Projects

Research grants

PI: Critical regularity, selection dynamics, and condensation in nonlinear balance laws: funding National Science Foundation (2021--2023). DMS2135470.

PI - Data-driven Optimal Control modeling of PDEs, TrAC research project.

Core co-PI Presidential interdisciplinary Research Initiative (PIRI), Iowa State University, (PI: Sarkar Soumik),
Translational AI Center for Research and Education (TrAC), 2021-2024.

PI: Simons Foundation Collaboration Travel Grant, 2018--2023.

PI: Critical regularity, selection dynamics, and condensation in nonlinear balance laws
funding National Science Foundation (2018-2021). DMS18-12666

PI: Recovery of High Frequency Wave Fields, Kinetic Theory of Photons and Entropy Satisfying Methods:
funding National Science Foundation (2013-2017). DMS13-12636.

Critical Threshold Phenomena in Nonlinear Balance Laws

H. Liu
Global orientation dynamics for liquid crystalline polymers, Physica D. 228 (2007), 122-129.

T. Li and H. Liu (2007)
Critical thresholds in a relaxation model for travel flows, to appear in J. Indiana Univ.

Read More about Critical Threshold Phenomena in Nonlinear Balance Laws
High Frequency Wave Propagation and Geometric Motion

H. Liu and C. Sparber (2007)

Rigorous Derivation of the Hydrodynamical Equations for Rotating Superfluids, to appear in M3AS.

Read More about High Frequency Wave Propagation and Geometric Motion
Hyperbolic Conservation Laws, Stability of Discrete and Viscous Shock Profiles

A. Haseena and H. Liu (2007)
Formulation and analysis of alternating evolution (AE) schemes for hyperbolic conservation laws, Submitted to SINUM.

A. Haseena and H. Liu (2007)

Read More about Hyperbolic Conservation Laws, Stability of Discrete and Viscous Shock Profiles
Multi-scale Wave Dynamics in Nonlinear Balance Laws

H. Liu and C. Sparber (2007)

Rigorous Derivation of the Hydrodynamical Equations for Rotating Superfluids, to appear in M3AS.

Read More about Multi-scale Wave Dynamics in Nonlinear Balance Laws
Orientation, Dynamics of Crystalline Polymers and Phase Transition Phenomena

C. Liu and H. Liu,

Read More about Orientation, Dynamics of Crystalline Polymers and Phase Transition Phenomena
Relaxation Dynamics, Scaling Limits and Convergence of Relaxation Schemes

T. Li and H. Liu (2007)
Critical thresholds in a relaxation model for travel flows, to appear in J. Indiana Univ.

T. Li and H. Liu (2006)

Read More about Relaxation Dynamics, Scaling Limits and Convergence of Relaxation Schemes