Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics Brown University; also Research Scientist at MIT George_Karniadakis at Brown.edu 
"People who wish to analyze nature without using mathematics must settle for a reduced understanding", Richard Feynman
2013Spring Course: [APMA2580]Exciting News!!! My former PhD student, Ronald D. Henrdesron, received an Oscar (2014) for the fluid system he built for DreamWorks! See the press release:

A new report by the National Research Council points to the direction and philosophy of my group practiced over the last 20 years Thank you NRC!: Here's a small sample: "...But the value of the mathematical sciences to the overall science and engineering enterprise and to the nation would be heightened if the number of mathematical scientists who share the following (3) They understand the role of the mathematical sciences in the wider world of science, engineering, medicine, defense, and business; and (4)They have some experience with computation..." 
George Karniadakis received his S.M. (1984) and Ph.D. (1987) from Massachusetts Institute of Technology. He was appointed Lecturer in the Department of Mechanical Engineering at MIT in 1987 and subsequently he joined the Center for Turbulence Research at Stanford / Nasa Ames. He joined Princeton University as Assistant Professor in the Department of Mechanical and Aerospace Engineering and as Associate Faculty in the Program of Applied and Computational Mathematics. He was a Visiting Professor at Caltech (1993) in the Aeronautics Department. He joined Brown University as Associate Professor of Applied Mathematics in the Center for Fluid Mechanics on January 1, 1994. He became a full professor on July 1, 1996. He has been a Visiting Professor and Senior Lecturer of Ocean/Mechanical Engineering at MIT since September 1, 2000. He was Visiting Professor at Peking University (Fall 2007 & 2013). He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM, 2010), Fellow of the American Physical Society (APS, 2004), Fellow of the American Society of Mechanical Engineers (ASME, 2003) and Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA, 2006). He received the CFD award (2007) and the J Tinsley Oden Medal (2013) by the US Association in Computational Mechanics. His hindex is 63 and he has been cited about 20,000 times (see my google scholar citations). See complete CV here. You can also check out our Geneaology Tree (remember to zoom in!).
Karniadakis is the lead PI of an OSD/AFOSR MURI on Uncertainty Quantification and Director of a new DOE Center of Mathematics for Mesoscale Modeling of Materials (CM4).
His research interests include diverse topics in computational science both on algorithms and applications. A main current thrust is stochastic simulation (in the context of uncertainty quantification and beyond), fractional PDEs, and multiscale modeling of physical and biological systems (especially the brain). Can you believe that we solve problems in 100 dimensions  check this out!. Read here about the exciting field of "New Biology" described by the National Research Council (2009). Read here about our work on sickle cell anemia and also on modeling malaria from first principles, which was also featured on the web site of the National Public Radio. Read here about our work on the first large multiscale modeling of a brain aneurysm (finalist in the Gordon Bell Award, Supercomputing'11). Our new area is neurovascular coupling in the brain, i.e., bridging the gap between neuroscience and vascular mechanics. New experimental evidence suggests the intriguing possibility that by slightly modulating the brain blood flow one can control information processing  read our paper here! Recent feature article of our work ("Blood in Motion") in American Scientist.
Particular aspects include:
Numerical solution of stochastic differential equations: SISC article, also PNAS article
Modeling uncertainty with polynomial chaos: PNAS article, CiSE, JCP
Biophysics  Multiscale modeling of biological systems: PNAS (sickle cell anemia); PNAS (blood viscosity); PNAS (malaria) article; PNAS (thrombosis) article, PRS article
Atomistic/Mesoscopic modeling  Dissipative Particle Dynamics: JCP (tripledecker); PRL (adaptive BCs) Low Dimensional Modeling  Gappy Data  Data assimilation: JCP article
Ongoing Interests:
Spectral/hp Element and Discontinuous Galerkin methods : OUP Book Turbulent Drag Reduction: Science article DNS/LES of turbulence in complex geometries: JFM article Flowstructure interactions: PRL article Microtransport and Dynamic selfassembly: Springer Book Flow and heat control applications: JFM article Parallel computing; Interactive/virtual reality computer graphics: CUP Book
The USACM J Tinsley Oden Medal, 2013
The USACM Computational Fluid Dynamics Award, 2007 SIAM Fellow 2010 Associate Fellow of the American Institute of Aeronautics & Astronautics (AIAA) 2006
Fellow of the American Physical Society (APS) 2004 Fellow of the American Society of Mechanical Engineers (ASME) 2003
17th Robert Bruce Wallace Lecture Award, MIT, 2003 Rheinstein Junior Faculty Award, Princeton University, 1992
Professor George Karniadakis Box F, Division of Applied Mathematics, Brown University, Providence RI 02912, USA. 

SHORT COURSE ON FRACTIONAL PDESMAY 22  31, 2013 

INTERNATIONAL SYMPOSIUM ON FRACTIONAL PDES:THEORY, NUMERICS AND APPLICATIONSJUNE 3  5, 2013 SALVE REGINA UNIVERSITY 