Shawn W. Walker

Professor
Department of Mathematics and Center for Computation & Technology (CCT)
Louisiana State University

Publications

• J. Shahan, S. Walker
  Exact Shape Derivatives with Unfitted Finite Element Methods
  submitted.
• A. Hicks, S. Walker
  Modelling and simulation of the cholesteric Landau-de Gennes model
  Proceedings of the Royal Society A: Math., Phys. and Eng. Sci., vol 480, no 2292, pg. 20230813, 2024.
• S. Walker
  A Descent Scheme for Thick Elastic Curves with Self-contact and Container Constraints
  Journal of Scientific Computing, vol 99, no 2, pg. 29, 2024.
• S. Walker
  Approximating the Shape Operator with the Surface HHJ Element
  SIAM Journal on Scientific Computing, vol 46, no 2, pg A1252-A1275, 2024.
  Supplementary Materials: Approximating the Shape Operator with the Surface HHJ Element
• T. Surowiec, S. Walker
  Optimal Control of the Landau--de Gennes Model of Nematic Liquid Crystals
  SIAM Journal on Control and Optimization, vol 61, no 4, pg. 2546–2570, 2023.
• P. Liu, J. Arsuaga, M.-C. Calderer, D. Golovaty, M. Vazquez, S. Walker
  Helical organization of DNA-like liquid crystal filaments in cylindrical viral capsids
  Proceedings of the Royal Society A, vol 478, no 2266, pg. 20220047, 2022.
• A. Adili, Y. Chen, R. Lipton, S. Walker
  Controlling the dispersion of metamaterials in three dimensions
  Proceedings of the Royal Society A: Math., Phys. Eng. Sci., vol 478, no 2263, pg 20220194, 2022.
• R. Koizumi, D. Golovaty, A. Alqarni, S. Walker, Y. Nastishin, M.-C. Calderer, O. Lavrentovich
  Toroidal nuclei of columnar lyotropic chromonic liquid crystals coexisting with an isotropic phase
  Soft Matter (The Royal Society of Chemistry), vol 18, pg. 7258-7268, 2022.
• S. Walker
  Poincare Inequality for a Mesh-dependent 2-norm on Piecewise Linear Surfaces with Boundary
  Computational Methods in Applied Mathematics, vol 22, no 1, pg 227-243, 2022.
• P. Liu, J. Arsuaga, M.-C. Calderer, D. Golovaty, M. Vazquez, S. Walker
  Ion-dependent DNA Configuration in Bacteriophage Capsids
  Biophysical Journal, vol 120, no 16, pg 3292-3302, 2021.
• C. Schimming, J. Vinals, S. Walker
  Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal
  Journal of Computational Physics, vol 441, pg 110441, 2021.
• A. Laurain, S. Walker
  Optimal control of volume-preserving mean curvature flow
  Journal of Computational Physics, vol 438, pg 110373, 2021.
• S. Walker
  The Kirchhoff Plate Equation on Surfaces: The Surface Hellan–Herrmann–Johnson Method
  IMA Journal of Numerical Analysis, 2021, doi = 10.1093/imanum/drab062.
• E. Chukwuemeka, S. Walker
  Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model
  Advances in Applied Mathematics and Mechanics, vol 14, no 1, pg 1 - 32, 2021.
  
• J.-P. Borthagaray, S. Walker
  The Q-tensor Model with Uniaxial Constraint
  Geometric Partial Differential Equations - Part II, ed. by A. Bonito and R. H. Nochetto,
  Handbook of Numerical Analysis, vol. 22, pg 313-382, 2021.
  
• J.-P. Borthagaray, R. Nochetto, S. Walker
  A structure preserving FEM for the uniaxially constrained Q-tensor model of nematic liquid crystals
  Numerische Mathematik, vol 145, no 4, pg 837 - 881, 2020.
  
