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All manuscripts and publications are available on my Ìýor my .

The listÌýbelow is no longer actively maintained.

Ìý

Preprints

1. J.M.WentzÌýand D. M.ÌýBortz. Analytical Singular Value Decomposition for a Class of Stoichiometry Matrices.Ìý(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.Ìý& Sim.Ìý(accepted).Ìý

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

4. D.A. Messenger and D.M. Bortz.ÌýWeak SINDy For Partial Differential Equations. J. Comp. Physics, 443:110525, October 15,Ìý2021. Ìý
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 Colorado in real-time. Emergning Infect. Dis.,Ìý27(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,ÌýJ.ÌýAdams, D. M.ÌýBortz, and E. J.ÌýCarlton. Infectious Disease Transmission Models to Predict, Evaluate and Improve Understanding of SARS-COV-2 Trajectory and Interventions.ÌýAnnals of the American Thoracic Society, 17(10):1204–1206, 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.ÌýA Posteriori Error Analysis of Fluid-Structure Interactions: Time Dependent Error. Computer Methods in Applied Mechanics and Engineering, 356(1 Nov.):1-15,Ìý2019. Ìý
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. Ìý
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.ÌýSIAM J. Appl. Dyn. Syst., 18(2):709-728, 2019. Ìý
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,ÌýDec. 2018Ìý
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. 2018Ìý
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,ÌýBulletin 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):1712–1736, 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.Ìý
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):933–952, Aug. 2017.
19. D.M. Bortz,ÌýCharacteristic roots for two-lag linear delay differential equations,ÌýDiscrete and Continuous Dynamical System - B, 21(8): 2409-2422, 2016.
20. I. Mirzaev, E.C. Byrne, & D.M. Bortz.ÌýAn Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations,ÌýInverse Problems, 32(9), 095005, September 2016.ÌýÌý
21. D.D. Keck & D.M. Bortz.ÌýGeneralized sensitivity functions for size-structured population models,ÌýJournal of Inverse and Ill-posed Problems, 24(3):309-321, June 2016.ÌýÌý
22. J.T. Nardini, D.A. Chapnick, X. Liu, D.M. Bortz.ÌýModeling Keratinocyte Wound Healing Dynamics: Cell-cell Adhesion Promotes Sustained Collective Migration,ÌýJournal of Theoretical Biology, 400(July):103-117, 2016.ÌýÌý
23. J.A. Stotsky, J.F. Hammond, L. Pavlovsky, E.J. Stewart, J.G. Younger, M.J. Solomon, D.M. Bortz.ÌýVariable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part II: Experimental Validation and the Heterogeneous Rheology-IBM,ÌýJournal of Computational Physics, 317(July):204-222, 2016Ìý.Ìý
24. D.M. Bortz.ÌýEigenvalues for a Two-lag linear delay differential equation, IFAC-PapersOnline, 48(12):13-16, 2015Ìý
25. I. Mirzaev & D.M. Bortz.ÌýLaplacian Dynamics with Synthesis and Degradation,ÌýBulletin of Mathematical Biology, 77(6):1013–1045, 2015ÌýÌý.
26. D.M. Bortz.ÌýChapter 17: Modeling and simulation for nanomaterials in fluids: Nanoparticle self-assembly. In V. Tewary & Y. Zhang, editors,Ìý, 419-441, Woodhead/Elsevier, 2015.
27. S. Sircar, E. Aisenbrey, S. Bryant & D.M. Bortz,ÌýDetermining average osmolarity in Poly(ethylene glycol)-Chondrotin sulfate gels mimicking cartillage.ÌýJournal of Theoretical Biology, 364(Jan):394-406, 2015.ÌýÌý
28. S. Sircar, J. G. Younger, & D.M. Bortz.ÌýSticky surface: sphere–sphere adhesion dynamics.ÌýJournal of Biological Dynamics, 9(sup1): 79-89, 2015ÌýÌý
29. S.M. Kissler, C. Cichowitz, S. Sankaranarayanan, & D.M. Bortz.ÌýDetermination of personalized diabetes treatment plans using a two-delay model.ÌýJournal of Theoretical Biology, 359(Oct), 101-111, 2014ÌýÌý
30. J. F. Hammond, E. J. Stewart, M. J. Solomon, J. G. Younger, & D.M. Bortz.ÌýVariable viscosity and density biofilm simulations using an Immersed Boundary Method, Part I: numerical scheme and convergence results.ÌýComputer Modeling in Engineering & Sciences, 98(3), 295-340, 2014ÌýÌýÌý(Invited paper as a part of aÌýspecial issue onÌýComputational Mechanobiology and Soft Matter Mechanics.)
31. G. Lambert, A. Bergman, Q. Zhang, D.M. Bortz, & R. Austin.ÌýPhysics of Biofilms: The Initial Stages of Biofilm Formation and Dynamics. New J. Physics, 16(4):045005, Apr. 2014.Ìý
