Associate Professor of Mathematical Sciences
Ph.D., Princeton University
- Modeling transport in turbulent flows
- Computer simulation of microphysiological systems
- Stochastic modeling in physics and biology
- Multiscale asymptotic methods
- Random field simulation
- Nonlinear wave turbulence
P. R. Kramer, O. Kurbanmuradov, and K. Sabelfeld, "Comparative Analysis of Multiscale Gaussian Random Field Simulation Algorithms," submitted to Journal of Computational Physics.
P. J. Atzberger and P. R. Kramer, "Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations," submitted to SIAM Journal of Numerical Analysis.
P. J. Atzberger, P. R. Kramer, and C. S. Peskin, "A stochastic immersed boundary method for biological fluid dynamics at microscopic length scales," submitted to Journal of Computational Physics.
E. Castronovo and P. R. Kramer, "Subdiffusion and Superdiffusion in Lagrangian Stochastic Models of Oceanic Transport," Monte Carlo Methods and Applications, 10 (3-4), 2004: 245-256.
P. R. Kramer, "Brownian Motion," Encyclopedia of Nonlinear Science, ed., Alwyn Scott. New York and London: Routledge, 2005.
P. R. Kramer, "Fokker-Planck Equation," Encyclopedia of Nonlinear Science, ed., Alwyn Scott. New York and London: Routledge, 2005.
L. J. Borucki, T. Witelski, C. Please, P. R. Kramer, and D. Schwendeman, "A theory of pad conditioning for chemical-mechanical polishing," Journal of Engineering Mathematics, 50 (1), 2004: 1--24.
P. R. Kramer and C. S. Peskin, "Incorporating Thermal Fluctuations into the Immersed Boundary Method," Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, K. J. Bathe, ed., Elsevier, 2, 1755--1758.
P. R. Kramer, J. A. Biello, and Y. Lvov, "Application of weak turbulence theory to FPU model," Discrete and Continuous Dynamical Systems, Expanded Volume for the Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, 2003: 482--491.
J. A. Biello, P. R. Kramer, and Yuri Lvov, "Stages of energy transfer in the FPU model," Discrete and Continuous Dynamical Systems, Expanded Volume for the Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, 2003: 113--122.
P. R. Kramer and A. J. Majda, "Stochastic mode reduction for immersed boundary method," SIAM J. Appl. Math. 64 (2), 2003: 369--400.
P. R. Kramer and A. J. Majda, "Stochastic mode reduction for particle-based simulation methods for complex microfluid systems," SIAM J. Appl. Math. 64 (2), 2003: 401--422.
P. R. Kramer, A. J. Majda, and E. Vanden-Eijnden, "Closure approximations for passive scalar turbulence: A comparative study on an exactly solvable model with complex features," J. Stat. Phys., 111 (3/4), 2003: 565--679.
P. R. Kramer, "Two different rapid decorrelation in time limits for turbulent diffusion," J. Stat. Phys., 110 (1/2), 2003: 87--136.
A. J. Majda and P. R. Kramer, ."Simplified models for turbulent diffusion: Theory, numerical modelling and physical phenomena," Physics Reports, 314 (4-5), 1999: 237-574.
P. R. Kramer, "A review of some Monte Carlo simulation methods for turbulent systems,'' Monte Carlo Methods and Applications, 7 (3--4) 2001: 229--244.