• S. Carter, A. Rotem, S. Walker
  A Domain Decomposition Approach to Accelerate Simulations of Structure Preserving Nematic Liquid Crystal Models
  Journal of Non-Newtonian Fluid Mechanics, vol 283, pg 104335, 2020.
• D. Arnold, S. Walker
  The Hellan--Herrmann--Johnson Method With Curved Elements
  SIAM Journal on Numerical Analysis, vol 58, no 5, pg 2829-2855, 2020.
  Supplementary Materials: The HHJ Method With Curved Elements
• S. Walker
  A Finite Element Method for the Generalized Ericksen Model of Nematic Liquid Crystals
  Mathematical Modelling and Numerical Analysis (M2AN), vol 54, pg 1181 - 1220, 2020.
• S. Walker, J. Arsuaga, M.-C. Calderer, L. Hiltner, M. Vazquez
  Fine Structure of Viral ds DNA Encapsidation
  Phys. Rev. E, vol 101, pg 022703, 2020.
• A. Diegel, S. Walker
  A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets
  Communications in Computational Physics, vol 25, pg 155-188, 2019.
• S. Walker
  On The Correct Thermo-dynamic Potential for Electrostatic Dielectric Energy
  ArXiv e-print (2018).
• H. Antil, S. W. Walker
  Optimal Control of a Degenerate PDE for Surface Shape
  Applied Mathematics & Optimization, vol 78, no 2, pg 297-328, 2018.
• J. Guzman, A. Madureira, M. Sarkis, S. Walker
  Analysis of the Finite Element Method for the Laplace-Beltrami Equation on Surfaces with Regions of High Curvature Using Graded Meshes
  Journal of Scientific Computing, vol 77, no 3, pg 1736 - 1761, 2018.
• A. Morvant, E. Seal, S. Walker
  A Coupled Ericksen/Allen-Cahn Model For Liquid Crystal Droplets
  Computers & Mathematics with Applications, vol 75, no 11, pg 4048 - 4065, 2018.
• R. H. Nochetto, S. W. Walker, W. Zhang
  The Ericksen Model of Liquid Crystals with Colloidal and Electric Effects
  Journal of Computational Physics, vol 352, pg 568 - 601, 2018.
• S. W. Walker
  FELICITY: A Matlab/C++ Toolbox For Developing Finite Element Methods And Simulation Modeling
  SIAM Journal on Scientific Computing, vol 40, No. 2, pg C234--C257, 2018.
  FELICITY: Supplementary Demos
• C. B. Davis, S. W. Walker
  Semi-discrete Error Estimates And Implementation Of A Mixed Method For The Stefan Problem
  Mathematical Modelling and Numerical Analysis (M2AN), vol 51, pg 2093 - 2126, 2017.
• R. H. Nochetto, S. W. Walker, W. Zhang
  A Finite Element Method For Nematic Liquid Crystals With Variable Degree Of Orientation
  SIAM Journal on Numerical Analysis, vol 55, no 3, pg 1357-1386, June 2017.
• S. W. Walker
  Shape Optimization Of Self-Avoiding Curves
  Journal of Computational Physics, vol 311, pg 275 - 298, Feb 2016.
• R. H. Nochetto, S. W. Walker, W. Zhang
  Numerics for Liquid Crystals with Variable Degree of Orientation
  MRS proceedings, Symposium NN – Math. and Comp. Aspects of Mater. Sci., vol. 1753, 2015.
• S. W. Walker
  The Shapes of Things: A Practical Guide to Differential Geometry and the Shape Derivative
  SIAM Book Series: Advances in Design and Control, 2015.
• J. Dey, S. W. Walker, D. Shumilov, K. Kirby, Y. Luo, J. Mathis
  Modeling and Analysis of a Physical Tumor Model Including the Effects of Necrotic Core
  Conference IEEE NSS-MIC, 2015.
• C. B. Davis, S. W. Walker
  A Mixed Formulation Of The Stefan Problem With Surface Tension
  Interfaces and Free Boundaries, vol 17, no 4, pg 427-464, Dec 2015.
• A. Laurain, S. W. Walker
  Droplet Footprint Control
  SIAM Journal on Control and Optimization, vol 53, no 2, pg 771-799, Mar 2015.
