Publications

  1. R. Kublik and D. L. Chopp. A Locally Adaptive Time-Stepping Algorithm for the Solution to Reaction-Diffusion Equations on Branched Structures, in revision, 2013.

  2. 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.

  3. B. V. Merkey and D. L. Chopp. The Performance of a Microbial Fuel Cell Depends Strongly on Anode Geometry: A Multidimensional Modeling Study, Bull. Math. Biology, 74:834-857, 2012.

  4. 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 J. of Plastic Surgery, 19(2):45-50, 2011.

  5. 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, J. Computational Physics, 230(4):1249-1264, 2010.

  6. 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, Engg. Fract. Mech., 77(14):2840-2863, 2010.

  7. B. L. Vaughan, B. G. Smith, D.L. Chopp. The Influence of Fluid Flow on Modeling Quorum Sensing in Bacterial Biofilms, Bull. Math. Biology, 72(5):1143-1165, 2010.

  8. D. L. Chopp. Another look at velocity extensions in the level set method. SIAM J. Sci. Comp., 31(5):3255-3273, 2009. (journal)

  9. B. Merkey, B. E. Rittmann, and D.L. Chopp. Modeling How Soluble Microbial Products (SMP) Support Heterotrophs in Autotroph-Based Biofilms, J. Theoretical Biology, 259:670-683, 2009.

  10. 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. (journal)

  11. 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, Int. J. Num. Meth. Eng., 76(5):727-748, 2008. (journal)

  12. M. J. Rempe, N. Spruston, W. L. Kath, and D. L. Chopp. Compartmental neural simulations with spatial adaptivity. J. Comp. Neuroscience, 25(3):465-480, 2008. (journal)

  13. R. Duddu, S. Bordas, D. L. Chopp, and B. Moran. A combined extended finite element and level set method for biofilm growth. Int. J. Num. Meth. Eng., 74(5):848-870, 2008. (journal)

  14. B. G. Smith, B. L. Vaughan, and D. L. Chopp. The extended finite element method for boundary layer problems in biofilm growth, CAMCoS, 2(1):35-56, 2007. (journal)

  15. 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, J. Bacteriology, 189(22):8357-8360, 2007. (journal)

  16. 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. CAMCoS, 1(1):207-228, 2006. (journal)

  17. 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. (journal)

  18. A. Tongen and D. L. Chopp. Simulation of multigrain thin film growth. Interfaces and Free Boundaries, 8:1-19, 2006. (journal)

  19. M. J. Rempe and D. L. Chopp. A predictor-corrector algorithm for reaction-diffusion equations associated with neural activity on branched structures. SIAM J Scientific Computing, 28(6):2139-2161, 2006. (journal)

  20. 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. (journal)

  21. 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. (journal)

  22. M. Stolarska and D. L. Chopp. Modeling spiral cracking due to thermal cycling in integrated circuits. Int. J. Num. Meth. Eng., 41(20):2381-2410, 2003. (journal)

  23. D. L. Chopp, M. J. Kirisits, M. R. Parsek, and B. Moran. The dependence of quorum sensing on the depth of a growing biofilm. Bull. Math. Biol., 65(6):1053-1079, 2003. (journal)

  24. D. L. Chopp and J. A. Velling. Foliations of hyperbolic space by constant mean curvature surfaces sharing ideal boundary. Exp. Math., 12(3):339-350, 2003. (journal)

  25. D. L. Chopp and N. Sukumar. Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. Int. J. Eng. Sci., 41(8):845-869, 2003. (journal)

  26. 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. (journal)
    Named one of the most highly cited papers of 2002-2005.

  27. 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. (journal)

  28. 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. (journal)

  29. 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. (journal)

  30. D. L. Chopp. Replacing iterative algorithms with single-pass algorithms. Proceedings of the National Academy of Sciences, 98(20):10992-10993, 2001. (journal)

  31. D. L. Chopp. Some improvements of the fast marching method, SIAM Journal of Scientific Computing, 23(1):230-244, 2001. (journal)

  32. 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. (journal)

  33. 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), March, 2001. (journal)

  34. 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. (journal)

  35. D. L. Chopp. A level-set method for simulating island coarsening. Journal of Computational Physics, 162:104-122, 2000. (journal)

  36. D. L. Chopp and J. A. Sethian, Motion by intrinsic Laplacian of curvature. Interfaces and Free Boundaries, 1(1):107-123, 1999. (journal)

  37. D. L. Chopp, L. C. Evans, and H. Ishii, Waiting time effects for Gauss curvature flows. Indiana U. Math Journal, 48(1):311-334, 1999. (journal)

  38. 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.

  39. D. L. Chopp, Numerical computation of self-similar solutions for mean curvature flow. Journal of Experimental Mathematics, 3(1):1-15, 1994. (journal)

  40. 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. (journal)

  41. D. L. Chopp, Computing minimal surfaces via level set curvature flow, Journal of Computational Physics, 106(1):77-91, May 1993. (journal)

Conference Proceedings

  1. M. Stolarska, D. L. Chopp, N. Moës, and T. Belytschko. Modelling crack growth by level sets. In the 14th European Conference on Fracture, 2002.

  2. J. E. Dolbow, H. Ji, and D. L. Chopp. Advances in the hybrid finite element / level set method for phase transformations. In the 5th World Congress on Computational Mechanics, 2002.

  3. J. A. Sethian and D. L. Chopp, "Physics and geometry of flow under curvature: Singularity formation, minimal surfaces, geodesics, and surface tension." In DeGruyter Trento Conference on Mean Curvature Flow, July 1994. (pdf)

  4. J. A. Sethian and D. L. Chopp, "Flow under mean curvature: Singularity formation and minimal surfaces." In Computational Crystal Growers Workshop, February, 1992. (pdf)

Book Chapters

  1. D. L. Chopp. Deformable Models: Biomedical and Clinical Applications, chapter Simulating Bacterial Biofilms. Springer, 2007.

  2. D. L. Chopp. Handbook of Biomedical Image Analysis, volume 1, chapter Recent Advances in the Level Set Method. Kluwer Academic, 2005.

  3. D. L. Chopp. State of the Art PDE and Level Sets Algorithms, Approaches to Static and Motion Imagery Segmentation, chapter Level Set Extensions, Flow and Crack Propagation. Kluwer Academic, 2002.

  4. J. S. Suri, D. L. Chopp, and S. Laxminarayan. State of the Art PDE and Level Sets Algorithms, Approaches to Static and Motion Imagery Segmentation, chapter The Future of PDEs and Level Sets. Kluwer Academic, 2002.

Technical Reports

  1. D. L. Chopp. Numerical computation of self-similar solutions for mean curvature flow. Technical Report LBL-34559, Lawrence Berkeley Laboratory, 1993.

  2. D. L. Chopp. Numerical computation os self-similar solutions for mean curvature flow. Technical Report CAM 93-17, UCLA, 1993.

  3. D. L. Chopp. Flow under geodesic curvature. Technical Report CAM 92-23, UCLA, 1992

  4. D. L. Chopp and J. A. Sethian. Flow under mean curvature: Singularity formation and minimal surfaces. Technical report CPAM-541, Center for Pure and Applied Mathematics, Univ. of Calif., Berkeley, 1991

  5. D. L. Chopp. Computing minimal surfaces via level set curvature flow. Technical Report LBL-30685, Lawrence Berkeley Laboratory, 1991.