Boris Baeumer, Our people, Department of Mathematics and Statistics

(PhD Louisiana State)

Postgraduate Adviser for Mathematics

Office: Science III, room 232A
Tel +64 3 479 7763
Email boris.baeumer@otago.ac.nz

About

Professor Boris Baeumer has been with the Department of Mathematics & Statistics at the University of Otago since 2001. His expertise is in applied mathematics focusing on movement of particles or organisms in nature that do not adhere to classical theories.

He obtained his Ph.D. in pure mathematics from Louisiana State University, USA in 1997, moved in to applied mathematics during a postdoctoral fellowship in hydrology at the University of Nevada, Reno in 2000. His research on Evolution Equations with Memory and Random Fluctuations is supported by the highly competitive Marsden Fund administered by the Royal Society of New Zealand.

He was awarded the Early Career Award for Distinction in Research by the University of Otago in 2005 and his research on Transport in Fractal Media was supported by the Royal Society of New Zealand through their Marsden Faststart funding scheme during 2004-2005. He has given invited addresses at international conferences and published over 45 scientific articles not just in mathematical journals but also in physics, geophysics, hydrology and computer science.

He served as Chair of the New Zealand Branch of ANZIAM from 2013-2016 and served on the MIS panel of the Marsden Fund 2015-2017.

Boris Baeumer is member of the editorial boards of Fractional Calculus & Applied Analysis, ANZIAM Journal, and Fractional Differential Calculus.

Research Interests

Boris Baeumer's current research interest is in modelling fractal flow and anomalous dispersion; in particular as it pertains to solute transport of (potentially toxic) particles in groundwater flow as well as dispersal of organisms such as viruses or invading species. He is using a new approach that incorporates heavy tailing and fractal pathways. Heavy tailing occurs whenever there is a power-law probability of catastrophic events, and therefore the approach has promising applications in hydrology, ecology (invasion of species), epidemiology, chemical engineering (for example, build-up on electrodes), physics (for example, rays going through the atmosphere), economics (stock-market), meteorology (rainfall patterns, flood events), etc.

Publications

Davis, L., Baeumer, B., & Wang, T. (2024). A fractional Hawkes process model for earthquake aftershock sequences. Journal of the Royal Statistical Society: Series C, qlae031. Advance online publication. doi: 10.1093/jrsssc/qlae031 Journal - Research Article

Baeumer, B., Kovács, M., & Parry, M. (2022). A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains. Fractional Calculus & Applied Analysis, 25, 299-319. doi: 10.1007/s13540-021-00013-z Journal - Research Article

Baeumer, B. (2021, May). The power of the limit of a power. University of Otago, Dunedin, New Zealand. [Inaugural Professorial Lecture]. Other Research Output

Knowles, A., Linsell, C., Baeumer, B., & Anakin, M. (2021). The development and efficacy of an undergraduate numeracy assessment tool. In Y. H. Leong, B. Kaur, B. H. Choy, J. B. W. Yeo & S. L. Chin (Eds.), Proceedings of the 43rd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). (pp. 243-250). Adelaide, Australia: Mathematics Education Research Group of Australasia (MERGA). Retrieved from https://www.merga.net.au Conference Contribution - Published proceedings: Full paper

Stoltz, M., Baeumer, B., Bouckaert, R., Fox, C., Hiscott, G., & Bryant, D. (2021). Bayesian inference of species trees using diffusion models. Systematic Biology, 70(1), 145-161. doi: 10.1093/sysbio/syaa051 Journal - Research Article

2024

Journal - Research Article

2022

Journal - Research Article

2021

Journal - Research Article

Conference Contribution - Published proceedings: Full paper

Other Research Output

Baeumer, B. (2021, May). The power of the limit of a power. University of Otago, Dunedin, New Zealand. [Inaugural Professorial Lecture].

