My research interests lie in the areas of computational mathematics and physics, specifically in the areas of finite-element methods and least squares approaches. Currently, my research focuses on the development of theoretically-supported nonlinear constrained optimization methods coupled with finite elements for static and dynamic liquid crystal simulations. Such development concerns both accurate physical modeling as well as efficient numerical computation. The coupling of liquid crystal free elastic effects with applied electric fields, flexoelectric effects, and fluid dynamics yields interesting theoretical challenges for the design of effective and efficient computational techniques. In addition, efficient algorithm development branches into adaptive mesh refinement techniques and linear solvers for saddle point systems.

Publications

• D. B. Emerson. Error Estimators and Marking Strategies for Electrically Coupled Liquid Crystal Systems. Under Review, 2018.


• J. H. Adler, D. B. Emerson, P. E. Farrell, S. P. MacLachlan, and T. J. Atherton. Computing Equilibrium States of Cholesteric Liquid Crystals in Elliptical Channels with Deflation Algorithms. Liquid Crystals, 45(3):341-350, 2018.


• D. B. Emerson. A Posteriori Error Estimators for the Frank-Oseen Model of Liquid Crystals. J. Coupled Syst. Multiscale Dyn. (JCSMD), 5(2):95-110, 2017.


• J. H. Adler, D. B. Emerson, P. E. Farrell, and S. P. MacLachlan. Combining Deflation and Nested Iteration for Computing Multiple Solutions of Nonlinear Variational Problems. SIAM J. Sci. Comput. (SISC), 39(1):B29-B52, 2017.


• J. H. Adler, D. B. Emerson, S. P. MacLachlan, and T. A. Manteuffel. Constrained Optimization for Liquid Crystal Equilibria. SIAM J. Sci. Comput. (SISC), 38(1):B50-B76, 2016.


• J. H. Adler, T. J. Atherton, T. R. Benson, D. B. Emerson, and S. P. MacLachlan. Energy Minimization for Liquid Crystal Equilibrium with Electric and Flexoelectric Effects. SIAM J. Sci. Comput. (SISC), 37(5):S157-S176, 2015.


• J. H. Adler, T. J. Atherton, D. B. Emerson, and S. P. MacLachlan. An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals. SIAM J. Numer. Anal. (SINUM), 53(5):2226-2254, 2015.


• A. DeBenedictis, T. J. Atherton, C. Anquetil-Deck, D. J. Cleaver, D. B. Emerson, M. Wolak, and J. H. Adler. Competition of Lattice and Basis for Alignment of Nematic Liquid Crystals. Phys. Rev. E, 92:042501, 2015.

Proceedings

• M. A. Stevens, C. Downs, D. Emerson, J. Adler, S. MacLachlan, and T. E. Vandervelde. Predicting VOC at Ultra-High Solar Concentration Using Computational Numerical Analysis. In Proceedings of the 31st European Photovoltaic Solar Energy Conference (EUPVSC). Hamburg, Germany, Sept. 14-18, 2015.


• M. Stevens, C. Downs, D. Emerson, J. Adler, S. MacLachlan, and T. E. Vandervelde. Studying Anomalous Open-Circuit Voltage Drop-Out in Concentrated Photovoltaics Using Computational Numerical Analysis. In Proceedings of the 42nd IEEE Photovoltaic Specialists Conference (PVSC). New Orleans, June 14-19, 2015.

Technical Reports

• J. H. Adler, T. J. Atherton, D. B. Emerson, and S. P. MacLachlan. An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis. Technical Report, Tufts University, 2014.


• J. H. Adler, D. B. Emerson, S. P. MacLachlan, and T. A. Manteuffel. Constrained Optimization for Liquid Crystal Equilibria: Extended Results. Technical Report, Tufts University, 2014.

PhD Thesis

• D. B. Emerson. Advanced Discretizations and Multigrid Methods for Liquid Crystal Configurations. Thesis (Ph.D.), Tufts University, 2015.