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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.