth…
Lagrangian, Game Theoretic and PDE Methods for Averaging G-equations in Turbulent Combustion: Existence and Beyond
Jack Xin, Yifeng Yu, Paul Ronney
G-equations are popular level set Hamilton-Jacobi nonlinear partial differential equations (PDEs) of first or second order arising in turbulent combustion. Characterizing the effec…