32. S. Sircar & D.M. Bortz.ÌýImpact of flow on ligand-mediated bacterial flocculation. Mathematical Biosciences, 245(2):314-321, Oct. 2013.Ìý
33. A. Satorius, J. Szafranski, A. Rivera, D. Pynes, M. Ghanesan, M. J. Solomon, D. Newton, D.M. Bortz, & J. G. Younger,ÌýComplement C5a Generation by Staphylococcus epidermidis Biofilms. SHOCK, 39(4):336-342, Apr. 2013.Ìý
34. E. C. Conrad, Y.-Y. Hsu, D.M. Bortz, & J. G. Younger.ÌýSpatiotemporal Dynamics of Complement C5a Production within Bacterial Extracellular Polymeric Substance. Journal of Innate Immunity, 5(2):114-123, Jan. 2013. (cover art!).Ìý
35. C. W. Curtis & D.M. Bortz,ÌýPropagation of fronts in the Fisher-Kolmogorov equation with quadratically varying diffusion. Phys. Rev. E, 86(6):066108, Dec. 2012.ÌýÌý
36. M. Thornton, C. Irvin, H. M. Chung, D.M. Bortz, M. J. Solomon, & J. G. Younger,ÌýMulticellularity and Antibiotic Resistance in Klebsiella pneumoniae Grown under Bloodstream-Mimicking Fluid Dynamic Conditions. Journal of Infectious Diseases, 206(4):588-595, Aug. 2012.Ìý
37. J. F. Hammond & D.M. Bortz,ÌýAnalytical solutions to Fisher’s equation with time-variable coefficients. Applied Mathematics and Computation, 218(6):2497-2508, 2011.Ìý
38. E. C. Byrne, S. Dzul, M. J. Solomon, J. G. Younger, & D.M. Bortz,ÌýPostfragmentation density function for bacterial aggregates in laminar flow. Phys. Rev. E, 83(4):41911, 2011.Ìý
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):1777–1782, Mar. 2011.Ìý
40. C. M. Nypaver, M. M. Thornton, S. M. Yin, D. O. Bracho, P. W. Nelson, A. E. Jones, D.M. Bortz, & J. G. Younger,ÌýDynamics of Human Complement―Mediated Killing of Klebsiella pneumoniae, American journal of respiratory cell and molecular biology, 43(5):585-590, 2010.Ìý
41. H. Chung, M. M. Cartwright, D.M. Bortz, T. L. Jackson, & J. G. Younger,ÌýDynamical System Analysis of Staphylococcus epidermidis Bloodstream Infection, SHOCK, 30(5):518-526, November 2008.ÌýÌý(cover art!)
42. D.M. Bortz, T. L. Jackson, K. A. Taylor, A. P. Thompson, & J. G. Younger,ÌýKlebsiella pneumoniae flocculation dynamics, Bulletin of Mathematical Biology, 70(3):745-768, April 2008.Ìý
43. D.M. Bortz & P. W. Nelson,ÌýModel selection and mixed-effects modeling of HIV infection dynamics, Bulletin of Mathematical Biology, 68(8):2005-2025, November 2006.Ìý
44. S. Ciupe, B. L. Bivort, D.M. Bortz, & P. W. Nelson,ÌýEstimating 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,ÌýDynamics of intrapulmonary bacterial growth in a murine model of repeated microaspirations, Am. J. Respiratory Cell & Molecular Biology, 33(5):476-482, November 2005.Ìý
46. H. T. Banks & D.M. Bortz,ÌýA parameter sensitivity methodology in the context of HIV delay equation models, Journal of Mathematical Biology, 50(6):607-625, June 2005.Ìý
47. H. T. Banks & D.M. Bortz,ÌýInverse Problems for a Class of Measure Dependent Dynamical Systems, Journal of Inverse and Ill-posed Problems, 13(2):103-121, April 2005.Ìý
48. D.M. Bortz & P. W. Nelson,ÌýSensitivity analysis of nonlinear lumped parameter models of HIV infection dynamics,ÌýBulletin of Mathematical Biology, 66(5):1009-1026, September 2004.Ìý
49. H. T. Banks, D.M. Bortz, G. A. Pinter, & L. K. Potter,ÌýChapter 6: Modeling and imaging techniques with potential for applications in bioterrorism. In H. T. Banks and C. Castillo-Chavez, editors,Ìý, volume 28 of Frontiers in Applied Mathematics, pages 129-154, SIAM, Phildelphia, PA, 2003.
50. H. T. Banks, D.M. Bortz, & S. E. Holte,ÌýIncorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics, Mathematical Biosciences, 183(1):63-91, May 2003.Ìý
51. D.M. Bortz, A. D. Rubio, H. T. Banks, A. B. Cain, & R. C. Smith,ÌýControl of open bay acoustics by harmonic mass injection, International Journal of Aeroacoustics, 1(1):65-81, March 2002.Ìý
52. A. B. Cain, A. D. Rubio, D.M. Bortz, H. T. Banks, & R. C. Smith,ÌýReduced Order Modeling in Control of Open Cavity Acoustics, Proceedings of the AIAA, AIAA-2000-1928, June 2000.
53. D.M. Bortz & C. T. Kelley,ÌýThe simplex gradient and noisy optimization problems. In J. T. Borggaard, J. Burns, E. Cliff, and S. Schreck, editors,Ìý, 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,ÌýStudies of Hadron-Electron Separators for the ZEUS Barrel Calorimeter, Nuclear Instruments and Methods in Physics Research Section A, 368(2):364-377, 1996.Ìý

