





Peter Kramer
Professor
Ph.D. Princeton University
Applied and Computational Mathematics

Publications:
 L. Yao, P. R. Kramer, D. Couvin, N. Rastogi, P. Supply, and K. P. Bennett, "
Evolutionary Analysis of mycobacterial interspersed repetitive
units of Mycobacterium tuberculosis complex," submitted to Infection, Genetics, and Evolution
 Y. Qian, P. R. Kramer, and P. T. Underhill, "Stochastic Kinetic Theory for Collective Behavior of Hydrodynamically Interacting Active Particles,'' Physical Review Fluids 2 (2017): 043104. (preprint version)
 K. A. Newhall, M. S. Shkarayev, P. R. Kramer, G. Kovacic, and D.
Cai, "Synchrony in stochastically driven neuronal networks with complex
topologies," Physical Review E 91 (2015): 052806. (preprint version)
J.
C. Latorre, P. R. Kramer, and G. A. Pavliotis, "Numerical Methods for
Computing Effective Transport Properties of Flashing Brownian Motors," Journal of Computational Physics 257A (2014): 5782. (preprint version) O.
Kurbanmuradov, K. Sabelfeld, and P. R. Kramer, "Randomized Spectral and
FourierWavelet Methods for Multidimensional Gaussian Random Vector
Fields," Journal of Computational Physics 245 (2013): 218234. (preprint version) K.
A. Newhall, E. P. Atkins, P. R. Kramer, G. Kovacic, and I. R. Gabitov,
"Random Polarization Dynamics in a Resonant Optical Medium," Optics Letters 38 (6), (2013): 893895. (preprint version) J.
C. Latorre, G. A. Pavliotis, and P. R. Kramer, "Corrections to
Einstein's relation for Brownian motion in a tilted periodic
potential," Journal of Statistical Physics 150 (4), (2013): 776803. (preprint version)  E.
P. Atkins, P. R. Kramer, G. Kovacic, and I. R. Gabitov, "Stochastic
Pulse Switching in a Degenerate Resonant Optical Medium," Physical Review A 85 (2012), 043834. (preprint version)
S.
A. McKinley, A. Athreya, J. Fricks, and P. R. Kramer, "Asymptotic
Analysis of MicrotubuleBased Transport by Multiple Identical Molecular
Motors," Journal of Theoretical Biology 305 (2012): 5469. (preprint version) A.
Porporato, P. R. Kramer, M. Cassiani, E. Daly, and J. Mattingly, "Local Kinetic Interpretation of Entropy Production through Reversed
Diﬀusion," Physical Review E 84 (2011): 041142. (preprint version) S.
R. Keating, K. S. Smith, and P. R. Kramer, "Diagnosing lateral
mixing in the upper ocean with virtual tracers: Spatial and temporal resolution dependence," Journal of Physical Oceanography 41 (8), (2011): 15121534. (preprint version) K.
A. Newhall, G. Kovacic, P. R. Kramer, and D. Cai, "CascadeInduced
Synchrony in StochasticallyDriven Neuronal Networks," Physical Review E 82, (2010): 049103. (preprint version) S.
R. Keating, P. R. Kramer, and K. S. Smith, "Homogenization and
Mixing Measures for a Replenishing Passive Scalar Field,"Phys. Fluids. 22, (2010): 075105. (PDF) Copyright 2010 American Institute of Physics. This article may be
downloaded for personal use only. Any other use requires prior
permission of the author and the American Institute of Physics. K.
A. Newhall, G. Kovacic, P. R. Kramer, D. Zhou, A. Rangan, and D. Cai,
"Dynamics of CurrentBased, Poisson Driven, IntegrateandFire Neuronal Networks," Communications in Mathematical Sciences 8 (2), 2010: 541600. (preprint version)
P. R. Kramer, J. C. Latorre, and A. A. Khan, "Two
CoarseGraining Studies of Stochastic Models in Molecular Biology," Communications in Mathematical Sciences 8 (2), 2010: 481517. (preprint version)
P. R. Kramer and S. R. Keating, "Homogenization Theory for a Replenishing Passive Scalar Field," Chin. Ann. Math. 30B (5), 2009: 631644. (preprint version) P. J. Atzberger and P. R. Kramer, "Error analysis
of a stochastic immersed boundary method incorporating thermal
fluctuations," Mathematics and Computers in Simulation,
79, 2008: 379408 (preprint version)
P. R. Kramer, C. S. Peskin, and P. J. Atzberger, "On the foundations
