## Professor Boris Baeumer

**Office:**232A

**Phone:**479-7763

**Email:**bbaeumer@maths.otago.ac.nz

** Head of Mathematics, Director of Studies (Graduate) **

### Curriculum Vitae

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.

### 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.

### Editorial Boards

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

### Publications

Most of Profesor Baeumer's publications are in A* (GRL, JDE, JGR, JHYDROL, SYSBIO, TRAN, WRR) or A (Bull.Math.Biol., CAMWA, DCDSB, JCAM, J.Appl.Prob., J.Evol.Eq., PAMS, Physica A, Phys. Rev E ) ranked journals according to the ARC Journal Rankings.

- A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains (with Mihaly Kovacs @ Pazmany Peter Catholic University, Hungary and Matthew Parry @ University of Otago),
*Fractional Calculus and Applied Analysis*, To Appear, 2022. - The development and efficacy of an undergraduate numeracy assessment tool (with Andrea Knowles, Chris Linsell and Megan Anakin @ Otago). In Y. H. Leong, B. Kaur, B. H. Choy, J. B. W. Yeo, & S. L. Chin (Eds),
*Excellence in Mathematics Education: Foundations and Pathways (Proceedings of the 43rd annual conference of the Mathematics Education Research Group of Australasia)*, 243--250, Singapore: MERGA, 2021. - Bayesian Inference of Species Trees using Diﬀusion Models (with Marnus Stoltz, Colin Fox, Gordon Hiscott and David Bryant @ Otago University and Remco Bouckaert @ University of Auckland),
*Systematic Biology*, 70(1), 145--161. DOI:10.1093/sysbio/syaa051, 2021. - Boundary conditions for fractional diffusion (with Mihaly Kovacs @ Chalmers University , Mark M. Meerschaert and Harish Sankaranarayanan @ Michigan State University),
*Journal of Computational and Applied Mathematics*, 336, 408--424. DOI:10.1016/j.cam.2017.12.053, 2018. Also available under Reprint of: Boundary conditions for fractional diffusion,*Journal of Computational and Applied Mathematics*, 339, 414-430, 2018. - Space-time fractional Dirichlet problems (with Tomasz Luks @ University of Paderborn and Mark M. Meerschaert),
*Mathematische Nachrichten*, 291, 2516-2535. DOI:10.1002/mana.201700111, 2018. - The self-thinning rule and plant population modelling with resource constraints (with Dimetre Triadis and Robert McKibbin), In:
*Proceedings of the 2016 Mathematics and Statistics in Industry NZ Study Group, MINZ-2016*, 58, M365-M378, 2018. - Fractional partial differential equations with boundary conditions (with Mihaly Kovacs and Harish Sankaranarayanan),
*Journal of Differential Equations*, 264(2), 1377-1410. DOI:10.1016/j.jde.2017.09.040 , 2018. - A calibration transform for families of spectroscopes (with R. Nicholson @ UC Merced and S. Taylor @ University of Auckland).
*ANZIAM J.*57 (MINZ2015), M268-M288, 2017. - A fully subordinated linear flow model for hillslope subsurface stormflow (with Yong Zhang @ University of Alabama, Li Chen @ State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Donald M Reeves @ Western Michigan University, and HongGuang Sun @ College of Mechanics and Materials, Hohai University).
*Water Resources Research*, 53(4), 3491-3504. DOI: 10.1002/2016WR020192, 2017. - Fokker-Planck and Kolmogorov backward equations for continuous time random walk limits (with Peter Straka @ University of New South Wales).
*Proceedings of the American Mathematical Society*, 145, 399-412, doi:10.1090/proc/13203, 2016. - Modeling mixed retention and early arrivals in multi-dimensional heterogeneous media using an explicit Lagrangian scheme (with Yong Zhang , Mark M. Meerschaert and Eric M. LaBolle @ UC Davis).
*Water Resources Research*, 51, doi:10.1002/2015WR016902, 2015. - Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise (with M.Geissert @ TU Darmstadt and M.Kovacs @ Chalmers University).
*Journal of Differential Equations*,**258**(2), 535–554 doi:10.1016/j.jde.2014.09.020, 2015. - Higher order Grunwald approximations of fractional derivatives and fractional powers of operators. (with M. Kovacs and H. Sankaranarayanan ).
*Transactions of the American Mathematical Society*,**367**, 813–834 doi:10.1090/S0002-9947-2014-05887-X, 2015. - Incorporating super-diffusion due to sub-grid heterogeneity to capture non-Fickian transport (with Y.Zhang and R.Schumer @ Desert Research Institute, Reno).
