D M Bortz
Associate Professor in Applied Mathematics
BioFrontiers Task Force Member
IQBio Graduate Faculty
Research Statement pdf
Teaching Statement pdf
Service Statement pdf
Google Scholar ORCID
- Note that I check my email once a day, typically in the early morning. For time-sensitive issues, please call the main Applied Math office at (303) 492-4668 and they will contact me.
- Email: dmbortz at colorado dot edu
- Campus Office: ECOT 234
- Postal Address:
University of Colorado, Box 526
Boulder, CO 80309-0526
Articles & Book Chapters
- D. D. Keck and D. M. Bortz. Generalized sensitivity functions for size-structured population models". (submitted) arXiv:1406.0212
- I. Mirzaev and D. M. Bortz. Analytical Equilibrium Solutions of Biochemical Systems with Synthesis and Degradation. (submitted) arXiv:1404.6477
- D. D. Keck and D. M. Bortz. Numerical simulation of solutions and moments of the Smoluchowski coagulation equation. (in revision) arXiv:1312.7240
- S. Sircar, E. Eisenbury, S. Bryant and D. M. Bortz, Determining average osmolarity in Poly(ethylene glycol)-Chondrotin sulfate gels mimicking cartillage. (in revision) arXiv:1308.4421
- D. M. Bortz and E. C. Byrne. Identification of the Post-Fragmentation Probability Measure in Flocculation Models. (in revision) preprint
- D. M. Bortz and C. W. Curtis. On Modeling Invasion with the Fisher-Kolmogorov Equation: Inverse and Forward Approaches. (in revision)
- D. M. Bortz, Eigenvalues for two-lag linear delay differential equations. (in revision) arXiv:1206.6364
- D. M. Bortz and A. J. Christlieb. Scandalously Parallelizable Mesh Generation. (in revision) arXiv:1103.5268
- S. Sircar, J. G. Younger, and D. M. Bortz. Sticky Surface: Adhesion Based Microbial Aggregation Dynamics. Journal of Biological Dynamics 2014 doi arXiv:1301.2504
- D.M. Bortz. Modeling and simulation for nanomaterials in fluids: Nanoparticle self-assembly. In V. Tewary and Y. Zhang, editors, Modeling, characterization, and production of nanomaterials (Electronics, Photonics and Energy applications). Woodhead/Elsevier, 2014.
- S.M. Kissler, C. Cichowitz, S. Sankaranarayanan, and D.M. Bortz. Determination of personalized diabetes treatment plans using a two-delay model. Journal of Theoretical Biology, 359(Oct), 101-111, 2014 doi arXiv:1403.0638
- J. F. Hammond, E. J. Stewart, M. J. Solomon, J. G. Younger, and D. M. Bortz. Variable viscosity and density biofilm simulations using and Immersed Boundary Method, Part I: numerical scheme and convergence results. Computer Modeling in Engineering & Sciences, 98(3), 295-340, 2014 doi arXiv:1302.3663 (Invited paper as a part of a special issue on Computational Mechanobiology and Soft Matter Mechanics.)
- G. Lambert, A. Bergman, Q. Zhang, D. M. Bortz, and R. Austin. Physics of Biofilms: The Initial Stages of Biofilm Formation and Dynamics. New J. Physics, 16(4), 045005, Apr. 2014. doi
- S. Sircar and D. M. Bortz. Impact of flow on ligand-mediated bacterial flocculation. Mathematical Biosciences, 245(2), 314-321, Oct. 2013. doi
- A. Satorius, J. Szafranski, A. Rivera, D. Pynes, M. Ghanesan, M. J. Solomon, D. Newton, D. M. Bortz, and J. G. Younger, Complement C5a Generation by Staphylococcus epidermidis Biofilms. SHOCK, 39(4), 336-342, Apr. 2013. doi
- E. C. Conrad, Y.-Y. Hsu, D. M. Bortz, J. G. Younger. Spatiotemporal Dynamics of Complement C5a Production within Bacterial Extracellular Polymeric Substance. Journal of Innate Immunity, 5, 114-123, Jan. 2013. (cover art!). doi
- C. W. Curtis and D. M. Bortz, Propagation of fronts in the Fisher-Kolmogorov equation with quadratically varying diffusion. Phys. Rev. E, 86(6), 066108, Dec. 2012. doi arXiv:1207.1097
- M. Thornton, C. Irvin, H. M. Chung, D. M. Bortz, M. J. Solomon, & J. G. Younger, Multicellularity and Antibiotic Resistance in Klebsiella pneumoniae Grown under Bloodstream-Mimicking Fluid Dynamic Conditions. Journal of Infectious Diseases, 206(4), 588-595, Aug. 2012. doi:10.1093/infdis/jis397
- J. F. Hammond and D. M. Bortz, Analytical solutions to Fisher’s equation with time-variable coefficients. Applied Mathematics and Computation, 218(6), 2497-2508, 2011. doi:10.1016/j.amc.2011.03.163
- E. C. Byrne, S. Dzul, M. J. Solomon, J. G. Younger, and D. M. Bortz, Postfragmentation density function for bacterial aggregates in laminar flow. Phys. Rev. E, 83(4), 41911, 2011. doi:10.1103/PhysRevE.83.041911
- C. M. Nypaver, M. M. Thornton, S. M. Yin, D. O. Bracho, P. W. Nelson, A. E. Jones, D. M. Bortz et al., Dynamics of Human Complement―Mediated Killing of Klebsiella pneumoniae, American journal of respiratory cell and molecular biology, 43(5), 585-590, 2010. doi:10.1165/rcmb.2009-0292OC
- H. Chung, M. M. Cartwright, D. M. Bortz, T. L. Jackson, and J. G. Younger, Dynamical System Analysis of Staphylococcus epidermidis Bloodstream Infection, SHOCK, 30(5):518-526, November 2008. doi:10.1097/SHK.0b013e31816a0b77 (cover art!)
