Institutions of higher education and the research community:- To develop curricula that encompass energy education;
- To encourage the development of international collaborations on energy related
issues.
The final set of recommendations is a sample list of areas of mathematics and
specific topics of research whose development would significantly enhance the role of
mathematicians in achieving sustainable energy production for a modern society:
- Stochastic optimization of complex, dynamic systems: e.g. for storage, R&D
portfolio optimization, grids, generators, users; - Incomplete economic models and stochastic games: e.g. for greenhouse gas
emissions policy, power generation policies; - Inverse problems for PDEs and SPDEs for the design of new materials: e.g. for
energy production, storage, transmission and conversion; - Modeling and simulation of multi-scale and multi-physics systems: e.g.
downscaling of fluid mechanics equations for wind turbines, thin films, nanoscale
materials; - Optimal sampling for estimation of climate change impact for market response to
price signals, understanding new materials, sensor placement.
References:
- National Science Foundation, CHE-DMR-DMS Solar Energy Initiative, NSF 10-613,
Technical report.
http://www.nsf.gov/publications/pub_summ.jsp?org=MPS&ods_key=nsf10613 - Barmak K, Emelianenko,M, Golovaty D, Kinderlehrer D, Ta’asan SA (2004). New
perspective on texture evolution. International Journal on Numerical Analysis Models
1(1): 1-18, - Bertsekas D, Tsitsiklis J (1996). Neuro-Dynamic Programming, Athena Scientific.
- Bhattacharya K, Friesecke G, James RD (1999). The mathematics of microstructure
and the design of new materials. Proceedings National Academy of Science 96 :
93328333. - Birge J, Louveaux F (1997). Introduction to Stochastic Programming, Springer-
Verlag. - Carmona R, Fehr F, Hinz J, Porchet A (2010). Market designs for emissions trading
schemes. SIAM Review 52 : 403-452. - Delville R, Kasinathan S, Zhang Z, Humbeeck V, James RD, Schryvers DA (2011).
Transmission electric microscopy study of phase compatibility in low hysteresis
shape memory alloys. Phil. Mag. - Fonseca I, Fusco N, Leoni G, Morini M (2007). Equilibrium configurations of
epitaxially strained crystalline films: Existence and regularity results. Archives
Rational Mechanical Analysis 186 : 477537. - Glimm J, Hou S, Lee YH, Sharp D, Ye K (2004). Sources of uncertainty and error in
the simulation of flow in porous media. Computational Applied Mathematics 23 : 109-
120. - Hastie T, Tibshirani R, Friedman J (2009).The Elements of Statistical Learning: Data
Mining, Inference and Prediction, Springer Verlag.