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Mark Paul

231C Goodwin Hall
635 Prices Fork Road
Blacksburg, VA 24061
MC: 0238

Ph.D., Mechanical Engineering, University of California, Los Angeles, 2000
M.S., Mechanical Engineering, University of California, Los Angeles, 1994
B.S., Aerospace Engineering, University of California, Los Angeles, 1993

Welcome to the Paul Research Group at Virginia Tech

We are exploring the engineering and scientific implications of nonlinear dynamics, nonequilibrium physics, and pattern formation on the physical and biological worlds. My goal is to improve our physical understanding of the world around us by employing analytical and numerical methods, from simple models to large-scale parallel numerical simulations. Most interesting are the questions posed today by spatiotemporal chaos, the rapid advance of experimental science to the nanoscale, and the complex behavior of biological systems.

Lab News







  1. H.N. Patel, I. Carroll, R. Lopez, S. Sankararaman, C. Etienne, S. Kodigala, M.R. Paul, and H. W.Ch. Postma, DNA-graphene interactions during translocation through nanogaps, PLOS One, (2017).
  2. M. Xu and M.R. Paul, Covariant Lyapunov Vectors of Chaotic Rayleigh-Benard Convection, Physical Review E, 93, 062208, (2016).
  3. M. Radiom, M.R. Paul, and W.A. Ducker, Dynamics of Single-Stranded DNA Tethered to a Solid, Nanotechnology, 27, 255701, (2016).
  4. M. Kramar, R. Levanger, J. Tithof, B. Suri, M. Xu, M.R. Paul, M.F. Schatz, and K. Mischaikow, Analysis of Kolmogorov Flow and Rayleigh-Benard Convection using Persistent Homology, Physica D, 334, (2016).
  5. K. Subramanian, M.R. Paul, and J.J. Tyson, Dynamical localization of DivL and PleC in the asymmetric division cycle of Caulobacter crescentus: A theoretical investigation of alternate modelsPLOS Computational Biology, 11, e1004348, (2015).
  6. M. Radiom, B.A. Robbins, M.R. Paul, and W.A. Ducker, Hydrodynamic interactions of two nearly touching Brownian spheres in a stiff potential: effect of fluid inertia, Physics of Fluids, 27, 022002, (2015).
  7. B.A. Robbins, M. Radiom, W.A. Ducker, J.Y. Walz, and M.R. Paul, The Stochastic Dynamics of Tethered Microcantilevers in a Viscous Fluid, Journal of Applied Physics, 116, 164905, (2014).
  8. C. Lissandrello, F. Inci, M. Francom, M. R. Paul, U. Demirci, and K. L. Ekinci, Nanomechanical Motion of Escherichia coli Adhered to a Surface, Applied Physics Letters, 105, 113701, (2014).
  9. C.O. Mehrvarzi and M.R. Paul, Front propagation in a chaotic flow field, Physical Review E, 90, 012905, (2014).
  10. M.R. Paul, M.T. Clark and M.C. Cross, Coupled motion of microscale and nanoscale elastic objects in a viscous fluid, Physical Review E, 88, 043012, (2013).
  11. S.E. Epstein and M.R. Paul, The stochastic dynamics of a nanobeam near an optomechanical resonator in a viscous fluid, Journal of Applied Physics, 114, 144901, (2013).
  12. K. Subramanian, M.R. Paul, and J.J. Tyson, Bistable histidine kinase switches in Caulobacter crescentus, PLOS Computational Biology, (2013).
  13. A. Karimi and M.R. Paul, Bioconvection in Spatially Extended DomainsPhysical Review E87, (2013).
  14. A. Karimi and M.R. Paul, Length Scale of a Chaotic Element in Rayleigh-Benard ConvectionPhysical Review E86, (2012).
  15. M. Radiom, C. Honig, J.Y. Walz, M.R. Paul, and W.A. Ducker, A Correlation Force Spectrometer for Single Molecule Measurements under Tensile LoadJournal of Applied Physics113, (2012).
  16. D. Seo, M.R. Paul, and W.A. Ducker, A Pressure Gauge based on Gas Density Measurement from Analysis of the Thermal Noise of an AFM CantileverReview of Scientific Instruments83, (2012).
  17. A. Karimi and M.R. Paul, Quantifying Spatiotemporal Chaos in Rayleigh-Benard ConvectionPhysical Review E85, (2012).
  18. M. Radiom, B. Robbins, C. Honig, J.Y. Walz, M.R. Paul, and W.A. Ducker, Rheology of Fluids Measured by Correlation Force Spectroscopy, Review of Scientific Instruments, 83, (2012).
  19. C. Honig, M. Radiom, B. Robbins, J.Y. Walz, M.R. Paul, and W.A. Ducker, Correlation Force Spectroscopy, Applied Physics Letters100, (2012).
  20. A. Karimi, Z-F. Huang, M.R. Paul, Exploring Spiral Defect Chaos in Generalized Swift-Hohenberg Models with Mean FlowPhysical Review E84, (2011).
  21. D. Barik, W.T. Baumann, M.R. Paul, B. Novak, and J.J. Tyson, A Model of Yeast Cell Cycle Regulation Based on Multisite PhosphorylationMolecular Systems Biology8, (2010).
