My research concerns the development of numerical algorithms for problems in continuum mechanics.  One recurring theme is multiphase flow, where the boundary between coexisting phases is fully resolved.

• G.H. Miller and T. Martin.   Reducing proof:  Farmar's Spirit Rule and some antecedents.  J. Oughtred Soc., 30(1):5-17, 2021.
• G.H. Miller.  Empirical functions of two variables, and Dicas' hydrometer correction.  J. Oughtred Soc., 30(1):18-24, 2021.
• S.M.H. Hashemi Amrei, M. Tahernia, T.C. Hui,  W.D. Ristenpart, and G.H. Miller. Non-antiperiodic force excitations with zero time average yield net motion.  arXiv:2201.00951.
• S.M.H. Hashemi Amrei, G.H. Miller, K.J.M. Bishop, and W.D. Ristenpart.  A perturbation solution to the full Poisson-Nernst-Planck equations yields an asymmetric electric field.  Soft Matter, 16:7052-7062, 2020.
• S.M.H. Hashemi Amrei, G.H. Miller, and W.D. Ristenpart.  Asymmetric rectified electric fields generate flows that can dominate induced-charge electrokinetics.  Phys. Rev. Fluids, 5:013712, 2020.
• K. Phetxumphou, G. Miller, P.L. Ashmore, T. Collins, and J. Lahne.  Mashbill and barrel aging effects on the sensory and chemometric profiles of American whiskeys.  J. Inst. Brew.,  126:194-205, 2020.
• S.C. Bukosky, S.M.H. Hashemi Amrei, S.P. Rader, J. Mora, G.H. Miller, and W.D. Ristenpart. Extreme levitation of colloidal particles in response to oscillatory electric fields.  Langmuir, 35:6971-6980, 2019.
• S.M.H. Hashemi Amrei, G. Miller, and W.D. Ristenpart.  Asymmetric rectified electric fields between parallel electrodes:  numerical and scaling analyses.  Phys. Rev. E, 99:062603, 2019.
• G. Miller.  Whisky Science:  A Condensed Distillation.  Springer.  2019.
• S.M.H. Hashemi Amrei, S.C. Bukosky, S.P. Rader, W.D. Ristenpart, and G.H. Miller.  Oscillating electric fields in liquids create a long-range steady field.  Phys. Rev. Lett., 121:185504, 2018.
• M. Vahab and G.H. Miller. A front-tracking shock-capturing method for two fluids.  Comm. App. Math. Comput. Sci., 11:1-35, 2016.
• G. Miller.  Numerical Analysis for Engineers and Scientists.  Cambridge University Press.  2014.
• G.H. Miller and E.G. Puckett. a Neumann-Neumann preconditioned iterative substructuring approach for computing solutions to Poisson’s equation with prescribed jumps on an embedded boundary.  J. Comput. Phys., 235:683-700, 2013.
• B. Kallemov, G.H. Miller, S. Mitran, and D. Trebotich. Calculation of viscoelastic bead-rod flow mediated by a homogenized kinetic scale with holonomic constraints, Mol. Simulat., 38:786-792, 2012.
• G.H. Miller and D. Trebotich.  An embedded boundary method for the Navier-Stokes equations on a time-dependent domain.  Comm. App. Math. Comput. Sci., 7(1):1-31, 2012.
• B. Wang, G. Miller, and P. Colella.  An adaptive high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations.  SIAM J. Sci. Comput., 34:B909-B924, 2012.
• B. Kallemov and G. H. Miller.  A second-order strong method for the Langevin equations with holonomic constraints.  SIAM J. Sci. Comput., 33(2):653-676, 2011.
• B. Kallemov, G. H. Miller, and D. Trebotich.  A higher-order accurate fluid-particle algorithm for polymer flows.  Mol. Simulat., 37(8):738-745, 2011.
• B. Wang, G.H. Miller, and P. Colella.  A particle-in-cell method with adaptive phase-space remapping for kinetic plasmas.  SIAM J. Sci. Comput., 33(6):3509-3537, 2011.
• B. Kallemov, G.H. Miller, and D. Trebotich.  Numerical simulation of polymer flow in microfluidic devices.  In Proc. 4th SIAM Conference on Mathematics for Industry, p. 93-98, 2010.
