All manuscripts and publications are available on my 听or my .

The list听below is no longer actively maintained.

听

Preprints

  1. J.M.Wentz听and D. M.听Bortz. Analytical Singular Value Decomposition for a Class of Stoichiometry Matrices.听(submitted)

Refereed Articles & Book Chapters

  1. G. E. Wheeler, A. Purkayastha, E. N. Bunker, D. M. Bortz, and X. Liu. Protocol for measurement and analysis of cell motility of HaCaT keratinocytes on both single-cell and population-wide levels. J. Vis. Exp., (accepted), 2021.
  2. D.A. Messenger and D.M. Bortz. Weak SINDy: Galerkin-Based Data-Driven Model Selection. SIAM Multiscale Mod.听& Sim.听(accepted).听

  3. J.M. Wentz and D.M. Bortz. Boundedness of a class of discretized reaction-diffusion systems. SIAM J. Appl. Math. (accepted).听

  4. D.A. Messenger and D.M. Bortz.听Weak SINDy For Partial Differential Equations. J. Comp. Physics, 443:110525, October 15,听2021. 听
  5. A. G. Buchwald, J. Bayham, j. adams, D. M. Bortz, K. Colborn, O. Zarella, M. Buran, J. Samet, D. Ghosh, R. Herlihy, and E. J. Carlton. Estimating the impact of state-wide policies to reduce the spread of SARS-CoV-2 in 蜜糖直播 in real-time. Emergning Infect. Dis.,听27(9), June 2021.
  6. H.J. Dudley, Z.J. Ren, and D.M. Bortz. Competitive Exclusion in a DAE Model for Microbial Electrolysis Cells. Math. Biosci. Eng. 17(5):6217-6239, 2020.
  7. A. G. Buchwald,听J.听Adams, D. M.听Bortz, and E. J.听Carlton. Infectious Disease Transmission Models to Predict, Evaluate and Improve Understanding of SARS-COV-2 Trajectory and Interventions.听Annals of the American Thoracic Society, 17(10):1204鈥�1206, Oct. 2020.
  8. N. C. Hill, J. W. Tay, S. L. Altus, D. M. Bortz, and J. C. Cameron. Life cycle of a cyanobacterial carboxysome. Science Advances 6(19):eaba1269, 2020.
  9. K. A. Moore, S. L. Altus, J. W. Tay, J. Fox, E. B. Johnson, D. M. Bortz, and J. C. Cameron. Mechanical Regulation of Photosynthesis. Nature Microbiology 5(23 Mar):757-767, 2020.
  10. J. A. Stotsky and D. M. Bortz.听A Posteriori Error Analysis of Fluid-Structure Interactions: Time Dependent Error. Computer Methods in Applied Mechanics and Engineering, 356(1 Nov.):1-15,听2019. 听
  11. J. T. Nardini and D. M. Bortz. The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models. Inverse Problems, 35(6):065003, 2019. 听
  12. H. J. Dudley, L. Lu, Z. J. Ren, and D. M. Bortz. Sensitivity and Bifurcation Analysis of a Differential-Algebraic Equation Model for a Microbial Electrolysis Cell.听SIAM J. Appl. Dyn. Syst., 18(2):709-728, 2019. 听
  13. J.A. Stotsky, V. Dukic, & D.M. Bortz. A Point Process Model for Generating Biofilms with Realistic Microstructure and Rheology, Eur. J. Appl. Math., 29(6):1141-1177,听Dec. 2018听
  14. E.P. Kightley, A. Pearson, J.A. Evans, & D.M. Bortz. Fragmentation of biofilm-seeded bacterial aggregates in shear flow, Eur. J. Appl. Math., 29(6):1062-1078, Dec. 2018听
  15. J.M. Wentz, A.R. Mendenhall, & D.M. Bortz. Pattern Formation in the Longevity-Related Expression of Heat Shock Protein-16.2 in Caenorhabditis elegans,听Bulletin of Mathematical Biology, 80(10):2669-2697, 2018.
  16. J.T. Nardini & D.M. Bortz. Investigation of a Structured Fisher's Equation with Applications in Biochemistry, SIAM J. Appl. Math., 78(3):1712鈥�1736, 2018
  17. V. Dukic & D.M. Bortz, Uncertainty Quantification Using Probabilistic Numerics: Application to Models in Mathematical Epidemiology, Inverse Problems in Science and Engineering, 28(2):223-232, 2018.听
  18. I. Mirzaev and D.M. Bortz. A numerical framework for computing steady states of structured population models and their stability. Math. Biosci. Eng., 14(4):933鈥�952, Aug. 2017.