of the stochastic immersed boundary method," Computer Methods
in Applied Mechanics and Engineering,
197(2528), 2008: 22322249 (preprint version)
P. R. Kramer, A. Khan, P. Stathos, and R. E. L. DeVille, "Method of Multiple
Scales with Three Time Scales," Proceedings in Applied
Mathematics and Mechanics 7(1), 2007: 2040031 
2040032. (preprint
version)
J. C. Latorre, P. R. Kramer, and G. A. Pavliotis, "Effective Transport
Properties for Flashing Ratchets Using Homogenization Theory,"
Proceedings in Applied Mathematics and Mechanics
7(1), 2007: 10805011080502. (preprint version)
P. J. Atzberger, P. R. Kramer, and C. S. Peskin, "Stochastic immersed
boundary method incorporating thermal fluctuations,"
Proceedings in Applied Mathematics and Mechanics
7(1), 2007: 11214011121402. (preprint version)
B. Baydil, P. R. Kramer, and K. S. Smith, "Parameterization for
Mesoscale Ocean Transport through Random Flow Models,"
Proceedings in Applied Mathematics and Mechanics
7(1), 2007: 2150021  2150022. (preprint
version)
P. J. Atzberger and P. R. Kramer, "Theoretical
Framework for Microscopic Osmotic Phenomena," Phys. Rev.
E 75, 2007, 061125. (preprint version)
P. R. Kramer, O. Kurbanmuradov, and K. Sabelfeld, "Comparative
Analysis of Multiscale Gaussian Random Field Simulation
Algorithms," Journal of
Computational Physics 226 (1), 2007: 897924.
(preprint version)
P. J. Atzberger, P. R. Kramer, and C. S. Peskin, "A stochastic immersed boundary method for
fluidstructure dynamics at microscopic length scales," Journal of Computational Physics
224 (2), 2007: 12551292. (preprint version)
P. R. Kramer, "Brownian Motion," Encyclopedia of Nonlinear
Science, ed., Alwyn Scott. New York and London:
Routledge, 2004. (preprint
version)
P. R. Kramer, "FokkerPlanck Equation," Encyclopedia of Nonlinear
Science, ed., Alwyn Scott. New York and London:
Routledge, 2004. (preprint version)
E. Castronovo and P. R. Kramer, "Subdiffusion and Superdiffusion
in Lagrangian Stochastic Models of Oceanic Transport," Monte Carlo
Methods and Applications, 10 (34), 2004: 245256.
(preprint version)
L. J. Borucki, T. Witelski, C. Please, P. R. Kramer, and D.
Schwendeman, "A theory
of pad conditioning for chemicalmechanical polishing,"
Journal of Engineering Mathematics, 50 (1), 2004: 124. (preprint version)
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, 2003:
17551758. (preprint
version)
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: 482491. (preprint
version)
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: 113122. (preprint
version)
P. R. Kramer and A. J. Majda, "Stochastic mode
reduction for immersed boundary method," SIAM J. Appl. Math.
64 (2), 2003: 369400.
(preprint version)
P. R. Kramer and A. J. Majda, "Stochastic mode reduction for particlebased
simulation methods for complex microfluid systems," SIAM J.
Appl. Math. 64 (2),
2003: 401422. (preprint version)
P. R. Kramer, A. J. Majda, and E. VandenEijnden, "Closure
approximations for passive scalar turbulence: A comparative study on
an exactly solvable model with complex features," J. Stat.
Phys., 111 (3/4), 2003: 565679. (preprint version)
P. R. Kramer, "Two different rapid
decorrelation in time limits for turbulent diffusion," J.
Stat. Phys., 110 (1/2), 2003: 87136. (preprint version)
P. R. Kramer, "A review of some Monte Carlo simulation methods for
turbulent systems,'' Monte Carlo Methods and Applications,
7 (34) 2001: 229244. (preprint version) A. J. Majda and P. R. Kramer, "Simplified
models for turbulent diffusion: Theory, numerical modelling and
physical phenomena," Physics Reports, 314
(45), 1999: 237574. (preprint version)

Contact Information
Peter Kramer
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
110 8th Street
Troy, New York 12180
Phone: (518) 2766896
Fax: (518) 2764824
Email: kramep@rpi.edu



