Publications

In Preparation

  1. D. P. Nicholls and J. Niu, "A Field Expansions Method for Acoustic Scattering by a Doubly Crossed Multilayered Media" .

Submitted

  1. T. McBride and D. P. Nicholls, "On Stability of Generalized Short-Crested Water Waves" download .
  2. B. Akers and D. P. Nicholls, "Spectral Stability of Deep Two-Dimensional Gravity Water Waves: Repeated Eigenvalues" download .

To Appear

  1. T. Sobayo, A. Fine, E. Gunnar, C. Kazlauskas, D. P. Nicholls, and D. Mogul, "Synchrony Dynamics across Brain Structures in Limbic Epilepsy Vary Between Initiation and Termination Phases of Seizures" download .
  2. R. Canning and D. P. Nicholls, "Numerical Simulation of a Weakly Nonlinear Model for Internal Waves," Communications in Computational Physics download .
  3. Y. He, D. P. Nicholls, and J. Shen, "An Efficient and Stable Spectral Method for Electromagnetic Scattering from a Layered Periodic Structure," Journal of Computational Physics download .

Appeared

  1. D. P. Nicholls, "Three-Dimensional Acoustic Scattering by Layered Media: A Novel Surface Formulation with Operator Expansions Implementation," Proceedings of the Royal Society of London, A Volume 468, 731-758, (2012). download .
  2. D. Ambrose, J. Bona, and D. P. Nicholls, "Well-Posedness of a Model for Water Waves with Viscosity," Discrete and Continuous Dynamical Systems, Series B, Volume 17, Number 4, xx-xx, (2012) download .
  3. D. P. Nicholls, "Efficient Enforcement of Far-Field Boundary Conditions in the Transformed Field Expansions Method," Journal of Computational Physics, Volume 230, Number 22, 8290-8303, (2011). download .
  4. A. Malcolm and D. P. Nicholls, "A Boundary Perturbation Method for Recovering Interface Shapes in Layered Media," Inverse Problems, Volume 27, Number 9, xx-xx, (2011) download .
  5. A. Malcolm and D. P. Nicholls, "A Field Expansions Method for Scattering by Periodic Multilayered Media," Journal of the Acoustical Society of America, Volume 129, Number 4, 1783-1793, (2011) download .
  6. D. P. Nicholls, "Spectral Stability of Traveling Water Waves: Eigenvalue Collision, Singularities, and Direct Numerical Simulation," Physica D, Volume 240, Issues 4-5, 376-381, (2011) download .
  7. D. P. Nicholls and J. Orville, "A Boundary Perturbation Method for Vector Electromagnetic Scattering from Families of Doubly Periodic Gratings," Journal of Scientific Computing, Volume 45, Number 1, 471-486, (2010) download .
  8. B. Akers and D. P. Nicholls, "Traveling Waves in Deep Water with Gravity and Surface Tension," SIAM Journal on Applied Mathematics, Volume 70, Number 7, 2373-2389, (2010) download .
  9. B. Hu and D. P. Nicholls, "The Domain of Analyticity of Dirichlet-Neumann Operators," Proceedings of the Royal Society of Edinburgh A, Volume 140, Number 2, 367-389, (2010) download .
  10. C. Fazioli and D. P. Nicholls, "Stable Computation of Variations of Dirichlet-Neumann Operators," Journal of Computational Physics, Volume 229, Number 3, 906-920 (2010) download .
  11. M. Kakleas and D. P. Nicholls, "Numerical Simulation of a Weakly Nonlinear Model for Water Waves with Viscosity," Journal of Scientific Computing, Volume 42, Number 2, 274-290 (2010) download .
  12. A. S. Fine, D. P. Nicholls, and D. J. Mogul, "Assessing Instantaneous Synchrony of Nonlinear, Nonstationary Oscillators in the Brain," Journal of Neuroscience Methods, Volume 186, Number 1, 42-51 (2010) download .
  13. J. Gorsky and D. P. Nicholls, "A Small Dispersion Limit to the Camassa-Holm Equation: A Numerical Study," Mathematics and Computers in Simulation, Volume 80, Number 1, 120-130 (2009) download .
  14. D. P. Nicholls and J. Shen, "A Rigorous Numerical Analysis of the Transformed Field Expansion Method," SIAM Journal on Numerical Analysis, Volume 47, Number 4, 2708-2734 (2009) download .
  15. T. Binford, D. P. Nicholls, N. Nigam, and T. Warburton, "Exact Non-Reflecting Boundary Conditions on Perturbed Domains and hp-Finite Elements," Journal of Scientific Computing, Volume 39, Number 2, 265-292 (2009) download .
  16. D. P. Nicholls, "Spectral Data for Traveling Water Waves: Singularities and Stability," Journal of Fluid Mechanics, Volume 624, 339-360 (2009) download .
  17. D. P. Nicholls, "A Rapid Boundary Perturbation Algorithm for Scattering by Families of Rough Surfaces," Journal of Computational Physics, Volume 228, Number 9, 3405-3420 (2009) download .
  18. D. P. Nicholls and M. Taber, "Detection of Ocean Bathymetry from Surface Wave Measurements," European Journal of Mechanics B/Fluids, Volume 28, Number 2, 224-233 (2009) download .
  19. D. P. Nicholls and F. Reitich, "Boundary Perturbation Methods for High-Frequency Acoustic Scattering: Shallow Periodic Gratings," Journal of the Acoustical Society of America, Volume 123, Number 5, 2531-2541 (2008) download .