  19. 锘緿.M. Bortz,听Characteristic roots for two-lag linear delay differential equations,听Discrete and Continuous Dynamical System - B, 21(8): 2409-2422, 2016.
  20. I. Mirzaev, E.C. Byrne, & D.M. Bortz.听An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations,听Inverse Problems, 32(9), 095005, September 2016.听听
  21. D.D. Keck & D.M. Bortz.听Generalized sensitivity functions for size-structured population models,听Journal of Inverse and Ill-posed Problems, 24(3):309-321, June 2016.听听
  22. J.T. Nardini, D.A. Chapnick, X. Liu, D.M. Bortz.听Modeling Keratinocyte Wound Healing Dynamics: Cell-cell Adhesion Promotes Sustained Collective Migration,听Journal of Theoretical Biology, 400(July):103-117, 2016.听听
  23. J.A. Stotsky, J.F. Hammond, L. Pavlovsky, E.J. Stewart, J.G. Younger, M.J. Solomon, D.M. Bortz.听Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part II: Experimental Validation and the Heterogeneous Rheology-IBM,听Journal of Computational Physics, 317(July):204-222, 2016听.听
  24. D.M. Bortz.听Eigenvalues for a Two-lag linear delay differential equation, IFAC-PapersOnline, 48(12):13-16, 2015听
  25. I. Mirzaev & D.M. Bortz.听Laplacian Dynamics with Synthesis and Degradation,听Bulletin of Mathematical Biology, 77(6):1013鈥�1045, 2015听听.
  26. D.M. Bortz.听Chapter 17: Modeling and simulation for nanomaterials in fluids: Nanoparticle self-assembly. In V. Tewary & Y. Zhang, editors,听, 419-441, Woodhead/Elsevier, 2015.
  27. S. Sircar, E. Aisenbrey, S. Bryant & D.M. Bortz,听Determining average osmolarity in Poly(ethylene glycol)-Chondrotin sulfate gels mimicking cartillage.听Journal of Theoretical Biology, 364(Jan):394-406, 2015.听听
  28. S. Sircar, J. G. Younger, & D.M. Bortz.听Sticky surface: sphere鈥搒phere adhesion dynamics.听Journal of Biological Dynamics, 9(sup1): 79-89, 2015听听
  29. S.M. Kissler, C. Cichowitz, S. Sankaranarayanan, & D.M. Bortz.听Determination of personalized diabetes treatment plans using a two-delay model.听Journal of Theoretical Biology, 359(Oct), 101-111, 2014听听
  30. J. F. Hammond, E. J. Stewart, M. J. Solomon, J. G. Younger, & D.M. Bortz.听Variable viscosity and density biofilm simulations using an Immersed Boundary Method, Part I: numerical scheme and convergence results.听Computer Modeling in Engineering & Sciences, 98(3), 295-340, 2014听听听(Invited paper as a part of a听special issue on听Computational Mechanobiology and Soft Matter Mechanics.)
  31. G. Lambert, A. Bergman, Q. Zhang, D.M. Bortz, & R. Austin.听Physics of Biofilms: The Initial Stages of Biofilm Formation and Dynamics. New J. Physics, 16(4):045005, Apr. 2014.听
  32. S. Sircar & D.M. Bortz.听Impact of flow on ligand-mediated bacterial flocculation. Mathematical Biosciences, 245(2):314-321, Oct. 2013.听
  33. A. Satorius, J. Szafranski, A. Rivera, D. Pynes, M. Ghanesan, M. J. Solomon, D. Newton, D.M. Bortz, & J. G. Younger,听Complement C5a Generation by Staphylococcus epidermidis Biofilms. SHOCK, 39(4):336-342, Apr. 2013.听
  34. E. C. Conrad, Y.-Y. Hsu, D.M. Bortz, & J. G. Younger.听Spatiotemporal Dynamics of Complement C5a Production within Bacterial Extracellular Polymeric Substance. Journal of Innate Immunity, 5(2):114-123, Jan. 2013. (cover art!).听
  35. C. W. Curtis & D.M. Bortz,听Propagation of fronts in the Fisher-Kolmogorov equation with quadratically varying diffusion. Phys. Rev. E, 86(6):066108, Dec. 2012.听听
  36. 锘縈. Thornton, C. Irvin, H. M. Chung, D.M. Bortz, M. J. Solomon, & J. G. Younger,听Multicellularity and Antibiotic Resistance in Klebsiella pneumoniae Grown under Bloodstream-Mimicking Fluid Dynamic Conditions. Journal of Infectious Diseases, 206(4):588-595, Aug. 2012.听
