| N. Ford and D. L. Chopp | A Dimensionally Reduced Model of Biofilm Growth Within a Flow Cell, Bulletin of Mathematical Biology, 82(3):40 | 2020 | Biofilms |
| A. Caruso, F. Boano, L. Ridolfi, D. L. Chopp, A. Packman | Biofilm-Induced Bioclogging Produces Sharp Interfaces in Hyporheic Flow, Redox Conditions and Microbial Community Structure, Geophysical Research Letters, 44:4917-4925 | 2017 | Biofilms |
| A. Sadeghirad, D. L. Chopp, X. Ren, E. Fang, J. Lua | A Novel Hybrid Approach for Level Set Characterization and Tracking of Non-Planar 3D Cracks in the Extended Finite Element Method, Engineering Fracture Mechanics, 160:1-14 | 2016 | Level Set Method, eXtended Finite Element Method, Fracture Mechanics |
| R. Kublik and D. L. Chopp | A Locally Adaptive Time-Stepping Algorithm for the Solution to Reaction-Diffusion Equations on Branched Structures, Advances in Computational Mathematics, 42(3):621-649 | 2016 | Numerical Methods, Computational Neuroscience |
| X. Li, D.L. Chopp, W.A. Russin, P.T. Brannon, M. R. Parsek, A.I. Packman | In Situ Biomineralization and Particle Deposition Distinctively Mediate Biofilm Susceptibility to Chlorine, Applied and Environmental Microbiology, 82(10):2886-2892 | 2016 | Biofilms |
| X. Li, D.L. Chopp, W.A. Russin, P.T. Brannon, M. R. Parsek, A.I. Packman | Spatial Patterns of Carbonate Biomineralization in Biofilms, Applied and Environmental Microbiology, 81(21):7403-7410 | 2015 | Biofilms |
| X. Li, J.L. Song, A. Culotti, W. Zhang, D.L. Chopp, N. Lu, A.I. Packman | Methods for Characterizing the Co-Development of Biofilm and Habitat Heterogeneity, Journal of Visualized Experiments, 97 | 2015 | Biofilms |
| B. V. Merkey and D. L. Chopp | Modeling the Impact of Interspecies Competition on Performance of a Microbial Fuel Cell, Bulletin of Mathematical Biology, 76(6):1429-1453 | 2014 | Level Set Method, Biofilms |
| B. S. Tseng, W. Zhang, J. J. Harrison, T. P. Quach, J. L. Song, J. Penterman, P. K. Singh, D. L. Chopp, A. I. Packman, and M. R. Parsek. | The Extracellular Matrix Protects Pseudomonas aerguinosa Biofilms by Limiting the Penetration of Tobramycin, Environmental Microbiology, 15(10):2865-2878 | 2013 | Biofilms |
| A. A. Davila, D. W. Buck, D. L. Chopp, C. M. Connor, S. Persing, V. Rawlani, and J. Y. S. Kim | A Novel Prospective Three-Dimensional Analysis of Nasolabial Fold Augmentation, Aesthetic Surgery Journal, 32(4):488-494 | 2012 | Plastic Surgery |
| B. V. Merkey and D. L. Chopp | The Performance of a Microbial Fuel Cell Depends Strongly on Anode Geometry: A Multidimensional Modeling Study, Bulletin of Mathematical Biology, 74:834-857 | 2012 | Biofilms, Level Set Method |
| D. L. Chopp, V. Rawlani, M. Ellis, S. A. Johnson, S. Khan, K. Bethke, N. Hansen, J. YS Kim | A Geometric Analysis of Mastectomy Incisions: Optimizing Intraoperative Breast Volume, Canadian Journal of Plastic Surgery, 19(2):45-50 | 2011 | Plastic Surgery |
| R. Duddu, D. L. Chopp, and P. Voorhees | Diffusional Evolution of Precipitates in Elastic Media Using the Extended Finite Element and the Level Set Methods, Journal of Computational Physics, 230(4):1249-1264 | 2011 | Materials Science, Level Set Method |
| J. Shi, D. L. Chopp, J. Lua, N. Sukumar, and T. Belytschko | Abaqus Implementation of Extended Finite Element Method Using a Level Set Representation for Three-Dimensional Fatigue Crack Growth and LIfe Predictions, Engineering Fracture Mechanics, 77(14):2840-2863 | 2010 | Level Set Method, eXtended Finite Element Method, Fracture Mechanics |
| B. L. Vaughan, B. G. Smith, D.L. Chopp | The Influence of Fluid Flow on Modeling Quorum Sensing in Bacterial Biofilms, Bulletin of Mathematical Biology, 72(5):1143-1165 | 2010 | Level Set Method, Biofilms |
