Discussion Highlights

I. Multiscale Problems
(a) Upscaling for computational purposes -- consistency
(b) Upscaling for analytical purposes/homogenization
(c) Multigrid/multiscale
.....Multigrid methods for physical multiscale information? Dynamic meshing
II. Stochastic Versus Deterministic Modeling
(a) Majority of current code calculations deterministic
.....Can stochastic approaches improve modeling capability?
.....Can stochastic methods improve/extend geostatistical methods for imaging applications
(b) Dynamic similarity, statistical invariant
(c) Ensemble predictions
.....Moment equations, Monte Carlo
III. Data Uncertainty
(a) Generalized inverse problems for sparse data sets
(b) Imaging physical quantities, resolution, etc.
(c) Need for analysis and improvements in data usage
.....Data mining/joint inversion of multiple data sets
IV. Specific Applications
(a) Geomorphology
.....Sediment transport/granular media mechanics/continuum approximations
(b) Hydrology
.....Coupled multiscale transport phenomena (e.g., subsurface)
.....Precipitation to flow routing
(c) Hydro-meterology
.....Atmospheric boundary layers, land/surface/atmosphere interactions
(d) Granular flows
.....Fundamentals of sediment transport?
(e) Interface dynamics
.....Example: Coastal zone bordering the oceans, beaches, etc.
(f) Intermittancy
.....Extreme value behavior/connection to physics/scale invariance
(g) Innovative methods for model verification (e.g., experimental)
(h) Improvements possible in numerical methods/analysis?
.....Examples: FFT, wavelets, simplex algorithm
V. Education and/or Teaming
(a) Encourage geosciences students to take appropriate math courses
(b) Encourage math faculty to develop appropriate math classes
(c) Math faculty on geosciences thesis committees
(d) Math faculty collaborating with geosciences groups
(e) Reciprocity/Post-docs