- D. M. Bortz et al., Klebsiella pneumoniae flocculation dynamics, Bulletin of Mathematical Biology, 70(3):745-768, April 2008. doi:10.1007/s11538-007-9277-y
- D. M. Bortz and P. W. Nelson, Model selection and mixed-effects modeling of HIV infection dynamics, Bulletin of Mathematical Biology, 68(8):2005-2025, November 2006. doi:10.1007/s11538-006-9084-x
- S. Ciupe, B. L. Bivort, D. M. Bortz, and P. W. Nelson, Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models, Mathematical Biosciences, 200(1):1-27, March 2006. doi:10.1016/j.mbs.2005.12.006
- I. Ben-David, S. E. Price, D. M. Bortz, S. Cohen, A. L. Bauer, T. L. Jackson, and J. G. Younger, Dynamics of intrapulmonary bacterial growth in a murine model of repeated microaspirations, Am. J. Respiratory Cell & Molecular Biology, 33(5):476-482, November 2005. doi:10.1165/rcmb.2005-0053OC
- H. T. Banks and D. M. Bortz, A parameter sensitivity methodology in the context of HIV delay equation models, Journal of Mathematical Biology, 50(6):607-625, June 2005. doi:10.1007/s00285-004-0299-x
- H. T. Banks and D. M. Bortz, Inverse Problems for a Class of Measure Dependent Dynamical Systems, Journal of Inverse and Ill-posed Problems, 13(2):103-121, April 2005. doi:10.1515/1569394053978515
- D. M. Bortz and P. W. Nelson, Sensitivity analysis of nonlinear lumped parameter models of HIV infection dynamics, Bulletin of Mathematical Biology, 66(5):1009-1026, September 2004. doi:10.1016/j.bulm.2003.10.011
- H. T. Banks, D. M. Bortz, G. A. Pinter, and L. K. Potter, Chapter 6: Modeling and imaging techniques with potential for applications in bioterrorism. In H. T. Banks and C. Castillo-Chavez, editors, Bioterrorism: Mathematical Modeling Applications in Homeland Security, volume 28 of Frontiers in Applied Mathematics, pages 129-154, SIAM, Phildelphia, PA, 2003.
- H. T. Banks, D. M. Bortz, and S. E. Holte, Incorporation of variability into the mathematical modeling of viral delays in HIV infection dynamics, Mathematical Biosciences, 183(1):63-91, May 2003. doi:10.1016/S0025-5564(02)00218-3
- D. M. Bortz, Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations, Ph.D. dissertation, North Carolina State University, Raleigh, NC, 2002.
- D. M. Bortz et al., Control of open bay acoustics by harmonic mass injection, International Journal of Aeroacoustics, 1(1), 65-81, March 2002. doi:10.1260/1475472021502677
- A. B. Cain, A. D. Rubio, D. M. Bortz, H. T. Banks, and R. C. Smith, Reduced Order Modeling in Control of Open Cavity Acoustics, Proceedings of the AIAA, AIAA-2000-1928, June 2000.
- D. M. Bortz and C. T. Kelley, The simplex gradient and noisy optimization problems. In J. T. Borggaard, J. Burns, E. Cliff, and S. Schreck, editors, Computational Methods in Optimal Design and Control, volume 24 of Progress in Systems and Control Theory, Birkhauser, 1998, pp. 77-90.