  22. A. Karimi, and M.R. Paul, Extensive Chaos in the Lorenz-96 ModelChaos20, (2010).
  23. A. Duggleby and M.R. Paul, Computing the Karhunen-Loeve dimension of an Extensively Chaotic Flow Field Given a Finite Amount of DataComputers and Fluids39, 9, (2010).
  24. M.T. Clark, J.E. Sader, J.P. Cleveland, and M.R. Paul, The Spectral Properties of Microcantilevers in Viscous Fluid81, 046306, Physical Review E (2010).
  25. S. Misra, H. Dankowicz, and M.R. Paul, Degenerate Discontinuity-Induced Bifurcations in Tapping-Mode Atomic-Force Microscopy239, Physica D, (2010).
  26. M.M. Villa and M.R. Paul, The Stochastic Dynamics of Micron Scale Doubly-Clamped Beams in a Viscous Fluid, Physical Review E79, 056314, (2009).
  27. H. Dankowicz and M.R. Paul, Discontinuity-Induced Bifurcations in Systems with Hysteretic Force Interactions, Journal of Computational and Nonlinear Dynamics4 (2009).
  28. S. Kar, W.T. Baumann, M.R. Paul, and J.J. Tyson, Exploring the Roles of Noise in the Eukaryotic Cell Cycle, Proceedings of the National Academy of Sciences, (2009).
  29. 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 LayerJournal of Applied Physics104, 063518, (2008).
  30. D. Barik, M.R. Paul, W.T. Baumann, Y. Cao, and J.J. Tyson, Stochastic Simulation of Enzyme-Catalyzed Reactions with Disparate Time ScalesBiophysical Journal95, (2008).
  31. 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 BoundaryJournal of Applied Physics103, 094910, (2008).
  32. N. Hashemi, H. Dankowicz and M.R. Paul, The Nonlinear Dynamics of Tapping Mode Atomic Force Microscopy with Capillary Force InteractionsJournal of Applied Physics103, 093512, (2008).
  33. S. Misra, H. Dankowicz, and M.R. Paul, Event-Driven Feedback Tracking and Control of Tapping-Mode Atomic Force MicroscopyProceedings of the Royal Society A2095, (2008).
  34. M.R. Paul, M.I. Einarsson, M.C. Cross and P.F. Fischer, Extensive Chaos in Rayleigh-Benard ConvectionPhysical Review E75, 045203, (2007).
  35. A. Duggleby, K.S. Ball, M.R. Paul, and P.F. Fischer, Dynamical Eigenfunction Decomposition of Turbulent Pipe FlowJournal of Turbulence8, 43, (2007).
  36. M.T. Clark and M.R. Paul, The Stochastic Dynamics of an Array of Atomic Force Microscopes in a Viscous FluidInternational Journal of Nonlinear Dynamics42, (2006).
  37. A. Duggleby, K.S. Ball, and M.R. Paul, The Effect of Spanwise Wall Oscillation on Turbulent Pipe Flow Structures Resulting in Drag ReductionPhysics of Fluids19, (2007).
  38. J.L. Arlett, M.R. Paul, J. Solomon, M.C. Cross, S.E. Fraser, and M.L. Roukes, BioNEMS: Nanomechanical Devices for Single Molecule Biophysics, Lecture Notes in Physics, 711, (2007).
  39. M.R. Paul, M.T. Clark, and M.C. Cross, The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipationNanotechnology17, (2006).
  40. J.E. Solomon and M.R. Paul, The Kinetics of Analyte Capture on Nanoscale SensorsBiophysical Journal90, (2006).
  41. M.R. Paul and J.E. Solomon, The Physics and Modeling of BioNEMS, in Nanodevices for Life Sciences, Wiley-VCH, (2006).
  42. M.R. Paul, K.-H. Chiam, M.C. Cross, and P.F. Fischer, Rayleigh-Benard Convection in Large-Aspect-Ratio DomainsPhysical Review Letters93, (2004).
  43. M.R. Paul and M.C. Cross, Stochastic Dynamics of Nanoscale Mechanical Oscillators Immersed in a Viscous FluidPhysical Review Letters92, 235501, (2004).
  44. M.R. Paul and I. Catton, The Relaxation of Two-Dimensional Rolls in Rayleigh-Benard ConvectionPhysics of Fluids16, 1262, (2004).
  45. 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 FlowPhysical Review E68, 066216, (2003).
  46. 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 GeometriesPhysica D184, 114-126, (2003).
  47. K.-H. Chiam, M. R. Paul, M. C. Cross, and H. S. Greenside, Mean flow and spiral defect chaos in Rayleigh-Benard convectionPhysical Review E67, 056206, (2003).
  48. M.R. Paul, M. C. Cross, and P. F. Fischer, Rayleigh-Benard Convection with a Radial Ramp in Plate SeparationPhysical Review E66, 046210 (2002).
  49. 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 ConvectionPhysical Review Letters87, (2001).
  50. M.R. Paul, F. Issacci, I. Catton, and G.E. Apostolakis, Characterization of Smoke Particles Generated in Terrestrial and Microgravity Environments, Fire Safety Journal28, 233-252 (1997).
  51. G.E. Apostolakis, I. Catton, F. Issacci, S. Jones, M.R. Paul, T. Paulos, and K. Paxton, Risk Based Fire Safety Experiments, Reliability Engineering and System Safety49, 275-291 (1995).

