and conversion often requires solving inverse problems for partial
differential equations and stochastic partial differential equations,
which present challenging problems.
- We need ways to reduce energy consumption, which leads to
mathematical challenges involving economic incentives for energy-
efficient construction, new pricing schemes for energy use, and use of
the “smart grid” to track consumption.
- We need new methods for modeling and simulation of multi-scale and
multi-physics systems, e.g., downscaling of fluid mechanics equations
for wind turbines, thin films, and nanoscale materials.
- New statistical methods of optimal sampling are needed for estimation
of climate change impact on market responses, for identifying signals
of environmental change, for understanding new materials, for
comparing readings from numerous sensors providing massive
amounts of data in a short time, and for placing sensors to maximize
their usefulness in providing relevant data.
