Stochastic Differential Equations/Uncertainty

1. P. Prempraneerach, C. Chryssostomidis, M.S. Triantafyllou, and G.E. Karniadakis, "Stochastic modeling of integrated power system coupled to hydrodynamics in the all-electric ship," International Symposium on Power Electronics, Electrical Drives, Automation and Motion, June 2008
2. P. Prempraneerach, F.S. Hover, M.S. Triantayllou, C. Chryssostomidis and G.E. Karniadakis, "Sensitivity analysis and low-dimensional stochastic modeling of shipboard integrated power systems," 39th Power Electronics Specialists Conference, June 2008.
3. X. Wan and G.E. Karniadakis, "Recent advances in polynomial chaos methods and extensions," NATO/OTAN, Paper Reference Number: RTO-MP-IST-999 Computational Uncertainty in Military Vehicle Design Meeting Proceedings 2008.
4. D. Venturi, X. Wan and G.E. Karniadakis ''Stochastic low-dimensionla modeling of random laminar wake past a circular cylinder,'' J. Fluid Mech. (under consideration for publication) 2007.
5. P. Prempraneerach, F.S. Hover, M.S. Triantayllou, T.J. McCoy, C. Chryssostomidis and G.E. Karniadakis, "Stochastic sensitivity methods and appliation to the shipboard power system, submitted to IEEE Transaction on Power system Engineering, April 2007 with 1st revsion in November 2007.
6. P. Prempraneerach, F.S. Hover, M.S. Triantayllou, T.J. McCoy, C. Chryssostomidis and G.E. Karniadakis, "Sensitivity analysis of the shipboard integrated power system," Naval Engineering Journal, 119(2), 2007.
7. G. Lin, C.-H. Su and G.E. Karniadakis ''Random roughness enhances lift in supersonic flow,'' Phy. Rev. Letts. 99(10), 104501-1 - 104501-4, 2007.
8. G. Lin, X. Wan, C.-H. Su and G.E. Karnidakis ''Stochstic computational fluid mechanics,'' IEEE Computing in Sci. Engin. 9(2) 21-29, March-April 2007.
9. P. Prempraneerach, F.S. Hover, M.S. Triantayllo and G.E. Karniadakis, "Uncertainty quantifiction in simulations of power systems: Multi-element polynomial chaos methods," submitted to International Journal of Electrical Power and Energy Systems, November 2007.
10. P. Prempraneerach, F.S. Hover, M.S. Triantayllou, T.J. McCoy, C. Chryssostomidis and G.E. Karniadakis, "Sensitivity analysis of the shipboard integrated power system," ASNE Proceedings on Fuel Tank to Target, Building the Electric Fighting Ship, June 2007.
11. P. Prempraneerach, F.S. Hover, M.S. Triantafyllou, C. Chryssostomidis and G.E. Karniadakis, "Effects of Uncertain Propulsion Loads on the Electric Ship Power Bus, Electric Ship Resarch and Development consortium (ESRDC), MIT, May 2007.
12. G. Lin, L. Grinberg and G.E. Karniadakis ''Numerical studies of the stochastic Korteweg de Vries equation,'' J. Comp. Phys., 213(2), 676-703, 2006.
13. X. Wan and G.E. Karniadakis "A sharp error estimate for the fast Gauss transform," J. Comp. Phys. 219(1), 7-12, 2006.
14. G. Lin, C.-H. Su and G.E. Karniadakis, ''Modeling uncertainties in supersonic flow past a wedge,'' 44th Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 9-12, 2006.
15. G. Lin, C.-H. Su and G.E. Karniadakis, ''Predicting shock dynamics in the presence of uncertainties,'' J. Comp. Phys. vol. 217, issue 1, 1-4, 2006.
16. X. Wan and G.E. Karniadakis, ''Stochastic heat transfer enhancement in a grooved channel,'' J. Fluid Mech., vol. 565, 255-278, 2006.
17. X. Wan and G.E. Karniadakis, ''Beyond Wiener-Askey expansions: Handling arbitrary PDFs,'' J. Sci. Comp., vol. 27, numbers 1-3, 455-464, 2006.
18. X. Wan and G.E. Karniadakis, ''Multi-element generalized polynomial chaos for arbitrary probability measures,'' SIAM J. Sci. Comp., 28(3), 901-928, 2006..
19. X. Wan and G.E. Karniadakis, ''Long-term behavior of polynomial chaos in stochastic flow simulations,'' Comput. Methods Appl. Mech. Engrg., vol. 195, issues 41-43, 5582-5596, 2006.
20. X. Wan and G. Karniadakis, ''Simulation of heat transfer with uncertainty,'' Proceedings of HT2005, 2005 ASME Summer Heat Transfer Conference, San Francisco, CA, July 17-22 2005.
21. G. Lin, C.-H. Su and G.E. Karniadakis, ''Stochastic solvers for the Euler equations,'' 43rd Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 10-13, 2005.