  37. J. F. Hammond & D.M. Bortz,听Analytical solutions to Fisher鈥檚 equation with time-variable coefficients. Applied Mathematics and Computation, 218(6):2497-2508, 2011.听
  38. E. 锘緾. Byrne, S. Dzul, M. J. Solomon, J. G. Younger, & D.M. Bortz,听Postfragmentation density function for bacterial aggregates in laminar flow. Phys. Rev. E, 83(4):41911, 2011.听
  39. S. P. Dzul, M. M. Thornton, D. N. Hohne, E. J. Stewart, A. A. Shah, D.M. Bortz, M. J. Solomon, and J. G. Younger.Contribution of the Klebsiella pneumoniae Capsule to Bacterial Aggregate and Biofilm Microstructures. Applied Environmental Microbiology, 77(5):1777鈥�1782, Mar. 2011.听
  40. 锘緾. M. Nypaver, M. M. Thornton, S. M. Yin, D. O. Bracho, P. W. Nelson, A. E. Jones, D.M. Bortz, & J. G. Younger,听Dynamics of Human Complement鈥昅ediated Killing of Klebsiella pneumoniae, American journal of respiratory cell and molecular biology, 43(5):585-590, 2010.听
  41. H. Chung, M. M. Cartwright, D.M. Bortz, T. L. Jackson, & J. G. Younger,听Dynamical System Analysis of Staphylococcus epidermidis Bloodstream Infection, SHOCK, 30(5):518-526, November 2008.听听(cover art!)
  42. D.M. Bortz, T. L. Jackson, K. A. Taylor, A. P. Thompson, & J. G. Younger,听Klebsiella pneumoniae flocculation dynamics, Bulletin of Mathematical Biology, 70(3):745-768, April 2008.听
  43. D.M. Bortz & P. W. Nelson,听Model selection and mixed-effects modeling of HIV infection dynamics, Bulletin of Mathematical Biology, 68(8):2005-2025, November 2006.听
  44. S. Ciupe, B. L. Bivort, D.M. Bortz, & P. W. Nelson,听Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Mathematical Biosciences, 200(1):1-27, March 2006.
  45. I. Ben-David, S. E. Price, D.M. Bortz, S. Cohen, A. L. Bauer, T. L. Jackson, & J. G. Younger,听Dynamics of intrapulmonary bacterial growth in a murine model of repeated microaspirations, Am. J. Respiratory Cell & Molecular Biology, 33(5):476-482, November 2005.听
  46. H. T. Banks & D.M. Bortz,听A parameter sensitivity methodology in the context of HIV delay equation models, Journal of Mathematical Biology, 50(6):607-625, June 2005.听
  47. H. T. Banks & D.M. Bortz,听Inverse Problems for a Class of Measure Dependent Dynamical Systems, Journal of Inverse and Ill-posed Problems, 13(2):103-121, April 2005.听
  48. D.M. Bortz & P. W. Nelson,听Sensitivity analysis of nonlinear lumped parameter models of HIV infection dynamics,听Bulletin of Mathematical Biology, 66(5):1009-1026, September 2004.听
  49. H. T. Banks, D.M. Bortz, G. A. Pinter, & L. K. Potter,听Chapter 6: Modeling and imaging techniques with potential for applications in bioterrorism. In H. T. Banks and C. Castillo-Chavez, editors,听, volume 28 of Frontiers in Applied Mathematics, pages 129-154, SIAM, Phildelphia, PA, 2003.
  50. H. T. Banks, D.M. Bortz, & S. E. Holte,听Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics, Mathematical Biosciences, 183(1):63-91, May 2003.听
  51. D.M. Bortz, A. D. Rubio, H. T. Banks, A. B. Cain, & R. C. Smith,听Control of open bay acoustics by harmonic mass injection, International Journal of Aeroacoustics, 1(1):65-81, March 2002.听
  52. A. B. Cain, A. D. Rubio, D.M. Bortz, H. T. Banks, & R. C. Smith,听Reduced Order Modeling in Control of Open Cavity Acoustics, Proceedings of the AIAA, AIAA-2000-1928, June 2000.
  53. D.M. Bortz & C. T. Kelley,听The simplex gradient and noisy optimization problems. In J. T. Borggaard, J. Burns, E. Cliff, and S. Schreck, editors,听, volume 24 of Progress in Systems and Control Theory, Birkhauser, 1998, pp. 77-90.
  54. I. Ambats, D.M. Bortz, A. Connolly, A. Derlicki, M. Derrick, W. Kahle, & J. Thron,听Studies of Hadron-Electron Separators for the ZEUS Barrel Calorimeter, Nuclear Instruments and Methods in Physics Research Section A, 368(2):364-377, 1996.听