2019

Conference Contribution - Published proceedings: Abstract

Baeumer, B. (2019). A conjecture: Higher order Grunwald formula. Proceedings of the New Zealand Mathematical Society Colloquium. (pp. 20-21). Retrieved from https://nzmathsoc.org.nz

Baeumer, B. (2019). Modelling deposition and erosion of clay in an aquifer. Proceedings of the 7th NZ Fluid Mechanics (FiNZ) Conference. (pp. 10). Retrieved from https://www.maths.otago.ac.nz/conferences/finz2019

Working Paper; Discussion Paper; Technical Report

Stoltz, M., Baeumer, B., Bouckaert, R., Fox, C., Hiscott, G., & Bryant, D. (2019). Bayesian inference of species trees using diffusion models. arXiv. 46p. Retrieved from https://arxiv.org/pdf/1909.07276.pdf

2018

Journal - Research Article

Baeumer, B., Luks, T., & Meerschaert, M. M. (2018). Space-time fractional Dirichlet problems. Mathematische Nachrichten, 291, 2516-2535. doi: 10.1002/mana.201700111

Baeumer, B., Kovács, M., Meerschaert, M. M., & Sankaranarayanan, H. (2018). Boundary conditions for fractional diffusion. Journal of Computational & Applied Mathematics, 336, 408-424. doi: 10.1016/j.cam.2017.12.053

Baeumer, B., Kovács, M., & Sankaranarayanan, H. (2018). Fractional partial differential equations with boundary conditions. Journal of Differential Equations, 264(2), 1377-1410. doi: 10.1016/j.jde.2017.09.040

Conference Contribution - Published proceedings: Abstract

Sund, N. L., Drummond, J. D., Roche, K. R., Baeumer, B., & Schumer, R. (2018). Reach-scale modeling of transport and reaction due to aerobic respiration in streams. Proceedings of the American Geophysical Union (AGU) Fall Meeting. H23K-2083. Retrieved from https://fallmeeting.agu.org/2018

2017

Journal - Research Article

Baeumer, B., & Straka, P. (2017). Fokker–Planck and Kolmogorov backward equations for continuous time random walk scaling limits. Proceedings of the American Mathematical Society, 145(1), 399-412. doi: 10.1090/proc/13203

Journal - Research Other

Zhang, Y., Baeumer, B., Chen, L., Reeves, D. M., & Sun, H. (2017). A fully subordinated linear flow model for hillslope subsurface stormflow [Technical report]. Water Resources Research, 53(4), 3491-3504. doi: 10.1002/2016WR020192

2016

Journal - Research Article

Baeumer, B., Kovács, M., Meerschaert, M. M., Schilling, R. L., & Straka, P. (2016). Reflected spectrally negative stable processes and their governing equations. Transactions of the American Mathematical Society, 368(1), 227-248. doi: 10.1090/tran/6360

Conference Contribution - Verbal presentation and other Conference outputs

Baeumer, B. (2016, December). Spectrally positive stable processes on bounded domains. Verbal presentation at the New Zealand Mathematical Society Colloquium, Wellington, New Zealand.

2015

Journal - Research Article

Zhang, Y., Meerschaert, M. M., Baeumer, B., & LaBolle, E. M. (2015). Modeling mixed retention and early arrivals in multidimensional heterogeneous media using an explicit Lagrangian scheme. Water Resources Research, 51, 6311-6337. doi: 10.1002/ 2015WR016902

Baeumer, B., Zhang, Y., & Schumer, R. (2015). Incorporating super-diffusion due to sub-grid heterogeneity to capture non-fickian transport. Groundwater, 53(5), 699-708. doi: 10.1111/gwat.12267

Baeumer, B., Kovács, M., & Sankaranarayanan, H. (2015). Higher order Grünwald approximations of fractional derivatives and fractional powers of operators. Transactions of the American Mathematical Society, 367(2), 813-834. doi: 10.1090/S0002-9947-2014-05887-X

Baeumer, B., Geissert, M., & Kovács, M. (2015). Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise. Journal of Differential Equations, 258(2), 535-554. doi: 10.1016/j.jde.2014.09.020

Conference Contribution - Published proceedings: Full paper

Taylor, S. W., Baeumer, B., & Nicholson, R. (2015). A calibration transform for families of spectroscopes. ANZIAM Journal, 57, (pp. M268-M288). doi: 10.21914/anziamj.v57i0.11238

