Roberto Camassa

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Primary Position: Kenan Professor of Mathematics
  • Laurea in Physics, Universita' Statale, Milano
  • M.Sc., Engineering Science, California Institute of Technology, Pasadena
  • Ph.D., Engineering Science and Applied Math, California Institute of Technology, Pasadena
Dynamical Systems
      • - Transport in time dependent Rayleigh-Benard convection, with S. Wiggins,  Phys. Rev. A 43 (1991), 774-797.
      • - Transport of a passive tracer in time-dependent Rayleigh-Benard convection, with S. Wiggins, Physica D 51 (1991), 472-481.
      • - Enhanced optical bistability by periodic layering, with R. Knapp and G. Forest, Nonlinearity 5 (1992), 721-742.
      • - On the geometry of an atmospheric slow manifold, Physica D 84 (1995), 357-397.
      • - Comment on: Do resonantly forced solitary waves protect the fuel hurricanes, Phys. Rev. Lett. 72 (1994), 2668.
      • - The global geometry of the slow manifold in the Lorenz-Krishnamurthy model, with S.K. Tin, Journal of the Atmospheric Sciences 53(1996), 3251-3264.
      • - A Melnikov method for homoclinic orbits with many pulses, with G. Kovacic and S.K. Tin, Arch. Rational Mech. and Anal. 143 (1998), 105-193.

Optics and Materials
      • - Enhanced optical bistability by periodic layering, with R. Knapp and G. Forest, Nonlinearity 5 (1992), 721-742.
      • - Nonadiabatic dynamics of dark solitons,  with S. Burtsev, J. Opt. Soc. Amer. B 14 (1997), 1782-1787.
      • - Numerical algorithms for the direct spectral transform with applications to Nonlinear Schroedinger type systems, with S. Burtsev and I. Timofeyev, J. Comput.  Phys. 147 (1998), 166-186.
      • - New potential applications of nonlinear dielectrics: microwave solitons and stochastic resonance, with A. Findikoglu, Q. Jia, D. Reagor, Y. Fan, G. Lythe, D. Cai, N. Jensen, A. Bishop, Integrated Ferroelectrics 22 (1998) 779-788.
      • - Solutal separation under centrifugation,  with N. Li, R. Ecke and F. Venneri, Separat. Sci. Tech. 33 (1998) 551-567.
      • - Dielectric nonlinearity and stochastic effects in strontium titanate, with Alp T. Findikoglu, Grant Lythe, and Q. X. Jia, Appl. Phys. Lett.  80 (2002), 3391-3393.
      • - Transmission, reflection and second-harmonic generation in a nonlinear waveguide, with A. Findikoglu and G. Lythe, SIAM J. Appl. Math. 66 (2005), 1-28.