- I. Ambats, D. M. Bortz, A. Connolly, A. Derlicki, M. Derrick, W. Kahle, and J. Thron, Studies of Hadron-Electron Separators for the ZEUS Barrel Calorimeter, Nuclear Instruments and Methods in Physics Research Section A, 368(2), 364-377, 1996. doi:10.1016/0168-9002(95)00621-4
- E. C. Conrad, A. E. Satorius, P. Sharma, D. M. Bortz, and J. G. Younger. "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.
- J. G. Younger, M. M. Thornton, C. Babcock, H. M. Chung-Esaki, D. M. Bortz, and M. J. Solomon. "Bloodstream-like fluid dynamic conditions promote multicellularity and antibiotic resistance in in Klebsiella pneumoniae". SHOCK, 37(1):58, 2012.
- M. M. Thornton, D. N. Hohne, M. J. Solomon, D. M. Bortz, and J. G. Younger. "Bacterial aggregation during growth under low shear: implications for bacteremia". SHOCK, 31(7):22, 2009.
- D.M. Bortz and A. J. Christlieb. Random numerical discretizations. In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 29–30, 2008.
- D. Li, D. Hohne, D.M. Bortz, et al. Modeling bacterial clearance from the bloodstream using computational fluid dynamics and monte carlo simulation. J. Critical Care, 22(4):344, Dec. 2007.
- J. G. Younger, H. Y. Chung, M. Cartwright, D. M. Bortz, and T. L. Jackson, Neutropenic S-epidermidis bacteremia modeled as a pharmacodynamic system, SHOCK, 27(Supplement 1):68-69, June 2007.
- D.M. Bortz. Accurate model selection computations. J. Critical Care, 21(4):359, Dec. 2006.
- H. Chung, T. L. Jackson, D. M. Bortz, M. Cartwright, and J. G. Younger, Multiple-compartment bacterial clearance kinetics during murine bacteremia, Journal of Critical Care, 21(4):359-360, December 2006.
- D. M. Bortz, T. L. Jackson, and J. G. Younger, Estimation and identification of Klebsiella pneumoniae flocculation dynamics, In Abstracts of the International Conference Inverse Problems: Modeling and Simulation, pages 15-17, 2006.
- J. G. Younger, K. Taylor, A. Thompson, and D. M. Bortz. Quantification and modeling of aggregate bacterial growth in suspension: Implications for bacteremia. SHOCK, pages 79–80, June 2006.
- I. Ben-David, S. E. Price, S. Cohen, D. M. Bortz, T. L. Jackson, and J. G. Younger, Complement C3 is necessary for early suppression of intrapulmonary bacterial growth, SHOCK, 23(Supplement 3):79-80, June 2005.
- A. L. Bauer, D. M. Bortz, D. Gammack, I. Ben-David, A. Stein, T. L. Jackson, and J. G. Younger, Virulence of Klebsiella pneumoniae predicted by nonlinear biodistributive mathematical model, SHOCK, 21(Supplement 2):29,2004.
- D. M. Bortz, et al., 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 CRSC-TR00-24, Center for Research in Scientific Computation, N. C. State University, Raleigh, NC, October 2000.
- A. B. Cain, A. D. Rubio, D. M. Bortz, H. T. Banks, and R. C. Smith, Optimizing control of open bay acoustics, Tech. Report CRSC-TR00-09, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC, May 2000.
- A. S. Bondarenko, D. M. Bortz, and J. J. Moré, COPS: Large-scale nonlinearly constrained optimization problems, Tech. Report ANL/MCS-TM-237, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, September 1998, revised October 1999.
- P. Barnes, D. M. Bortz, S. Frank, I. Loladze, E. Packard, and M. Santhanam, 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.
(post group activities in parentheses, if known)
List of fellowships for grad students
NSF Graduate Fellowship Program
DOE Computational Science Graduate Fellowship
DOD Science and Engineering Graduate Fellowship
NIH Individual Predoctoral Fellowship
Science, Mathematics And Research for Transformation (SMART) Scholarship for Service Program
NASA Graduate Student Researchers Program
Hertz Foundation Graduate Fellowship
Ford Foundation Fellowship Program
Google PHD Fellowships
NVIDIA Graduate Fellowships
Intel PHD Fellowship Program
IBM PHD Fellowship
Microsoft PhD Fellowship Program
List of Fellowships for Postdocs
L'Oreal For Women in Science fellowship program
NRC Research Associateship (deadlines)
List of Free Math Books
American Institute of Mathematics Open Textbook Initiative