2014

Journal - Research Article

Zhang, Y., Martin, R. L., Chen, D., Baeumer, B., Sun, H., & Chen, L. (2014). A subordinated advection model for uniform bed load transport from local to regional scales. Journal of Geophysical Research: Earth Surface, 119(12), 2711-2729. doi: 10.1002/2014JF003145

Zhang, Y., Green, C. T., & Baeumer, B. (2014). Linking aquifer spatial properties and non-Fickian transport in mobile-immobile like alluvial settings. Journal of Hydrology, 512, 315-331. doi: 10.1016/j.jhydrol.2014.02.064

Conference Contribution - Published proceedings: Abstract

Baeumer, B., Geissert, M., & Kovács, M. (2014). Volterra integral equations with multiplicative noise. Proceedings of the 8th Australia and New Zealand Mathematics Convention (AustMS and NZMS). (pp. 97). Retrieved from http://www.austms2014.ms.unimelb.edu.au/

2013

Journal - Research Article

Bolster, D., Benson, D. A., Meerschaert, M. M., & Baeumer, B. (2013). Mixing-driven equilibrium reactions in multidimensional fractional advection-dispersion systems. Physica A, 392(10), 2513-2525. doi: 10.1016/j.physa.2012.12.040

2012

Journal - Research Article

Baeumer, B., & Kovács, M. (2012). Approximating multivariate tempered stable processes. Journal of Applied Probability, 49(1), 167-183.

Conference Contribution - Published proceedings: Abstract

Zhang, Y., Green, C. T., Fogg, G. E., & Baeumer, B. (2012). Tempered stable models for preasymptotic pollutant transport in alluvial settings: The influence of medium heterogeneity. Proceedings of the American Geophysical Union (AGU) 45th Annual Fall Meeting. Retrieved from http://fallmeeting.agu.org/2012/

Conference Contribution - Verbal presentation and other Conference outputs

Baeumer, B. (2012, December). Markovian subordination for fractional Cauchy problems. Verbal presentation at the New Zealand Mathematical Society Colloquium, Palmerston North, New Zealand.

2011

Journal - Research Article

Schumer, R., Baeumer, B., & Meerschaert, M. (2011). Extremal behavior of a coupled continuous time random walk. Physica A, 390(3), 505-511. doi: 10.1016/j.physa.2010.10.018

Conference Contribution - Published proceedings: Abstract

García, J. A., Jalilzadeh, A., & Baeumer, B. (2011). A reinforced random walk model for studying the acute inflammatory response. Proceedings of the 8th European Conference on Mathematical and Theoretical Biology (ECMTB) and Annual Meeting of The Society for Mathematical Biology. Retrieved from http://www.impan.pl/~ecmtb11/showabstract.php?id=Garcia_JoseA

Baeumer, B., Meerschaert, M. M., & Kovacs, M. (2011). Reaction-diffusion for the fractional mobile-immobile model. Proceedings of the American Geophysical Union (AGU) Fall Meeting. Retrieved from http://fallmeeting.agu.org/2011/

Conference Contribution - Verbal presentation and other Conference outputs

Baeumer, B. (2011, November). Fractional differential equations on bounded domains. Invited presentation at the Hot Topics Workshop on Laplace Transform Methods and Their Applications, Daejeon, Korea.

2010

Journal - Research Article

Baeumer, B., Meerschaert, M., & Naber, M. (2010). Stochastic models for relativistic diffusion. Physical Review E: Statistical, Nonlinear, & Soft Matter Physics, 82, 011132. doi: 10.1103/PhysRevE.82.011132

Zhang, Y., Baeumer, B., & Reeves, D. M. (2010). A tempered multiscaling stable model to simulate transport in regional-scale fractured media. Geophysical Research Letters, 37, L11405. doi: 10.1029/2010GL043609

Harman, C. J., Reeves, D. M., Baeumer, B., & Sivapalan, M. (2010). A subordinated kinematic wave equation for heavy-tailed flow responses from heterogeneous hillslopes. Journal of Geophysical Research, 115, F00A08. doi: 10.1029/2009jf001273

