Associate Professor
114T Randolph Hall
540-231-4758
540-231-9100- FAX
mrp@vt.edu
Personal Research Page
| Education | Research | Experience |
Education
| Ph.D. | Mechanical Engineering | University of California at Los Angeles | July 2000 |
| M.S. | Mechanical Engineering | University of California at Los Angeles | June 1994 |
| B.S. | Aerospace Engineering | University of California at Los Angeles | June 1993 |
Research
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Spatiotemporal Chaos and the Nonlinear Dynamics Fluid Systems
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Micro and Nanoscale Physics
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Computational Systems Biology
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The Analytical and Numerical Modeling of MEMS and NEMS
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Large-Scale Scientific Computation
Teaching Activities
ME 5404 Fluid Dynamics
Fundamental fluid mechanics: kinematics and dynamics. Continuum fluid dynamics including hydrostatics, flow kinematics, the concept of stress, constitutive relations, the equations of motion and energy for compressible and incompressible viscous and inviscid flows. Incompressible Newtonian viscous flows, similitude and physical modeling, inviscid potential flows, inviscid flows with vorticity, boundary layers, and an introduction to turbulent flow. (3H,3C) I.
ME/BMES 5764 Modeling of MEMS and NEMS
This course is about the construction, analysis and interpretation of mathematical models of microelectromechanical and nanoelectromechanical (MEMS and NEMS) systems. The major goal will be to develop a physical intuition for the fundamental and dominant physics at these small scales. This knowledge is necessary to understand and contribute to the exciting technological and scientific developments occurring at the micron- and nano-scales. The material covered will be broad and interdisciplinary including: dimensional analysis and scaling, a review of continuum mechanics, microfluidics and low Reynolds number flow, biological applications, an introduction to the calculus of variations, the modeling of a variety of MEMS/NEMS systems, stochastic and deterministic approaches, an introduction to statistical thermodynamics, and approaches beyond the continuum theory.
ME 2124 Introduction to Thermal and Fluid Engineering
Basics of thermodynamics, fluid mechanics, and heat transfer. Fluid and thermal properties of materials. Ideal gas equation of state. First law of thermodynamics in closed systems. Transient heat transfer. First law of thermodynamics in open systems. Fluid mechanics balances, open systems. Emphasis on applications in all topic areas. Pre: ESM 2104. Co: MATH 2214. (2H,2C) II,III.
Experience
| Assistant Professor | Dept. of Mechanical Engineering Virginia Tech Blacksburg, VA |
2004 - Present |
| Post Doctoral Scholar and Computational Molecular Biology Fellow | Department of Physics California Institute of Technology |
2001 - 2004 |
| Post Doctoral Scholar | Department of Physics California Institute of Technology |
2001 |
| Post Doctoral Scholar | Department of Physics Duke University |
2000 - 2001 |
| Engineering Consultant | Onward, Inc. Mountain View, CA |
1999 - 2000 |
Selected Journal Papers
- N. Hashemi, M.R. Paul, H. Dankowicz, M. Lee, W. Jhe, The Dissipated Power in Atomic Force Microscopy due to Interactions with a Capillary Fluid Layer, Journal of Applied Physics, 104, 063518, (2008).
- D. Barik, M.R. Paul, W.T. Baumann, Y. Cao, and J.J. Tyson, Stochastic Simulation of Enzyme-Catalyzed Reactions with Disparate Time Scales, Biophysical Journal, 95, 3563-3574, (2008).
- M.T. Clark and M.R. Paul, The Stochastic Dynamics of Rectangular and V-shaped Atomic Force Microscope Cantilevers in a Viscous Fluid and Near a Solid Boundary, Journal of Applied Physics, 103, 094910, (2008).
- N. Hashemi, H. Dankowicz and M.R. Paul, The Nonlinear Dynamics of Tapping Mode Atomic Force Microscopy with Capillary Force Interactions, Journal of Applied Physics, 103, 093512, (2008).
- S. Misra, H. Dankowicz, and M.R. Paul, Event-Driven Feedback Tracking and Control of Tapping-Mode Atomic Force Microscopy, Proceedings of the Royal Society A, 2095, 2113-2133, (2008)
- M.R. Paul, M.I. Einarsson, M.C. Cross and P.F. Fischer, Extensive Chaos in Rayleigh-Benard Convection, Physical Review E, 75, 045203, (2007).
- A. Duggleby, K.S. Ball, M.R. Paul, and P.F. Fischer, Dynamical Eigenfunction Decomposition of Turbulent Pipe Flow, Journal of Turbulence, 8, 43, 1-25, (2007).
- M.T. Clark and M.R. Paul, The Stochastic Dynamics of an Array of Atomic Force Microscopes, International Journal of Nonlinear Dynamics, (2007).
- M.R. Paul, M.T. Clark, and M.C. Cross, The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation, Nanotechnology, 17, (2006).
- J.E. Solomon and M.R. Paul, The Kinetics of Analyte Capture on Nanoscale Sensors, Biophysical Journal, 90, 1842-1852 (2006).
- M.R. Paul, K.-H. Chiam, and M.C. Cross, Rayleigh-Benard Convection in Large-Aspect-Ratio Domains, Physical Review Letters, 93, 064503 (2004).
- M.R. Paul and M.C. Cross, The Response of Nanoscale Cantilevers Immersed in a Viscous Fluid, Physical Review Letters, 92, 235501 (2004).
- M.R. Paul and I. Catton, The Relaxation of Two-Dimensional Rolls in Rayleigh-Benard Convection, Physics of Fluids, 16, 1262--1266 (2004).
- J.D. Scheel, M.R. Paul, M.C. Cross, and P.F. Fischer, Traveling Waves in Rotating Rayleigh-Benard Convection: Analysis of modes and mean flow, Physical Review E, 69, (2003).
- M.R. Paul, K.-H. Chiam, M.C. Cross, P.F. Fischer, and H.S. Greenside, Pattern Formation and Dynamics in Rayleigh-Benard Convection: Numerical Simulations of Experimentally Realistic Geometries, Physica D, 184, (2003).
- K.-H. Chiam, M. R. Paul, M. C. Cross, and H. S. Greenside, Mean flow and spiral defect chaos in Rayleigh-Benard convection, Physical Review E, 67, 056206, (2003).
- M.R. Paul, M. C. Cross, and P. F. Fischer, Rayleigh-Benard Convection with a Radial Ramp in Plate Separation, Physical Review E, 66, 046210 (2002).
- M.R. Paul, M.C. Cross, P.F. Fischer, and H.S. Greenside, Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection, Physical Review Letters, 87, (2001).