Ralf Wittenberg

Journal publications:

• Clinton Innes, Razvan C. Fetecau & RWW, Modelling the effect of open-mindedness on opinion dynamics, submitted (January 2015).
  
• Jared P. Whitehead & RWW, Persistently logarithmic: a bound on the vertical transport of heat in Rayleigh-Bénard convection at infinite Prandtl number with mixed thermal boundary conditions. Journal of Mathematical Physics 55, 093104 (2014).
  [ DOI:10.1063/1.4896223 / PDF ]
• RWW, Optimal parameter-dependent bounds for Kuramoto-Sivashinsky-type equations. Discrete and Continuous Dynamical Systems - Series A 34(12), 5325-5357 (2014).
  [ DOI:10.3934/dcds.2014.34.5325 / PDF ]
• Bojan Ramadanovic, Krisztina Vasarhelyi, Ali Nadaf, RWW, Julio S.G. Montaner, Evan Wood & Alexander R. Rutherford, Changing risk behaviours and the HIV epidemic: A mathematical analysis in the context of Treatment as Prevention, PLoS ONE 8(5), e62321 (2013).
  [ DOI:10.1371/journal.pone.0062321 / PDF ]
• Ka-Fai Poon & RWW, Coarsening to chaos-stabilized fronts. Physical Review E 83, 016211 (2011).
  [ DOI:10.1103/PhysRevE.83.016211 / PDF ]
• RWW, Bounds on Rayleigh-Bénard convection with imperfectly conducting plates. Journal of Fluid Mechanics 665, 158-198 (2010).
  [ DOI:10.1017/S0022112010003897 / PDF ]
• RWW & Jian Gao, Conservative bounds on Rayleigh-Bénard convection with mixed thermal boundary conditions. European Physical Journal B 76, 565-580 (2010).
  [ DOI:10.1140/epjb/e2010-00227-x / PDF ]
• RWW & Ka-Fai Poon, Anomalous scaling on a spatiotemporally chaotic attractor. Physical Review E 79, 056225 (2009).
  [ DOI:10.1103/PhysRevE.79.056225 / PDF ]
• Jens D.M. Rademacher & RWW, Viscous shocks in the destabilized Kuramoto-Sivashinsky equation. Journal of Computational and Nonlinear Dynamics 1, 336-347 (2006).
  [ DOI:10.1115/1.2338656 / PDF ]
• Jesse Otero, RWW, Rodney A. Worthing & Charles R. Doering, Bounds on Rayleigh-Bénard convection with an imposed heat flux. Journal of Fluid Mechanics, 473, 191-199 (2002).
  [ DOI:10.1017/S0022112002002410 / PDF ]
• RWW, Dissipativity, analyticity and viscous shocks in the (de)stabilized Kuramoto-Sivashinsky equation. Physics Letters A, 300, 407-416 (2002).
  [ DOI:10.1016/S0375-9601(02)00861-7 / PDF ]
• RWW & Philip Holmes, Spatially localized models of extended systems. Nonlinear Dynamics, 25, 111-132 (2001).
  [ DOI:10.1023/A:1012902732610 / PDF ]
• RWW and Philip Holmes, Scale and space localization in the Kuramoto-Sivashinsky equation. Chaos, 9, 452-465 (1999).
  [ DOI:10.1063/1.166419 / PDF ]
• Philip J. Holmes, John L. Lumley, Gal Berkooz, Jonathan C. Mattingly & RWW, Low-dimensional models of coherent structures in turbulence. Physics Reports, 287, 337-384 (1997).
  [ DOI:10.1016/S0370-1573(97)00017-3 / PDF ]
• RWW & Philip Holmes, The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE. Physica D, 100, 1-40 (1997).
  [ DOI:10.1016/S0167-2789(96)00187-X / PDF ]

Refereed conference proceedings:

• Philip J. Holmes, Jonathan C. Mattingly and Ralf W. Wittenberg, Low-Dimensional Models of Turbulence or, the Dynamics of Coherent Structures. In From Finite to Infinite Dimensional Dynamical Systems (J.C. Robinson and P.A. Glendinning, eds.), NATO Science Series II, vol.19 (Proceedings of the NATO Advanced Study Institute, Cambridge, UK, 21 August-1 September 1995), Kluwer Academic Publishers, Dordrecht, 2001, pp.177-215.

Other contributions:

• Kuramoto-Sivashinsky equation. Invited article, Encyclopaedia of Mathematics, Supplement III (managing editor: M. Hazewinkel), Kluwer Academic Publishers, 2002, pp.230-234.
  [ link ]
• Local Dynamics and Spatiotemporal Chaos. The Kuramoto-Sivashinsky Equation: A Case Study. Ph.D. thesis, Princeton University, 1998.
• Models of Self-Organization in Biological Development. M.Sc. thesis, University of Cape Town, 1993.