Meerschaert, M. M., Zhang, Y., & Baeumer, B. (2010). Particle tracking for fractional diffusion with two time scales. Computers & Mathematics with Applications, 59(3), 1078-1086. doi: 10.1016/j.camwa.2009.05.009

Baeumer, B., & Meerschaert, M. M. (2010). Tempered stable Lévy motion and transient super-diffusion. Journal of Computational & Applied Mathematics, 233(10), 2438-2448. doi: 10.1016/j.cam.2009.10.027

Conference Contribution - Published proceedings: Abstract

Schumer, R., Meerschaert, M. M., & Baeumer, B. (2010). Fractional diffusion in geologic systems. Proceedings of the American Geophysical Union (AGU) Fall Meeting. Retrieved from http://www.agu.org/meetings/fm10/waisfm10.html

Baeumer, B. (2010). Parallel splitting and tempered operator stable random variables. Proceedings of the New Zealand Mathematics Colloquium. (pp. 5). Retrieved from http://nzmathsoc.org.nz/colloquium/programme.php

Conference Contribution - Verbal presentation and other Conference outputs

Schumer, R., Meerschaert, M. M., & Baeumer, B. (2010, December). Fractional diffusion in geologic systems. Invited presentation at the American Geophysical Union (AGU) Fall Meeting, San Francisco, CA.

2009

Journal - Research Article

Baeumer, B., Meerschaert, M. M., & Nane, E. (2009). Space-time duality for fractional diffusion. Journal of Applied Probability, 46(4), 1100-1115.

Schumer, R., Meerschaert, M. M., & Baeumer, B. (2009). Fractional advection-dispersion equations for modeling transport at the Earth surface. Journal of Geophysical Research, 114, F00A07. doi: 10.1029/2008JF001246

Baeumer, B., Chatterjee, L., Hinow, P., Rades, T., Radunskaya, A., & Tucker, I. (2009). Predicting the drug release kinetics of matrix tablets. Discrete & Continuous Dynamical Systems Series B, 12(2), 261-277. doi: 10.3934/dcdsb.2009.12.261

Baeumer, B., Haase, M., & Kovács, M. (2009). Unbounded functional calculus for bounded groups with applications. Journal of Evolution Equations, 9(1), 171-195. doi: 10.1007/s00028-009-0012-z

Baeumer, B., Meerschaert, M. M., & Nane, E. (2009). Brownian subordinators and fractional Cauchy problems. Transactions of the American Mathematical Society, 361(7), 3915-3930.

2008

Chapter in Book - Research

Baeumer, B., Kovács, M., & Meerschaert, M. M. (2008). Subordinated multiparameter groups of linear operators: Properties via the transference principle. In H. Amann, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise & J. von Below (Eds.), Functional Analysis and Evolution Equations (The Günter Lumer Volume). (pp. 35-50). Basel, Switzerland: Birkhäuser. doi: 10.1007/978-3-7643-7794-6_3

Journal - Research Article

Zhang, Y., Meerschaert, M. M., & Baeumer, B. (2008). Particle tracking for time-fractional diffusion. Physical Review E: Statistical, Nonlinear, & Soft Matter Physics, 78, 036705. doi: 10.1103/PhysRevE.78.036705

Meerschaert, M. M., Zhang, Y., & Baeumer, B. (2008). Tempered anomalous diffusion in heterogeneous systems. Geophysical Research Letters, 35(17), L17403. doi: 10.1029/2008GL034899

Baeumer, B., Kovács, M., & Meerschaert, M. M. (2008). Numerical solutions for fractional reaction-diffusion equations. Computers & Mathematics with Applications, 55(10), 2212-2226. doi: 10.1016/j.camwa.2007.11.012

Zhang, Y., Benson, D. A., & Baeumer, B. (2008). Moment analysis for spatiotemporal fractional dispersion. Water Resources Research, 44(4), W04424. doi: 10.1029/2007WR006291

2007

Journal - Research Article

Baeumer, B., & Meerschaert, M. M. (2007). Fractional diffusion with two time scales. Physica A, 373, 237-251.