*Groundwater*,**53**(5), 699-708, doi:10.1111/gwat.12267, 2015. - Reflected spectrally negative stable processes and their governing equations (with M.Kovacs, M.M.Meerschaert, R.L.Schilling @ Technical University of Dresden and P.Straka).
*Transactions of the American Mathematical Society*, published electronically, doi:10.1090/tran/6360, 2015. - A subordinated advection model for uniform bedload transport from local to regional scales (with Y.Zhang, R.L.Martin (UCLA), D.Chen (Chinese Academy of Sciences, Beijing), H.Sun, and L.Chen (DRI Las Vegas and Hohai University).
*Journal of Geophysical Research - Earth Surface*,119, 2711–2729, doi:10.1002/2014JF003145, 2014. - Linking aquifer spatial properties and non-Fickian transport in mobile-immobile like alluvial settings (with Y.Zhang and Chris T. Green @ USGS Menlo Park, CA).
*Journal of Hydrology*, 512, 315-331, doi:10.1016/j.jhydrol.2014.02.064, 2014. - Mixing-Driven Equilibrium Reactions in Multidimensional Fractional Advection Dispersion Systems (with D. Bolster @ University of Notre Dame, D.A. Benson @ Colorado School of Mines and M.M.Meerschaert)
*Physica A*392, 2513-2525, doi:10.1016/j.physa.2012.12.040, 2013. - Approximating multivariate tempered stable processes (with M. Kovacs).
*Journal of Applied Probability***49**(1), 167-183, doi:10.1239/jap/1331216840, 2012. - Extremal behavior of coupled continuous time random walks (with Rina Schumer and Mark M. Meerschaert). Physica A 390, 505–511, doi:10.1016/j.physa.2010.10.018, 2011.
- Stochastic models for relativistic diffusion (with Mark M. Meerschaert and Mark Naber @ Monroe County Community College).
*Physical Review E*,**82**, 011132,doi:10.1103/PhysRevE.82.011132, 2010. - A tempered multiscaling stable model to simulate transport in regional-scale fractured media (with Yong Zhang and Donald M. Reeves).
*Geophysical Research Letters*,**37**, L11405, doi:10.1029/2010GL043609, 2010. - A Subordinated Kinematic Wave Equation for Heavy-Tailed Flow Responses from Heterogeneous Hillslopes (with Ciaran J. Harman and Murugesu Sivapalan @ University of Illinois at Urbana-Champaign and Donald M. Reeves).
*Journal of Geophysical Research - Earth Surface*, 115, F00A08, doi:10.1029/2009JF001273, 2010. - Particle tracking for fractional diffusion with two time scales (with Mark M. Meerschaert and Yong Zhang).
*Computers and Mathematics with Applications*,**59**, 1078-1086, doi:10.1016/ doi:10.1016/j.camwa.2009.05.009, 2010. - Tempered stable Lévy motion and transient super-diffusion (with Mark M. Meerschaert).
*Journal of Computational and Applied Mathematics*,**233**, 2438-2448, doi:10.1016/j.cam.2009.10.027, 2010. - Space-Time Duality for Fractional Diffusion (with Mark M. Meerschaert and E. Nane @ Auburn University).
*Journal of Applied Probability*,**46**(4), 1100-1115, doi:10.1239/jap/1261670691, 2009. - Fractional advection-dispersion equations for modeling transport at the Earth surface (with Rina Schumer and Mark M. Meerschaert).
*Journal of Geophysical Research - Earth Surface*, 114, F00A07, doi:10.1029/2008JF001246, 2009. - Predicting the Drug Release Kinetics of Matrix Tablets (with Peter Hinow @ University of Minnesota, Ami Radunskaya @ Pomona College and Lipika Chatterjee, Thomas Rades and Ian Tucker @ University of Otago).
*Discrete and Continuous Dynamical Systems - Series B*,**12**(2), 261-277, doi:10.3934/dcdsb.2009.12.261, 2009. - Unbounded functional calculus for bounded groups with applications (with M. Haase @ Delft University of Technology and M. Kovacs).
*Journal of Evolution Equations***9**, 171-195, doi:10.1007/s00028-009-0012-z, 2009. - Brownian subordinators and fractional Cauchy problems (with M.M. Meerschaert and E. Nane).
*Transactions of the American Mathematical Society*,**361**(7), 3915-3930, doi:10.1090/S0002-9947-09-04678-9, 2009. - Particle tracking for time-fractional diffusion (with M.M. Meerschaert and Y. Zhang).
*Physical Review E*78, 036705, doi:10.1103/PhysRevE.78.036705, 2008. - Tempered anomalous diffusion in heterogeneous systems (with M.M. Meerschaert and Y. Zhang).
*Geophysical Research Letters*, 35, L17403, doi:10.1029/2008GL034899, 2008. - Moment analysis for spatiotemporal fractional dispersion (with Y. Zhang and D.A. Benson).