Completely Integrable Systems
      • - The half plane problem for the Korteweg-de Vries equation, with T.Y. Wu, in Quaderni del Consiglio Nazionale delle Ricerche, Proceedings of the Euromech Colloquium 240, D. G. Crighton & F. Mainardi eds., Bologna 1989, Italy.
      • - An integrable shallow water equation with peaked solitons, with D. D. Holm, Phys. Rev. Lett. 71 (1993), 1661-1665.
      • - A new integrable shallow water equation, with D. Holm and J. M. Hyman, Advances in Applied Mechanics 31 (1994), 1-33.
      • - On the link between umbilic geodesics and soliton solutions of nonlinear PDE's, with M. Alber, D. Holm and J. Marsden, Proceedings of the Royal Society of London A 450, (1995) 677-692.
      • - The geometry of peaked solitons and billiard solutions of a class of integrable PDE's, Letters in Mathematical Physics 32, with M. Alber, D. Holm and J. Marsden,  (1994), 137-151.
      • - Nonadiabatic dynamics of dark solitons,  with S. Burtsev, J. Opt. Soc. Amer. B 14 (1997), 1782-1787.
      • - Numerical algorithms for the direct spectral transform with applications to Nonlinear Schroedinger type systems, with S. Burtsev and I. Timofeyev, J. Comput.  Phys. 147 (1998), 166-186.
      • - On billiard solutions of nonlinear PDE's, with M. Alber , Y. Fedorov, D. Holm and J. Marsden, Phys. Lett. A 264 (2000), 171-178.
      • - Characteristic variables for a completely integrable shallow water equation. In: Boiti, M. et al. (eds.) “Nonlinearity, Integrability  and All That: Twenty Years After NEEDS '79.” World Scientific, Singapore (2000).
      • - Billiard weak solutions of nonlinear PDE's and Toda flows, with M. Alber and M. Gekhtman, CRM Proceedings & Lecture Notes,  (2000), 1-11.
      • - The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type, with M. Alber , Y. Fedorov, D. Holm and J. Marsden, Comm. Math. Phys. 221 (2001), 197-227.
      • - On the initial value problem for a completely integrable shallow water equation, with A. I. Zenchuk,  Phys. Lett. A 281 (2001), 26-33.
      • - Characteristics and the initial value problem of a completely integrable shallow water equation,  DCDS-B 3 (2003), 115-139.
      • - On a completely integrable numerical scheme for a nonlinear shallow-water wave equation, with J. Huang and L. Lee,  J. Nonl. Math. Phys. 12 (2005), 146-162.
      • -  Integral and integrable algorithms for a nonlinear shallow water wave equation, with J. Huang and L. Lee, J. Comp. Phys. 216 (2006), 547-572.
      • - A completely integrable particle method for a nonlinear shallow-water wave equation in periodic domains, with L. Lee, Dyn. Cont. Discr. Impuls. Sys. A, 14 (2007), 1-5.
      • - Completely integrable particle methods and the recurrence of initial states for a nonlinear shallow-water wave equation, with L. Lee, J. Comp. Phys. 227 (2008), 7206-7221.
      • - A particle method and numerical study of a quasi-linear partial differential equation, with P.H. Chiu, L. Lee, and T.W.H. Sheu, Disc. Cont. Dyn. Syst. S (2011) 10, 1503-1515.
      • - Viscous and inviscid regularizations in a class of evolutionary partial differential equations, P.H. Chiu, L. Lee and T.W.H. Sheu, J. Comp. Phys. 229 (2010), 6676-6687.