Other Publications

1. T. Kusher, D.M. Bortz, D. Maahs, S. Sankaranarayanan,ÌýA data-driven approach to artificial pancreas verification and synthesis,ÌýICCPS '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.ÌýCriteria for linearized stability for a size-structured population model.Ìý
5. E. C. Conrad, A. E. Satorius, P. Sharma, D.M. Bortz, & J. G. Younger.ÌýThe 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.ÌýBloodstream-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.ÌýScandalously Parallelizable Mesh Generation.Ìý
8. M. M. Thornton, D. N. Hohne, M. J. Solomon, D.M. Bortz, & J. G. Younger.ÌýBacterial aggregation during growth under low shear: implications for bacteremia. SHOCK, 31(7):22, 2009.
9. D.M. Bortz & A. J. Christlieb.ÌýRandom numerical discretizations. In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 29–30, 2008.
10. D. Li, D. Hohne, D.M. Bortz, J. Bull, & J. G. YoungerÌýModeling 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,ÌýNeutropenic S-epidermidis bacteremia modeled as a pharmacodynamic system,ÌýSHOCK, 27(Supplement 1):68-69, June 2007.
12. D.M. Bortz.ÌýAccurate 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,ÌýMultiple-compartment bacterial clearance kinetics during murine bacteremia,ÌýJournal of Critical Care, 21(4):359-360, December 2006.
14. D.M. Bortz, T. L. Jackson, & J. G. Younger,ÌýEstimation and identification of Klebsiella pneumoniae flocculation dynamics, In Abstracts of the International ConferenceÌýInverse Problems: Modeling and Simulation, pages 15-17, 2006.
15. J. G. Younger, K. Taylor, A. Thompson, & D.M. Bortz.ÌýQuantification and modeling of aggregate bacterial growth in suspension: Implications for bacteremia. SHOCK, pages 79–80, June 2006.
16. I. Ben-David, S. E. Price, S. Cohen, D.M. Bortz, T. L. Jackson, & J. G. Younger,ÌýComplement C3 is necessary for early suppression of intrapulmonary bacterial growth,ÌýSHOCK, 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,ÌýVirulence of Klebsiella pneumoniae predicted by nonlinear biodistributive mathematical model,ÌýSHOCK, 21(Supplement 2):29,2004.
18. D.M. Bortz,ÌýModeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations,Ìý, North Carolina State University, Raleigh, NC, 2002.
19. D.M. Bortz, R. Guy, J. Hood, K. Kirkpatrick, V. Nguyen, & V. Shimanovich,ÌýModeling 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 ReportÌý, 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,ÌýOptimizing control of open bay acoustics, Tech. ReportÌý, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May 2000.
21. A. S. Bondarenko, D.M. Bortz, & J. J. Moré,ÌýCOPS: Large-scale nonlinearly constrained optimization problems, Tech. ReportÌýANL/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,ÌýPower 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.