and research and education are sorely needed in this context. This should offer a
chance to applied mathematicians to weigh in on this important debate.
Development of New Energy Sources
The development of non-hydrocarbon-based energy sources is central to the
sustainability of technologically advanced civilization (MacKay, 2009). There are a wide
variety of areas of research aimed at developing or improving such nontraditional energy
sources. Some mathematical challenges in fundamental research for the discovery of
new physical mechanisms for energy sources include:
- Modeling and simulation of multi-scale, multi-physics systems
- Development of computational chemistry
- Nanoscale modeling for materials-by-design
- Data assimilation in phenomenological models
- Exploration of data in large parameter spaces
The energy-source research areas listed below will profit from increased involvement
of mathematical scientists in mathematical modeling, simulation, data mining, and
optimization, used in the design of materials, simulation of chemical processes, and
device design.
- Electricity Generation
o Wind: blade materials and design, generator design, power conditioning
o Solar: photovoltaic, semiconductor, organic, nanostructure, new phenomena,
concentrated solar photovoltaic (solar concentrators), concentrated solar
power (alternative working fluids, high-temperature materials), distributed
solar thermoelectric - Chemical: fuel cells
- Hydropower: turbines, micro-turbines, advanced water power (waves, tidal)
- Thermoelectric processes
- Energy Storage: batteries, capacitive, salts, phase change materials, flywheel,
microturbines, pumped fluids, compressed air energy storage, water splitting /
water assembly - Energy Distribution & Transmission
- Power Electronics: high voltage components, power systems, distributed
generation, electric vehicles, smart grid - Fuels
o Hydrogen: water splitting, photocatalytic, photoelectrochemical, solar thermal
decomposition of water, photobiological and other chemical hydrogen
production technologies.
o Nuclear power (e.g. fusion, fission, materials for extreme environments)
In the following section, we outline examples of specific mathematical
investigations that are poised to make significant impact in transforming sources of
energy.
For examples of U.S. National Science Foundation funding of some solar energy
research projects that involve collaborations between chemists, materials scientists, and
mathematical scientists, see the award list for the NSF CHE-DMR-DMS Solar Energy
Initiative (National Science Foundation, 2010).