C. W. Gear (Bill)

Senior Scientists, Chem-Bio Engineering, Princeton University (zero-time appointment)
Emeritus President, NEC Research Institute
Emeritus Professor, Department of Computer Science, University of Illinois at Urbana-Champaign

Mug Shot

  •         17 Honey Brook Drive
  •         Princeton, NJ 08540
  •         609-737-7023
  •         wgear <at> princeton <dot> edu
  • Brief resume

    Publication List

    Recent papers and Reports

    Note:  if an on-line version and published version are shown, the on-line version is different (usually longer and shortened for publication.)

    Manifold defined by points: Parametrizing and Boundary Detection

    Parameterization of non-linear manifolds, Aug 2012

    Analysis and computation of a discrete KdV-Burgers type equation with fast dispersion and slow diffusion,  with  Z. Artstein,  I. G. Kevrekidis, M. Slemrod and E. S. Titi.  SINUM 49 #5, pp2124-2143, 2011

    Computing on Virtual Slow Manifolds of Fast Stochastic Systems, with D. Givon & I. Kevrekids, Mar 2010

    Analysis of the accuracy and convergence of equation-free projection to a slow manifold, with A. Zagaris, T. J. Kaper & I. Kevrekidis,  Math. Mod. Num. Anal. 43 (4)    pp.757-784 (2009)

    Invariants of fast solutions of KdV-Burgers Equations, Sep, 2008

    Optimum Choice of Weights in Slope Calculation with Noisy Data, June, 2008

    Backward differentiation formulas. Scholarpedia, 2(8):3162 (2007)

    Projective and coarse projective integration for problems with continuous symmetries,  with M. E. Kavousanakis, R. Erban, A. G. Boudouvis, and I. G. Kevrekidis, to appear, J. Comp. Phys. (2007)

    On-the-Fly Local Error Estimation for Projective Integrators  (with S. L. Lee)  LLNL report UCRL-JRNL-224892 (Oct, 2006)

    Towards Explicit Methods for DAEs   BIT Num. Math. 46, pp 505-514 (2006)

    Second-order accurate projective integrators for multiscale problems (with S. L. Lee). JCAM (to appear) Also Lawrence Livermore Report UCRL-JRNL-212640, June 2005

    Constraint-defined manifolds: a legacy-code approach to low-dimensional computation, (with I. G. Kevrekidis), J. Sci. Comp. in press, (2004); also physics/0312094 at arXiv.org.

    Application of Coarse Integration to Bacterial Chemotaxis (with S. Setayeshgar, H. G. Othmer, & I. G. Kevrekidis) SIAM MMS   4 (1) pp.307-327 (2005); also physics/0308040 at arXiv.org

    Computing in the Past with Forward Integration (with I. G. Kevrekidis) Physics Letters A, 321 pp335-342 (2004)

    Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes, (with T. J. Kaper,  I.G. Kevrekidis, & A. Zagaris) 

    SIAM J. Dynamical Systems,  4, pp 711-732, 2005

    From Molecular Dynamics to coarse self-similar solutions: a simple example using equation-free computation", (with L. Chen, P. G. Debenedetti, & I. G. Kevrekidis,  JNNFM  120 pp.215-223 (2004)

    Equation-free: the computer-assisted analysis of complex, multiscale systems, (with I. G. Kevrekidis, & G. Hummer)  A.I.Ch.E Journal.  50 (7), pp.1346-1354 (2004)

    Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models (with {J. Cisternas,  S. Levin & I.G. Kevrekidis} Proc. Roy. Soc. London, in press, (2004); can be found as nlin.AO/0310011 at arXiv.org

    Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems,  (with R. Rico-Martinez & I. G. Kevrekidis)   Journal of Computational Physics, 196, #2, pp 474-489 (2004)

    Deciding the Nature of the “Coarse Equation” through Microscopic Simulations (with Ju Li, P. G. Kevrekidis, & I. G. Kevrekidis) SIAM MMS 1(3)  pp391-407 (2003)

    “The gaptooth method in particle simulations" (with  J. Li and I. G. Kevrekidis,), Phys. Lett. A, 316 pp.190-195 (2003).

    Telescopic Projective Methods for Stiff Differential Equations, (with I. G. Kevrekidis) JCP. 187, #1,  pp 95-109, (2003).

    Boundary processing for Monte Carlo Simulations in the Gap-Tooth Scheme NECI Technical Report TR 2002-031N,Oct 2002

    Finding Stationary States of Noisy Processes, NECI Technical Report TR 2002-025N, Oct 2002

    Coarse Integration/Bifurcation Analysis via Microscopic Simulators: micro-Galerkin methods, (with I. G. Kevrekidis and C.Theodoropoulos) NECI Technical Report  TR 2001-106,  3 Oct 2001,  Comp. Chem. Engng. 26 pp941-963 (2002);
    Projective Integration Methods for Distributions, NEC Technical Report TR 2001-130, 26 Nov, 2001

    Projective Methods for Differential Equations,  (with I. G. Kevrekidis) NECI Technical Report NECI-TR 2001-029, Apr. 2001, also SIAM J. Sci. Comp. 24(4) pp1091-1106 (2003)

    Equation-Free Multiscale Computation: enabling microscopic simulators to perform system-level tasks,  (with  I. G. Kevrekidis, J. M. Hyman, P. G. Kevrekidis, O. Runborg, and C.Theodoropoulos)  Comm. Math. Sciences 1(4) 715-762 (2003); also physics/0209043 at arXiv.org. Original version was NECI Technical Report TR 2002-010N, 19 Aug, 2002