*Water Resources Research*VOL. 44, W04424, doi:10.1029/2007WR006291, 2008. - Numerical solutions for fractional reaction-diffusion equations (with M. Kovacs and M.M. Meerschaert).
*Computers and Mathematics with Applications*55 (2008), 2212–2226, doi:10.1016/j.camwa.2007.11.012. - Subordinated multiparameter groups of linear operators: Properties via the transference principle (with M. Kovacs and M.M. Meerschaert),
*Functional Analysis and Evolution Equations, Dedicated to Gunter Lumer*(H. Amann, W. Arendt, M. Hieber, F. Neubrander, S. Nicaise, J. von Below eds.), Birkhaeuser Verlag, 35-50, 2008. - Fractional reproduction-dispersal equations and heavy tail dispersal kernels (with M. Kovacs and M.M. Meerschaert).
*Bulletin of Mathematical Biology*69(7), 2281-2297, doi:10.1007/s11538-007-9220-2, 2007. - Predicting the Tails of Breakthrough Curves in Regional-scale Alluvial Systems (with Y. Zhang and D.A. Benson).
*Ground Water*45(4), 473-484, doi: 10.1111/j.1745-6584.2007.00320.x,2007. - Fractional diffusion with two time scales (with M.M. Meerschaert).
*Physica A: Statistical and Theoretical Physics*373 (2007), pp.237-251. - The relationship between flux and resident concentrations for anomalous dispersion (with Y. Zhang and D.A. Benson).
*Geophysical Research Letters*VOL. 33, L18407, doi:10.1029/2006GL027251, 2006. - Aquifer Operator-Scaling and the Effect on Solute Mixing and Dispersion (with D.A. Benson, M.M. Meerschaert and H.-P.Scheffler, University of Siegen, Germany).
*Water Resources Research*, 42 (2006), W01415, doi:10.1029/2004WR003755. - Inhomogeneous fractional diffusion equations (with M.M. Meerschaert and S. Kurita, University of Nevada, Reno).
*Fractional Calculus and Applied Analysis*, Vol. 8 (2005), No. 4, pp. 371-386. - Advection and Dispersion in Time and Space (with D.A. Benson and M.M. Meerschaert).
*Physica A: Statistical and Theoretical Physics*, Vol. 350 (2005), No. 2-4, pp. 245-262. - Space-time fractional derivative operators (with M.M. Meerschaert and J. Mortenson, University of Nevada, Reno).
*Proceedings of the American Mathematical Society*, Vol. 133 (2005), No. 8, pp. 2273-2282. - Properties of scaling limits of random walks with waiting times (with M.M. Meerschaert). Proceedings of the 1st IFAC workshop on fractional differentiation and its applications. Bordeaux 2004.
- Fractal mobile/immobile solute transport (with R. Schumer, D.A. Benson, and M.M. Meerschaert).
*Water Resources Research*, Vol. 39 (2003), No. 10, p. 1296. - On the inversion of the Laplace and convolution transform
*Transactions of the American Mathematical Society*, 355, no. 3, 1201-1212, 2003. - Multiscaling fractional advection-dispersion equations and their solutions (with R. Schumer, M.M. Meerschaert, and D.A. Benson).
*Water Resources Research*39(1), 1022, 2003. - Stochastic solutions of space-time fractional diffusion equations (with M.M. Meerschaert, D.A. Benson, H.-P. Scheffler).
*Physical Review E*Vol. 65, 041103, 2002. - Stochastic solutions for fractional Cauchy problem (with M.M. Meerschaert).
*Fractional Calculus and Applied Analysis*, vol. 4, No 4 (2001), pp.481-500. - Operator Levy motion and multiscaling anomalous diffusion (with M.M. Meerschaert and D.A. Benson).
*Physical Review E*, Vol. 63 (2001), pp. 1112-1117. - Subordinated advection-dispersion equation for contaminant transport (with M.M. Meerschaert, D.A. Benson and S.W. Wheatcraft, University of Nevada, Reno).
*Water Resources Research*, Vol. 37 (2001), No. 6, pp.1543-1550. - Approximate solutions to the abstract Cauchy problem.
*Evolution equations and their applications in physical and life sciences.*Bad Herrenalb, Lecture Notes in Pure and Applied Mathematics, 215, Marcel Dekker, New York, 33-41, 2001. - Multidimensional advection and fractional dispersion (with M.M. Meerschaert, D.A. Benson).
*Physical Review E*59: 5026-5028 (1999). - Convolution kernels and generalized functions. (with G. Lumer and F. Neubrander)
*Generalized functions, operator theory, and dynamical systems.*Brussels, Chapman & Hall/CRC Research Notes in Mathematics, 399, Chapman & Hall/CRC, Boca Raton, 68-78, 1999. - Laplace transform methods for evolution equations (with F. Neubrander, Louisiana State University)
*Conferenze del Seminario di Matematica dell'Università di Bari*259: 27-60, 1994.

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Last updated, May 4, 2011.