52 citations · 95 across the 6 of their papers we have counts for
7 papers
Error Bounds for Boundary-Stopped Positive Cubature Schemes for Hamilton--Jacobi--Bellman Equations
Haoran Xu, Xingye Yue
We derive error bounds for a boundary-stopped positive cubature scheme for degenerate parabolic Hamilton--Jacobi--Bellman equations with Dirichlet data on bounded domains. The sche…
A Positivity-Preserving Expectation Scheme for Hamilton--Jacobi--Bellman Equations with Oblique Robin Boundary Conditions
Haoran Xu, Xingye Yue
For anisotropic diffusion with mixed derivatives, standard compact coordinate-aligned stencils and some local finite-volume or finite-element constructions can lose nonnegative coe…
Collision and coalescence dynamics of bosonic quantum Hall droplets
Xinyi Liu, Zhendong Li, Yuwen Zhou +5
Recently bosonic quantum Hall droplets have been observed in rapidly rotating two-dimensional Bose-Einstein condensates (BECs), which exhibit robust dynamical stability. Inspired b…
A Non-compact Positivity-Preserving Numerical Scheme for Elliptic Differential Equations Based on Mathematical Expectation
Haoran Xu, Kunyang Li, Xingye Yue
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form elliptic equations. Based on the Feynman--Kac formula, the solution is represented as a…
A Non-compact Positivity-Preserving Scheme for Parabolic PDE via Conditional Expectation
Haoran Xu, Jie Ren, Xingye Yue
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form parabolic equations. Based on the Feynman-Kac formula, the solution is expressed as a co…
Self-enhanced mobility enables vortex pattern formation in living matter
Haoran Xu, Yilin Wu
Emergence of regular spatial patterns is a hallmark in living matter ranging from subcellular organelles to developing embryos and to ecosystems. Mechanisms for the formation of or…
Autonomous waves and global motion modes in living active solids
Haoran Xu, Yulu Huang, Rui Zhang +1
Elastic active matter or active solid consists of self-propelled units embedded in an elastic matrix. Active solid resists deformation; the shape-preserving property and the intrin…