Waves
      • - Multiple Stationary Solutions for the fKdV Equation, in "Engineering Science, Fluid Mechanics. A Symposium in honor of Doctor T.Y. Wu", G. T. Yates ed., World Scientific, Singapore, 1990.
      • - Stability of forced steady solitary waves, with  T.Y. Wu, Phil. Trans. R. Soc. A 337 (1991), 429-466.
      • - Stability of some stationary solutions for the forced KdV equation, with T.Y. Wu, Physica D 51 (1991), 295-307.
      • - Dispersive barotropic equations for stratified mesoscale ocean dynamics, with D. Holm, Physica D 60, 1-15, 1992.
      • - Nonlinear internal waves in a two-layer fluid, with W. Choi, Journal of Fluid Mechanics 313 (1996), 83-103.
      • - Long internal waves of finite amplitude, with W. Choi, Phys. Rev. Lett. 77 (1996), 1759-1763.
      • - Long time evolution equations for shallow water with a varying bottom, with D. Holm and D. Levermore,J. Fluid Mech. 349 (1997), 173-189.
      • - Layer-mean quantities, local conservation laws, and vorticity, with D. Levermore, Phys. Rev. Lett. 78 (1997), 650-653.
      • - Exact evolution equations for surface waves, with W. Choi, Journal of Engineering Mechanics-ASCE 125 (1999), 756-760.
      • - Fully nonlinear internal waves in a two-fluid system, with W. Choi, J. Fluid Mech. 396 (1999), 1-36.
      • - Traveling waves in rotating Rayleigh-Benard convection, with W. Choi, D. Prasad, R. Ecke, Phys. Rev. E (2004) 056301.
      • - Thin film dynamics in a liquid lined circular pipe, with L. Lee, in Advances in Engineering Mechanics, A.T. Chwang, M.H. Teng, and D.T. Valentine, Editors. World Scientific: London. (2006), 222-238.
      • - On the realm of validity of strongly nonlinear asymptotic approximations for internal waves, with W. Choi, H. Michallet, P.-O. Rusas and J.K. Sveen, J. Fluid. Mech. 147, (2006), 166-186.
      • - Fully nonlinear periodic internal waves in a two-fluid system of finite depth, with P.O. Rusas, A. Saxena and R. Tiron, J. Fluid Mech. 652 (2010), 259-298.
      • - Optimal two-layer approximation for continuous density stratification, with R. Tiron, J. Fluid. Mech. (2011) 669,  32-54.
      • - An inertia ‘paradox’ for incompressible stratified Euler fluids, with S. Chen, G. Falqui, G. Ortenzi, and M. Pedroni,  J. Fluid Mech. (2012) 695, 330-340.
      • - On the response to upstream disturbances of large-amplitude internal waves, with C. Viotti, J. Fluid Mech. (2012). doi:10.1017/jfm.2012.147
      • - A model for large-amplitude internal waves with finite-thickness pycnocline, with C. Viotti, Acta Appl. Math. (2012) doi:10.1007/s10440-012-9727-x
      • - Shear instability of internal solitary waves in Euler fluids with thin pycnoclines, with A. Almgren and R. Tiron, J. Fluid. Mech. (2012) 719, 324-361.
      • - Ring-waves as a mass transport mechanism in air-driven core-annular flows, with M. G. Forest, L. Lee, R. Ogrosky and J. Olander, Phys. Rev. E (2012)doi:10.1103/ PhysRevE.86.066305
      • - Transient dynamics by continuous spectrum perturbations in stratified shear flows, with Claudio Viotti, J. Fluid Mech. Rapids (2013) 717, R5 1-12, doi:101.1017/jfm.2013.19
      • - Effects of inertia and stratification in incompressible ideal fluids: pressure imbalances by rigid confinement, with S. Chen, G. Falqui, G. Ortenzi, and M. Pedroni,  J. Fluid Mech. (2013), 726, 404-438.
      • - Topological selection in stratified fluids: an example from air-water systems, with S. Chen, G. Falqui, G. Ortenzi, and M. Pedroni,  J. Fluid Mech. (2013), to appear
      • - Viscous film flow coating the interior of a vertical tube: Part I. Gravity-driven flow, with R. Ogrosky and J. Olander, J. Fluid Mech. (2013), to appear

Low Reynolds Number Flows
      • - Epicyclic orbits in a viscous fluid about a precessing rod: Theory and experiments at the micro and macro scales, with A. Brooks et al., Phys. Rev. E 76 (2007), 016313
      • - Trajectory and flow properties for a rod spinning in a viscous fluid. Part I: An exact solution, with T.J. Leiterman and R.M.  McLaughlin, J. Fluid Mech. 612 (2008), 153-200.
      • - Prolonged residence times for particles settling through stratified miscible fluids in the Stokes regime, with C. Falcon, J. Lin, R.M. McLaughlin and R. Parker, Phys. of Fluids 21 (2009), 031702
      • - A first-principle predictive theory for a sphere falling through sharply stratified fluid at low Reynolds number, with, C. Falcon, J. Lin, R.M. McLaughlin and N. Myksin, to appear in J. Fluid. Mech. 664 (2011), 436-465.
      • - Lagrangian blocking in highly viscous shear flows past a sphere, with R.M. McLaughlin and L. Zhao, to appear in J. Fluid. Mech. (2011) 669, 120-166.
      • - Stratified flows with vertical layering of density: experimental and theoretical study of the time evolution of flow configurations and their stability, with R.M. McLaughlin, M.N.J. Moore and K. Yu,  J. Fluid Mech. (2012) 690, 571-606.
      • - Delayed settling of marine snow at sharp density transitions driven by fluid entrainment and diffusion-limited retention, with C. Arnosti, C. Falcon, S. Khatri, R. McLaughlin, J. Prairie, B. White, S. Yu, K. Ziervogel, MEPS (2013), 487, 185–200.
      • -  Retention and entrainment effects: Experiments and theory for porous spheres settling in sharply stratified fluids, with S. Khatri, R. M. McLaughlin, J.C. Prairie, B.L. White, and S. Yu, Phys. Fluids Letters, (2013), 25, 081701
      • - Viscous film flow coating the interior of a vertical tube: Part I. Gravity-driven flow, with R. Ogrosky and J. Olander, J. Fluid Mech. (2013), to appear