Baeumer, B., Kovács, M., & Meerschaert, M. M. (2007). Fractional reproduction-dispersal equations and heavy tail dispersal kernels. Bulletin of Mathematical Biology, 69, 2281-2297.

Zhang, Y., Benson, D. A., & Baeumer, B. (2007). Predicting the tails of breakthrough curves in regional-scale alluvial systems. Ground Water, 45(4), 473-484.

2006

Journal - Research Article

Benson, D. A., Meerschaert, M. M., Baeumer, B., & Scheffler, H.-P. (2006). Aquifer operator scaling and the effect on solute mixing and dispersion. Water Resources Research, 42. Retrieved from http://www.agu.org/journals/wr/wr0601/2004WR003755/2004WR003755.pdf

Zhang, Y., Baeumer, B., & Benson, D. A. (2006). Relationship between flux and resident concentrations for anomalous dispersion. Geophysical Research Letters, 33. doi: 10.1029/2006GL027251

2005

Journal - Research Article

Baeumer, B., Kurita, S., & Meerschaert, M. (2005). Inhomogeneous fractional diffusion equations. Fractional Calculus & Applied Analysis, 8(4), 371-386.

Baeumer, B., Benson, D. A., & Meerschaert, M. M. (2005). Advection and dispersion in time and space. Physica A, 350, 245-262.

Baeumer, B., Meerschaert, M. M., & Mortensen, J. (2005). Space-time fractional derivative operators. Proceedings of the American Mathematical Society, 133(8), 2273-2282.

2003

Journal - Research Article

Baeumer, B. (2003). On the inversion of the convolution and Laplace transform. Transactions of the American Mathematical Society, 355(3), 1201-1212.

Schumer, R., Benson, D. A., Meerschaert, M. M., & Baeumer, B. (2003). Multiscaling fractional advection-dispersion equations and their solutions. Water Resources Research, 39(1), 1022.

Schumer, R., Benson, D. A., Meerschaert, M. M., & Baeumer, B. (2003). Fractal mobile/immobile solute transport. Water Resources Research, 39(10), 1296.

2002

Journal - Research Article

Meerschaert, M. M., Benson, D. A., Scheffler, H.-P., & Baeumer, B. (2002). Stochastic solution of space-time fractional diffusion equations. Physical Review E: Statistical Physics, Plasmas, Fluids, & Related Interdisciplinary Topics, 65(4), 041103-1-041103-4. doi: 10.1103/PhysRevE.65.041103

2001

Journal - Research Article

Meerschaert, M. M., Benson, D. A., & Baeumer, B. (2001). Operator Lévy motion and multiscaling anomalous diffusion. Physical Review E: Statistical Physics, Plasmas, Fluids, & Related Interdisciplinary Topics, 63(2), 1112-1117. doi: 10.1103/PhysRevE.63.021112

Baeumer, B., Benson, D. A., Meerschaert, M. M., & Wheatcraft, S. W. (2001). Subordinated advection-dispersion equation for contaminant transport. Water Resources Research, 37(6), 1543-1550.

Baeumer, B., & Meerschaert, M. M. (2001). Stochastic solutions for fractional Cauchy problems. Fractional Calculus & Applied Analysis, 4(4), 481-500.

Conference Contribution - Published proceedings: Full paper

Baeumer, B. (2001). Approximate solutions to the abstract Cauchy problem. In B. Herrenalb (Ed.), Evolution Equations and their Applications in Physical and Life Sciences. (pp. 33-41). New York: Marcel Dekker. [Full Paper]

1999

Journal - Research Article

Meerschaert, M., Benson, D. A., & Baeumer, B. (1999). Multidimensional advection and fractional dispersion. Physical Review E: Statistical Physics, Plasmas, Fluids, & Related Interdisciplinary Topics, 59(5), 5026-5028.

Conference Contribution - Published proceedings: Full paper

Baeumer, B., Gunter, L., & Neubrander, F. (1999). Convolution kernals and generalized functions. In I. Antoniou & G. Lumer (Eds.), Generalized Functions, Operator Theory and Dynamical Systems Conference. 399, (pp. 68-78). Boca Raton: Chapman & Hall/CRC. [Full Paper]