Other Publications

  1. T. Kusher, D.M. Bortz, D. Maahs, S. Sankaranarayanan,听A data-driven approach to artificial pancreas verification and synthesis,听ICCPS '18 Proceedings of the 9th ACM/IEEE International Conference on Cyber-Physical Systems Pages 242-252, 2018.
  2. S. H. Friedman, A. R. A. Anderson, D. M. Bortz, A. G. Fletcher, H. B. Frieboes, A. Ghaffarizadeh, D. R. Grimes, A. Hawkins-Daarud, S. Hoehme, E. F. Juarez, C. Kesselman, R. Merks, S. M. Mumenthaler, P. K. Newton, K.-A. Norton, R. Rawat, R. C. Rockne, D. Ruderman, J. Scott, S. S. Sindi, J. L. Sparks, K. Swanson, D. B. Agus, and P. Macklin. MultiCellDS: A community-developed standard for curating microenvironment-dependent multicellular data. , Nov. 2016.
  3. S. H. Friedman, A. R. A. Anderson, D. M. Bortz, A. G. Fletcher, H. B. Frieboes, A. Ghaffarizadeh, D. R. Grimes, A. Hawkins-Daarud, S. Hoehme, E. F. Juarez, C. Kesselman, R. M. H. Merks, S. M. Mumenthaler, P. K. Newton, K.-A. Norton, R. Rawat, R. C. Rockne, D. Ruderman, J. Scott, S. S. Sindi, J. L. Sparks, K. Swanson, D. B. Agus, and P. Macklin. MultiCellDS: A standard and a community for sharing multicellular data. , Sept. 2016.
  4. I. Mirzaev & D.M. Bortz.听Criteria for linearized stability for a size-structured population model.听
  5. E. C. Conrad, A. E. Satorius, P. Sharma, D.M. Bortz, & J. G. Younger.听The Host Response to Line Sepsis: Experimental and Computational Analysis of Complement Activation against Coagulase-Negative Staphylococcal Biofilms. Annals of Emergency Medicine, 62(4):S153, 2013.
  6. J. G. Younger, M. M. Thornton, C. Babcock, H. M. Chung-Esaki, D.M. Bortz, & M. J. Solomon.听Bloodstream-like fluid dynamic conditions promote multicellularity and antibiotic resistance in in Klebsiella pneumoniae. SHOCK, 37(1):58, 2012.
  7. D.M. Bortz & A. J. Christlieb.听Scandalously Parallelizable Mesh Generation.听
  8. M. M. Thornton, D. N. Hohne, M. J. Solomon, D.M. Bortz, & J. G. Younger.听Bacterial aggregation during growth under low shear: implications for bacteremia. SHOCK, 31(7):22, 2009.
  9. D.M. Bortz & A. J. Christlieb.听Random numerical discretizations. In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 29鈥�30, 2008.
  10. D. Li, D. Hohne, D.M. Bortz, J. Bull, & J. G. Younger听Modeling bacterial clearance from the bloodstream using computational fluid dynamics and monte carlo simulation. J. Critical Care, 22(4):344, Dec. 2007.
  11. J. G. Younger, H. Y. Chung, M. Cartwright, D.M. Bortz, & T. L. Jackson,听Neutropenic S-epidermidis bacteremia modeled as a pharmacodynamic system,听SHOCK, 27(Supplement 1):68-69, June 2007.