| D. L. Chopp | Another look at velocity extensions in the level set method. SIAM Journal of Scientific Computing, 31(5):3255-3273 | 2009 | Level Set Method |
| B. Merkey, B. E. Rittmann, and D.L. Chopp | Modeling How Soluble Microbial Products (SMP) Support Heterotrophs in Autotroph-Based Biofilms, Journal of Theoretical Biology, 259:670-683 | 2009 | Level Set Method, Biofilms |
| R. Duddu, D.L. Chopp, and B. Moran | A Two-Dimensional Continuum Model of Biofilm Growth Incorporating Fluid Flow and Shear Stress Based Detachment, Biotechnology and Bioengineering, 103(1):92-104 | 2009 | Level Set Method, Biofilms |
| N. Sukumar, D. L. Chopp, E. Béchet, N. Möes | Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method, International Journal of Numerical Methods in Engineering, 76(5):727-748 | 2008 | Level Set Method, eXtended Finite Element Method, Fracture Mechanics |
| M. J. Rempe, N. Spruston, W. L. Kath, and D. L. Chopp | Compartmental neural simulations with spatial adaptivity. Journal of Computational Neuroscience, 25(3):465-480 | 2008 | Computational Neuroscience, Numerical Methods |
| R. Duddu, S. Bordas, D. L. Chopp, and B. Moran | A combined extended finite element and level set method for biofilm growth. International Journal of Numerical Methods in Engineering, 74(5):848-870 | 2008 | Level Set Method, Biofilms |
| B. G. Smith, B. L. Vaughan, and D. L. Chopp | The extended finite element method for boundary layer problems in biofilm growth, Communications in Applied Mathematics and Computational Science, 2(1):35-56 | 2007 | Level Set Method, Biofilms, eXtended Finite Element Method |
| M. J. Kirisits, J. Margolis, B. L. Purevdorj-Gage, B. Vaughan, D. L. Chopp, P. Stoodley, and M. R. Parsek | The influence of the hydrodynamic environment on quorum sensing in Pseudomonas aeruginosa biofilms, Journal of Bacteriology, 189(22):8357-8360 | 2007 | Biofilms, Level Set Method |
| B. L. Vaughan, Jr., B. G. Smith, and D. L. Chopp | A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources. Communications in Applied Mathematics and Computational Science, 1(1):207-228 | 2006 | eXtended Finite Element Method |
| J. D. Shrout, D. L. Chopp, C. L. Just, M. Hentzer, M. Givskov, and M. R. Parsek | The impact of quorum sensing and swarming motility on Pseudomonas aeruginosa biofilm formation is nutritionally conditional. Molecular Microbiology, 62(5):1264-1277 | 2006 | Biofilms |
| A. Tongen and D. L. Chopp | Simulation of multigrain thin film growth. Interfaces and Free Boundaries, 8:1-19 | 2006 | Materials Science, Level Set Method |
| M. J. Rempe and D. L. Chopp | A predictor-corrector algorithm for reaction-diffusion equations associated with neural activity on branched structures. SIAM Journal of Scientific Computing, 28(6):2139-2161 | 2006 | Numerical Methods, Computational Neuroscience |
| M. Torres, D. L. Chopp, and T. Walsh | Level set methods to compute minimal surfaces in a medium with exclusions (voids). Interfaces and Free Boundaries, 7(2) | 2005 | Differential Geometry, Level Set Method |
| S. Kodambaka, D. L. Chopp, I. Petrov, and J. E. Greene | Coalescence kinetics of two-dimensional TiN islands on atomically-smooth TiN(001) and TiN(111) terraces. Surface Science, 540(2-3):L611-L616 | 2003 | Materials Science, Level Set Method |
| M. Stolarska and D. L. Chopp | Modeling spiral cracking due to thermal cycling in integrated circuits. International Journal of Numerical Methods in Engineering, 41(20):2381-2410 | 2003 | Level Set Method, Fracture Mechanics |
| D. L. Chopp, M. J. Kirisits, M. R. Parsek, and B. Moran | The dependence of quorum sensing on the depth of a growing biofilm. Bulletin of Mathematical Biology, 65(6):1053-1079 | 2003 | Biofilms |