• S.A. Conley, I. Faloona, G.H. Miller, D.H. Lenshow, B. Blomquist, and A. Bandy.  Closing the dimethyl sulfide budget in the tropical marine boundary layer during the Pacific Atmospheric Sulfur Experiment.  Atmos. Chem. Phys., 9:8745-8756, 2009.
• B. Kallemov, G.H. Miller, and D. Trebotich.  A Duhamel approach for the Langevin equations with holonomic constraints.  Mol. Simulat., 35(6):440-447, 2009.
• A. Nonaka, D. Trebotich, G.H. Miller, D.T. Graves, and P. Colella.  A higher-order upwind method for viscoelastic flow.  Comm. App. Math. Comput. Sci., 4:57-83, 2009.
• D.T. Graves, D. Trebotich, G.H. Miller, and P. Colella.  An efficient solver for the equations of resistive MHD with spatially-varying resistivity.  J. Comput. Phys., 227:4797-4804, 2008.
• B. Kallemov, G.H. Miller, and D. Trebotich.  A higher-order approach to fluid-particle coupling in microscale polymer flows.  In Nanotechnology 2008:  Microsystems, Photonics, Sensors, Fluidics, Modeling, and Simulation, v3, Boston, MA, June 1-5, 2008.
• G.H. Miller.  An iterative boundary potential method for the infinite-domain Poisson problem with interior Dirichlet boundaries.  J. Comput. Phys., 227:7917-7928, 2008.
• G.H. Miller and D. Trebotich.  Toward a mesoscale model for the dynamics of polymer solutions.  J. Comput. Theor. Nanosci., 4:797-801, 2007.
• D. Trebotich, G.H. Miller, and M.D. Bybee.  A penalty method to model particle interactions in DNA-laden flows.  J. Nanosci. Nanotech., 8:1-8, 2007.
• D. Trebotich, P. Colella, and G.H. Miller.  A stable and convergent scheme for viscoelastic flow in contraction channels.  J. Comput. Phys., 205:315-342, 2005.
• D. Trebotich and G.H. Miller.  Modeling and simulation of DNA flow in a microfluidic-based pathogen detection system.  In Proc. 3rd Annual International IEEE EMBS Special Topic Conference on Microtechnologies in Medicine and Biology, Kahuku, Oahu, Hawaii. 12-15 May 2004, p. 353-355, 2005.
• D. Trebotich, G.H. Miller, P. Colella, D.T. Graves, D.F. Martin, and P.O. Schwartz.  A tightly-coupled particle-fluid method for DNA-laden flows in complex microscale geometries.  In Computational Fluid and Solid Mechanics 2005, p. 1018-1022, 2005.
• J.E. Bowen , M.W. Wactor, G.H. Miller, and M. Capelli-Schellpfeffer.  Catch the Wave: Modeling of the Pressure Wave Associated with Arc Fault.  IEEE Industry Applications Magazine, 10:59-67, 2004.
• G.H. Miller.  Minimal rotationally-invariant bases for hyperelasticity.  SIAM J. Appl. Math., 64:2050-2075, 2004.
• D. Trebotich, P. Colella, G.H. Miller, A. Nonaka, T. Marshall, S. Gulati, and D. Liepmann.  A numerical algorithm for complex biological flow in irregular microdevice geometries.  In Technical Proceedings of the 2004 Nanotechnology Conference and Trade Show, v2, p. 470-473, 2004.
• G.H. Miller.  An iterative Riemann solver for systems of hyperbolic conservation laws, with application to hyperelastic solid mechanics.  J. Comput. Phys., 193:198-225 2003.
• D. Trebotich, P. Colella, G. Miller, and D. Liepmann.  A numerical model of viscoelastic flow in microchannels.  In Technical Proceedings of the 2003 Nanotechnology Conference and Trade Show, v. 2, p. 520-523, 2003.
• G.H. Miller and P. Colella, A conservative three-dimensional Eulerian method for coupled fluid-solid shock capturing.  J. Comput. Phys., 183:26-82, 2002.
• J.G. Blank, G.H. Miller, M.H. Ahrens, and R.E. Winans.  Experimental shock chemistry of aqueous amino acid solutions and the cometary delivery of prebiotic compounds.  Origins of Life Evol. B., 31:15-51, 2001.
• G.H. Miller and P. Colella, A high-order Eulerian Godunov method for elastic-plastic flow in solids.  J. Comput. Phys., 167:131-176, 2001.