  12. D.M. Bortz.听Accurate model selection computations. J. Critical Care, 21(4):359, Dec. 2006.
  13. H. Chung, T. L. Jackson, D.M. Bortz, M. Cartwright, & J. G. Younger,听Multiple-compartment bacterial clearance kinetics during murine bacteremia,听Journal of Critical Care, 21(4):359-360, December 2006.
  14. D.M. Bortz, T. L. Jackson, & J. G. Younger,听Estimation and identification of Klebsiella pneumoniae flocculation dynamics, In Abstracts of the International Conference听Inverse Problems: Modeling and Simulation, pages 15-17, 2006.
  15. J. G. Younger, K. Taylor, A. Thompson, & D.M. Bortz.听Quantification and modeling of aggregate bacterial growth in suspension: Implications for bacteremia. SHOCK, pages 79鈥�80, June 2006.
  16. I. Ben-David, S. E. Price, S. Cohen, D.M. Bortz, T. L. Jackson, & J. G. Younger,听Complement C3 is necessary for early suppression of intrapulmonary bacterial growth,听SHOCK, 23(Supplement 3):79-80, June 2005.
  17. A. L. Bauer, D.M. Bortz, D. Gammack, I. Ben-David, A. Stein, T. L. Jackson, & J. G. Younger,听Virulence of Klebsiella pneumoniae predicted by nonlinear biodistributive mathematical model,听SHOCK, 21(Supplement 2):29,2004.
  18. D.M. Bortz,听Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations,听, North Carolina State University, Raleigh, NC, 2002.
  19. D.M. Bortz, R. Guy, J. Hood, K. Kirkpatrick, V. Nguyen, & V. Shimanovich,听Modeling HIV infection dynamics using delay equations, In P. A. Gremaud, Z. Li, R. C. Smith, and H. T. Tran, editors, Proceedings of the 2000 Industrial Mathematics Modeling Workshop for Graduate Students, pages 48-58. Technical Report听, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October 2000.
  20. A. B. Cain, A. D. Rubio, D.M. Bortz, H. T. Banks, & R. C. Smith,听Optimizing control of open bay acoustics, Tech. Report听, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May 2000.
  21. A. S. Bondarenko, D.M. Bortz, & J. J. Mor茅,听COPS: Large-scale nonlinearly constrained optimization problems, Tech. Report听ANL/MCS-TM-237, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, September 1998, revised October 1999.
  22. P. Barnes, D.M. Bortz, S. Frank, I. Loladze, E. Packard, & M. Santhanam,听Power transformer clearance checking, In F. Reitich, J. S. Scroggs, and H. T. Tran, editors, Proceedings of the 1997 Industrial Mathematics Modeling Workshop for Graduate Students. Technical Report CRSC-TR98-09, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, February, 1998.