Spring 2018

Chaos and Nonlinear Dynamics (ME6744)

Course Announcement:


ME 6744: Chaos and Nonlinear Dynamics, Spring 2018

Instructor: Prof. Mark Paul

Time:        Tuesday and Thursday, 11-12:15

Location:   241 Goodwin Hall

Course Description:

Many open challenges in science and engineering involve nonlinear dynamical systems that exhibit chaotic dynamics. Important examples include fluid turbulence, the dynamics of the weather and climate, excitable media such as cardiac tissue and nerve fibers,  population dynamics, transport in complex flow fields, the dynamics of the biomass in the oceans, and the complex motion of the cantilever of an atomic force microscope. Despite the great importance of these systems the aperiodic nature of their dynamics makes them difficult to control, design, analyze, and predict. This course will discuss analytical and numerical approaches to gain fundamental physical insights into these systems, and others, using both simplified mathematical models and physical examples that can be directly compared with experimental measurements.

Course Content:

Overview of theoretical and numerical approaches for the study of nonlinear and chaotic dynamics in science and engineering. Fractals, bifurcation analysis, predictability, strange attractors, and routes to chaos. Roles of dissipation and noise in deterministic chaos. Use of Lyapunov spectra, fractal dimension, information, entropy, correlation functions, and attractor reconstruction to describe chaos.