| D. L. Chopp and J. A. Velling | Foliations of hyperbolic space by constant mean curvature surfaces sharing ideal boundary. Journal of Experimental Mathematics, 12(3):339-350 | 2003 | Level Set Method, Differential Geometry |
| D. L. Chopp and N. Sukumar | Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. International Journal of Engineering Science, 41(8):845-869 | 2003 | Level Set Method, eXtended Finite Element Method, Fracture Mechanics |
| N. Sukumar, D. L. Chopp, and B. Moran | Extended finite element for three-dimensional fatigue crack propagation, Engineering Fracture Mechanics, 70(1):29-48 | 2003 | Level Set Method, eXtended Finite Element Method, Fracture Mechanics |
| D. L. Chopp, M. J. Kirisits, M. R. Parsek, and B. Moran | A mathematical model of quorum sensing in a growing P. aeruginosa biofilm. Journal of Industrial Microbiology and Biotechnology, 29(6):339-346 | 2002 | Biofilms |
| K. A. Smith, F. J. Solis, and D. L. Chopp | A projection method for motion of triple junctions by level sets. Interfaces and Free Boundaries, 4(3):263-276 | 2002 | Level Set Method |
| H. Ji, D. L. Chopp, and J. E. Dolbow | A hybrid extended finite element/level set method for modeling phase transformations. International Journal for Numerical Methods in Engineering, 54(8):1209-1233 | 2001 | Level Set Method, eXtended Finite Element Method, Materials Science |
| D. L. Chopp | Replacing iterative algorithms with single-pass algorithms. Proceedings of the National Academy of Sciences, 98(20):10992-10993 | 2001 | Level Set Method |
| D. L. Chopp | Some improvements of the fast marching method, SIAM Journal of Scientific Computing, 23(1):230-244 | 2001 | Level Set Method |
| M. Stolarska, D. L. Chopp, N. Möes, and T. Belytschko | Modelling crack growth by level sets in the extended finite element method, International Journal for Numerical Methods in Engineering, 51(8):943-960 | 2001 | Level Set Method, eXtended Finite Element Method, Fracture Mechanics |
| F. H. Baumann, D. L. Chopp, G. H. Gilmer, J. E. Greene, H. Huang, S. Kodambaka, P. O'Sullivan, and T. Diaz de la Rubia | Multi-scale modelling of thin film deposition: Applications to Si device processing, Materials Research Society Bulletin, 26(3), | 2001 | Materials Science |
| N. Sukumar, D. L. Chopp, N. Möes, and T. Belytschko | Modelling holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanics and Engineering, 190(46-47):6183-6200 | 2001 | Level Set Method, Fracture Mechanics |
| D. L. Chopp | A level-set method for simulating island coarsening. Journal of Computational Physics, 162:104-122 | 2000 | Level Set Method, Materials Science |
| D. L. Chopp and J. A. Sethian | Motion by intrinsic Laplacian of curvature. Interfaces and Free Boundaries, 1(1):107-123 | 1999 | Level Set Method, Differential Geometry |
| D. L. Chopp, L. C. Evans, and H. Ishii | Waiting time effects for Gauss curvature flows. Indiana University Math Journal, 48(1):311-334 | 1999 | Level Set Method, Differential Geometry |
| S. Angenent, T. Ilmanen, and D.L. Chopp | A computed example of nonuniqueness of mean curvature flow in R3. Communications on Partial Differential Equations, 20(11-12):1937-1958 | 1995 | Level Set Method, Differential Geometry |
| D. L. Chopp | Numerical computation of self-similar solutions for mean curvature flow. Journal of Experimental Mathematics, 3(1):1-15 | 1994 | Level Set Method, Differential Geometry |
| D. L. Chopp and J. A. Sethian | Flow under curvature: Singularity formation, minimal surfaces, and geodesics, Journal of Experimental Mathematics, 2(4):235-255 | 1993 | Level Set Method, Differential Geometry |
| D. L. Chopp | Computing minimal surfaces via level set curvature flow, Journal of Computational Physics, 106(1):77-91 | 1993 | Level Set Method, Differential Geometry |
