• Numerical simulation of buckle folding
• Numerical simulation of rock fabric evolution
• Fracture initiation
• Salt tectonics
• Deformation bands
• Wellbore and reservoir geomechanics

Dr. Gao's research emphasizes the combination of geology, physics, mathematics, and computer science to explore the Earth. We image the structure of the Earth's deep interior using elastic waves produced by earthquakes, and study the distribution of earthquakes and volcanic eruptions in space and time.

I am a geophysicist  with a teaching and research interest in both exploration geophysics and solid-earth geophysics. My expertise includes 3-D seismic data interpretation, digital signal processing, computational and observational seismology, seismic hazard mitigation, and layered structure detection in the earth's mantle.

climate change-related and seismic hazards, infrastructure resilience against natural hazards, applications of remote sensing and AI in geological (geotechnical) engineering, and carbon detection and capture.

Interface problems, computational fluid dynamics, computational electromagnetics, stochastic PDEs, boundary integral equations, feedback control

Finite element methods, domain decomposition methods, extrapolations

Computational plasma physics (Particle-In-Cell method)

My general research areas are applied mathematics, scientific computing, and numerical analysis. I am particularly interested in reduced order modeling of partial differential equations (PDEs), computational feedback control of PDEs, and applications in control theory, engineering, and mathematics.

• Efficient numerical methods for computing ground states of spin-1 Bose-Einstein condensates based on their characterizations
• Modeling, analysis, and applications of complex systems
• Abel dynamic equations of the first and second kind
• Maximizing critical currents in superconductors by optimization of normal inclusion properties
• Dynamical laws of the coupled Gross-Pitaevskii equations for spin-1 bose-einstein condensates

• Statistical modeling of genomics, epigenomic, and biomedical data
• Statistical methods for explainability in unsupervised learning applications
• Modeling sleep in Drosophila melanogaster

Aerodynamics, aerothermodynamics, uncertainty quantification, hypersonic flows and systems, computational fluid dynamics, planetary entry/descent/landing of spacecraft, multidisciplinary analysis and design of aerospace vehicles, robust design, numerical methods.

Micro/nanoscale thermodynamics and heat transfer, Dynamics of nanodroplets, nanobubbles, and nanoparticles, Structure-property relationship for materials and interfaces, and Computational modeling

Advanced li-ion battery, beyond li-ion battery, energy storage system, renewable energy system, grid energy storage, nano, macro-mechanics of materials, self-assembly of nanoparticles, nanostructure, multiphysics, multiscale experiment and simulation.

 Plasma aerospace applications; Space propulsion; Plasma-material interactions; Plasma physics and rarefied gas dynamics; High-performance computing.

• Quantum field theory
• Classical and nonequilibrium phase transitions
• Critical behavior
• Magnetism and superconductivity in correlated quantum materials
• Transport in disordered media
• Renormalization group
• Monte-Carlo simulations

• Wave Diffusion in Confined Geometries
• Localization Phenomena
• Coherent Control of Wave Transport
• Imaging in Turbid Media
• Lasing in Complex Photonic Media
• Metamaterials

• Transparent conducting oxides
  • Composition and defect formation
• Amorphous oxide semiconductors
  • Crystallization, transport and flexibility
• Thermoelectric and topological materials
  • Spin-orbital coupling and superconductivity
• Advanced steels
  • Alloying, fracture, and deformation
• Dilute magnetic wide-bandgap semiconductors
  • Multilayers, digital alloys, interface engineering
• Magnetoresistivity in strongly-correlated oxides
  • Spin, charge, orbital degrees of freedom