Transport
      • - Dynamics of probability density functions for decaying passive scalars in periodic velocity fields, with N. Martinsen-Burrell and R.M. McLaughlin, Phys. of Fluids 19 (2007), 117104
      • - An explicit family of probability measures for passive scalar diffusion in a random flow, with J.C. Bronski, Z. Lin, R.M. McLaughlin, and A. Scotti, J. Stat. Phys. 128 (2007), 927-968.
      • - Evolution of the probability measure for the Majda model: new invariant measures and breathing PDFs, with Z. Lin and R.M. McLaughlin, J. Stat. Phys. 227 (2008), 343-371.
      • - Brachistochrones in potential flow and the connection to Darwin's theorem, with R.M. McLaughlin, M.N.J. Moore and A. Vaidya, Phys. Lett. A 372 (2008), 6742-6749.
      • - The exact evolution of the scalar variance in pipe and channel flow, with Z. Lin and R.M. McLaughlin, Comm. Math. Sci. 8 (2010), 601-626.
      • - Analysis of passive scalar advection in parallel shear flows: Sorting of modes at intermediate time scales, with R.M. McLaughlin and C. Viotti,  Phys. Fluids (2010), 22, 117103.
      • - Subsurface trapping of oil plumes in stratification: laboratory investigations, with D. Adalsteinsson, S. Harenberg, Z. Lin, R. McLaughlin, K. Mertens, J. Reis, W. Schlieper, and B.White, Geophys. Mon. Series 195 (2011)  10.1029/2011GM001115
      • - Ring-waves as a mass transport mechanism in air-driven core-annular flows, with M. G. Forest, L. Lee, R. Ogrosky and J. Olander, Phys. Rev. E (2012)doi:10.1103/ PhysRevE.86.066305
      • - Numerical simulations of dense-core vortex rings in a sharply stratified environment, with S. Khatri, R. McLaughlin, K. Mertens, D. Nenon, C. Smith, C. Viotti, J. Comp. Sci. Disc.  (2013) doi:10.1088/1749-4699/6/1/014001
      • - Delayed settling of marine snow at sharp density transitions driven by fluid entrainment and diffusion-limited retention, with C. Arnosti, C. Falcon, S. Khatri, R. McLaughlin, J. Prairie, B. White, S. Yu, K. Ziervogel, MEPS (2013), 487, 185–200.
      • -  Retention and entrainment effects: Experiments and theory for porous spheres settling in sharply stratified fluids, with S. Khatri, R. M. McLaughlin, J.C. Prairie, B.L. White, and S. Yu, Phys. Fluids Letters, (2013), 25, 081701
      • - The time varying shear layer: rigorous joint asymptotics for an enhanced diffusion surface, with J. Bonn, K.D.T.R. McLaughlin, and R.M. McLaughlin, Discr. Cont. Dyn. Syst. B (2013), to appear
                                                       
      • Evolution Equations
      • Mathematical Modeling
      • Fluid Mechanics
      • Optics
 
Address Department of Mathematics University of North Carolina Chapel Hill, NC, 27599-3250 Email camassa (at) amath.unc.edu
Telephone 919-962-8476 Fax 919-962-2568
Office Phillips 318 Web