  20. D. P. Nicholls and M. Taber, "Joint Analyticity and Analytic Continuation for Dirichlet-Neumann Operators on Doubly Perturbed Domains," Journal of Mathematical Fluid Mechanics, Volume 10, Number 2, 238-271 (2008) download .
  21. C. Fazioli and D. P. Nicholls, "Parametric Analyticity of Functional Variations of Dirichlet-Neumann Operators," Differential and Integral Equations, Volume 21, Number 5-6, 541-574 (2008) download .
  22. P. Guyenne and D. P. Nicholls, "A High-Order Spectral Method for Nonlinear Water Waves over Bottom Topography," SIAM Journal on Scientific Computing, Volume 30, Number 1, 81-101 (2007) download .
  23. D. P. Nicholls, "Spectral Stability of Traveling Water Waves: Analytic Dependence of the Spectrum," Journal of Nonlinear Science, Volume 17, Number 4, 369-397 (2007) download .
  24. Q. Fang, D. P. Nicholls, and J. Shen, "A Stable, High-Order Method for Three-Dimensional Bounded-Obstacle Scattering," Journal of Computational Physics, Volume 224, Number 2, 1145-1169 (2007) download .
  25. D. P. Nicholls, "Boundary Perturbation Methods for Water Waves," GAMM-Mitteilungen, Volume 30, Number 1, 44-74 (2007) download .
  26. L. Chindelevitch, D. P. Nicholls and N. Nigam, "Error Analysis and Preconditioning for an Enhanced DtN-FE Algorithm for Exterior Scattering Problems," Journal of Computational and Applied Mathematics, Volume 204, 493-504 (2007) download .
  27. D. P. Nicholls and N. Nigam, "Error Analysis of an Enhanced DtN-FE Method for Exterior Scattering Problems," Numerische Mathematik, Volume 105, Number 2, 267-298 (2006) download .
  28. D. P. Nicholls and J. Shen, "A Stable, High-Order Method for Two-Dimensional Bounded-Obstacle Scattering," SIAM Journal on Scientific Computing, Volume 28, Issue 4, 1398-1419 (2006) download .
  29. D. P. Nicholls and F. Reitich, "Stable, High-Order Computation of Traveling Water Waves in Three Dimensions," European Journal of Mechanics B/Fluids, Volume 25, Number 4, 406-424 (2006) download .
  30. B. Hu and D. P. Nicholls, "Analyticity of Dirichlet-Neumann Operators on Hölder and Lipschitz Domains," SIAM Journal on Mathematical Analysis, Volume 37, Number 1, 302-320 (2005) download .
  31. D. P. Nicholls and F. Reitich, "On Analyticity of Traveling Water Waves," Proceedings of the Royal Society of London A, Volume 461, Number 2057, 1283-1309 (2005) download .
  32. W. Craig, P. Guyenne, D. P. Nicholls and C. Sulem, "Hamiltonian Long Wave Expansions for Water Waves over a Rough Bottom," Proceedings of the Royal Society of London A, Volume 461, Number 2055, 839-873 (2005) download .
  33. P. Guyenne and D. P. Nicholls, "Numerical Simulation of Solitary Waves on Plane Slopes," Mathematics and Computers in Simulation, Volume 69, 269--281 (2005) download .
  34. D. P. Nicholls and F. Reitich, "Shape Deformations in Rough Surface Scattering: Improved Algorithms," Journal of the Optical Society of America, A, Volume 21, Issue 4, 606-621 (2004) download .
  35. D. P. Nicholls and F. Reitich, "Shape Deformations in Rough Surface Scattering: Cancellations, Conditioning, and Convergence," Journal of the Optical Society of America, A, Volume 21, Issue 4, 590-605 (2004) download .
  36. D. P. Nicholls and N. Nigam, "Exact Non-Reflecting Boundary Conditions on General Domains," Journal of Computational Physics, Volume 194, Number 1, 278-303 (2004) download .
  37. M. Haragus, D. P. Nicholls, and D. H. Sattinger, "Solitary Wave Interactions of the Euler-Poisson Equations," Journal of Mathematical Fluid Mechanics, Volume 5, 92-118 (2003) download .
  38. W. Craig and D. P. Nicholls, "Traveling Gravity Water Waves in Two and Three Dimensions," European Journal of Mechanics B/Fluids, Volume 21, Number 6, 615-641 (2002) download .
  39. D. P. Nicholls and F. Reitich, "Analytic Continuation of Dirichlet-Neumann Operators," Numerische Mathematik, Volume 94, Number 1, 107-146 (2003) download .
  40. D. P. Nicholls and F. Reitich, "Stability of High-Order Perturbative Methods for the Computation of Dirichlet-Neumann Operators," Journal of Computational Physics, Volume 170, Number 1, 276-298 (2001) download .
  41. D. P. Nicholls and F. Reitich, "A New Approach to Analyticity of Dirichlet-Neumann Operators," Proceedings of the Royal Society of Edinburgh A, Volume 131, Number 6, 1411-1433 (2001) download .
  42. D. P. Nicholls, "On Hexagonal Gravity Water Waves," Mathematics and Computers in Simulation, Volume 55, Number 4-6, 567-575 (2001) download .
  43. W. Craig and D. P. Nicholls, "Traveling Two and Three Dimensional Capillary Gravity Water Waves," SIAM Journal on Mathematical Analysis, Volume 32, Number 2, 323-359 (2000) download .
  44. D. P. Nicholls, "Traveling Water Waves: Spectral Continuation Methods with Parallel Implementation," Journal of Computational Physics, Volume 143, Number 1, 224-240 (1998) download .