22. G. Lin, C.-H. Su and G.E. Karniadakis, ''The stochastic piston problem,'' Proc. National Academy of Sciences, vol. 101, pp. 15840-15845, 2004.
23. D. Lucor, C.-H. Su and G.E. Karniadakis, ''Generalized polynomial chaos and random oscillators,'' Int. J. Numer. Meth. Eng., 60(3), 571-596, 2004.
24. D. Lucor, C.-H. Su and G.E. Karniadakis, ''Karhunen-Loeve representation of periodic second-order autoregressive processes,'' International Conference on Computational Science, June 6-9 2004, Krakow, Poland.
25. D. Lucor and G.E. Karniadakis, ''Adaptive generalized polynomial chaos for nonlinear random oscillators,'' SIAM J. Sci. Comp., vol. 26, no. 2, pp. 720-735, 2004.
26. X. Wan, D. Xiu and G.E. Karniadakis, ''Modeling uncertainty in three-dimensional heat transfer problems,'' Heat Transfer 2004, March 24-26 2004, Lisbon, Portugal.
27. D. Xiu and G.E. Karniadakis, ''Generalized Polynomial Chaos: Performance Evaluation and Applications,'' DDDAS/Kluwer 2004.
28. D. Lucor and G.E. Karniadakis, ''Noisy inflows cause shedding-mode switching in flow past an oscillating cylinder,'' Physical Review Letters, 92(15), 154501-1 - 154501-4 2004.
29. D. Lucor and G.E. Karniadakis, ''Predictability and uncertainty in flow-structure interactions,'' European Journal of Mechanics/B Fluids, Vol. 23 pp. 41-49 (2004) Special Issue: Proc. Conference on Bluff Body Wakes and Vortex-Induced Vibrations (BBVIV3; invited paper), 17-20 December 2002, Queensland, Australia, Edited by T. Leweke, K. Hourigan and C.H.K. Williamson.
30. D. Xiu and G.E. Karniadakis, ''Supersensitivity due to uncertain boundary conditions,'' Int. J. Num. Meth. Eng., vol. 61, pp. 2114-2138, 2004.
31. X. Wan, D. Xiu and G.E. Karniadakis, ''Stochastic solutions for the two-dimensional advection-diffusion equation,'' SIAM J. Sci. Comp., vol. 26, no. 2, pp. 578-590, 2004.
32. D. Xiu and G.E. Karniadakis, ''Uncertainty modeling of Burgers' Equation by generalized polynomial chaos,'' Computational Stochastic Mechanics, Proceedings of the 4th International Conference on Computational Stochastic Mechanics, Corfu, Greece, June 2002. Edited by P.D. Spanos and G. Deodatis, pp. 655-661, Millpress Rotterdam, 2003.
33. D. Lucor, D. Xiu, C.-H. Su and G.E. Karniadakis, ''Predictability and Uncertainty in CFD,'' Int. J. Num. Meth. Fluids, 43(5), 485-505, 2003.
34. D. Xiu and G.E. Karniadakis, ''Modeling uncertainty in flow simulations via generalized polynomial chaos,'' J. Comp. Phys., 187, 137-167, 2003.
35. D. Xiu and G.E. Karniadakis, ''Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos,''Computer Methods in Applied Mechanics and Engineering, vol. 191, pp. 4927-4948, 2002.
36. G.E. Karniadakis, ''Quantifying Uncertainty in CFD,'' Editor of special issue of J. Fluids Engineering, March 2002.
37. D. Xiu and G.E. Karniadakis, ''The Wiener-Askey polynomial chaos for stochastic differential equations,'' SIAM J. Sci. Comput., 24(2), 619-644, 2002.
38. D. Xiu, D. Lucor, C.-H. Su and G.E. Karniadakis, ''Stochastic modeling of flow-structure interactions using generalized polynomial chaos,'' J. Fluids Engin., vol. 124, pp. 51-59, 2002.
39. D. Xiu and G.E. Karniadakis, ''Modeling uncertainty of elliptic partial differential equations via generalized polynomial chaos,'' Proceedings of the 5th ASCE Engineering Mechanics Division Conference, Columbia University, New York City, June 2002.
40. M. Jardak, C.-H. Su and G.E. Karniadakis, ''Spectral polynomial chaos solutions of the stochastic advection equation,'' J. Sci. Comp., vol. 17, Nos. 1-4, pp. 319-338, 2002.
41. D. Xiu, D. Lucor and G.E. Karniadakis, ''Modeling uncertainty in flow-structure interactions,'' Computational Fluid and Solid Mechanics, Proc. First MIT Conference, Cambridge, Massachusetts, USA, June 12-15, 2001, edited K.J. Bathe, vol. 2, pp. 1420-1423, 2001.
42. G.E. Karniadakis, ''Towards a numerical error bar in CFD,'' Editorial Article, J. Fluids Engineering, March 1995.