• S. W. Walker
  A Mixed Formulation Of A Sharp Interface Model Of Stokes Flow With Moving Contact Lines
  Mathematical Modelling and Numerical Analysis (M2AN), vol 48, no 4, pg 969-1009, 2014.
• R. H. Nochetto, A. J. Salgado, S. W. Walker
  A Diffuse Interface Model For Electrowetting With Moving Contact Lines
  Mathematical Models and Methods in Applied Sciences (M3AS), vol 24, no 1, pg 67 - 111, 2014.
• R. S. Falk, S. W. Walker
  A Mixed Finite Element Method For EWOD That Directly Computes the Position of the Moving Interface
  SIAM Journal on Numerical Analysis, vol 51, no 2, pg 1016-1040, Mar 2013.
• S. W. Walker
  Tetrahedralization of Isosurfaces with Guaranteed-quality by Edge Rearrangement (TIGER)
  SIAM Journal on Scientific Computing, vol 35, no 1, pg A294 - A326, Jan 2013.
• E. E. Keaveny, S. W. Walker, M. J. Shelley
  Optimization of Chiral Structures for Micro-Scale Propulsion
  Nano Letters, vol 13, no 2, pg 531-537, Jan 2013.
• S. W. Walker, E. E. Keaveny
  Analysis of Shape Optimization for Magnetic Micro-Swimmers
  SIAM Journal on Control and Optimization, vol 51, no 4, pg 3093 - 3126, 2013.
• M. Armani, Z. Cummins, J. Gong, P. Mathai, R. Probst, C. Ropp, E. Waks, S. Walker, B. Shapiro
  Feedback Control of Microflows
  in book: "Feedback Control of MEMS to Atoms", Springer, pg 269-319, 2012.
• S. W. Walker, M. J. Shelley
  Shape Optimization of Peristaltic Pumping
  Journal of Computational Physics, vol 229, no 4, pg 1260-1291, Feb 2010.
• S. W. Walker, A. Bonito, R. H. Nochetto
  Mixed Finite Element Method for Electrowetting On Dielectric (EWOD) with Contact Line Pinning
  Interfaces and Free Boundaries, vol 12, no 1, pg 85-119, March 2010.
• R. H. Nochetto, S. W. Walker
  A Hybrid Variational Front Tracking-Level Set Mesh Generator For Problems Exhibiting Large Deformations and Topological Changes
  Journal of Computational Physics, vol 229, no 18, pg 6243-6269, Sept 2010.
• S. W. Walker, B. Shapiro, R. H. Nochetto
  Electrowetting with Contact Line Pinning: Computational Modeling and Comparisons with Experiments
  Physics of Fluids, vol 21, no 10, pg 102103, Oct 2009.
• S. W. Walker, B. Shapiro
  Modeling the Fluid Dynamics of Electro-Wetting On Dielectric (EWOD)
  Journal of Microelectromechanical Systems (JMEMS), vol 15, no 4, pg 986-1000, Aug 2006.
• S. W. Walker, B. Shapiro
  A Control Method for Steering Individual Particles Inside Liquid Droplets Actuated by Electrowetting
  Lab on a Chip Journal, vol 12, no 1, pg 1404 - 1407, 2005.
• M. Armani, S. Chaudhary, R. Probst, S. W. Walker, B. Shapiro
  Control of Micro-Fluidic Systems: Two Examples, Results, and Challenges
  International Journal of Robust and Nonlinear Control, vol 15, issue 16, pg 785-803, 10 November 2005 [Invited paper].
• S. W. Walker, B. Shapiro
  Modeling the Fluid Dynamics of Electro-Wetting on Dielectric (EWOD)
  Technical Proceedings of the 2004 NSTI Nanotechnology Conference and Trade Show, vol 2, pg 391 - 394, 2004.

Copyright © 2019. This material is based upon work supported by the National Science Foundation
under the following grants: DMS-1115636, DMS-1418994, DMS-1555222 (CAREER), DMS-2111474.

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Mailing Address:   Dept. of Mathematics · Louisiana State University · Baton Rouge, LA 70803-4918
Phone:   225-578-1603 (voice), 225-578-4276 (fax)
Office Location:   Lockett Hall, Room 210
E-mail:   walker@math.lsu.edu