Early work

• singular parabolic PDEs (existence-uniqueness-potentials)
• singular perturbations
• 4th order elliptic boundary value problems
• almost periodic solutions of integrodifferential delay equations

• Pure materials:
  • Stefan-type problems
  • hyperbolic Stefan problems
  • laser-induced melting
  • supercooling and nucleation
  • void formation, shrinkage effects
  • latent heat energy storage
    • for power system for space station
    • for oxygen production on the moon
  • convection in the melt ( benchmark solutions for Tin and Gallium melting)
  • laser ablation

• Binary alloys/mixtures:
  • simple mushy zone models
  • dilute alloys
  • Mercury-Cadmium-Tellurite (HgCdTe) infrared detector alloy
  • Ge-Si alloys
  • in situ vitrification
    • Diopside-Anorthite
    • Feldspar-Pyroxene
  • gas hydrates in seafloor sediments
  • convection in the melt

Cellular Physiology

• synaptic transmission
• visual transduction in retinal rod cells
• electrical propagation in excitable tissue (action potentials in heart)

Assorted other

• stress-assisted diffusion
• free energy minimization for fluid interfaces
• heat pumps
• inverse problems in geophysics (airborne EM surveying)
• super-time-stepping acceleration of explicit schemes
• molecular dynamics computations - time stepping