## Publications

### Preprints

- Y. Li, P. van Heijster, R. Marangell and
**M.J. Simpson**(2019). Travelling wave solutions in a negative nonlinear diffusion-reaction model. - A. Surendran, M.J. Plank and
**M.J. Simpson**(2019). Spatial structure arising from chase-escape interactions with crowding.

### Publications

- N.T. Fadai, R.E. Baker and
**M.J. Simpson**(2019). Accurate and efficient discretisations for stochastic models providing near agent-based spatial resolution at low computational cost. - O.M. Matsiaka, R.E. Baker and
**M.J. Simpson**(2019). Continuum descriptions of spatial spreading for heterogeneous cell populations: theory and experiment. Journal of Theoretical Biology. - M. El-Hachem, S.W. McCue, W. Jin, Y. Du and
**M.J. Simpson**(2019). Revisiting the Fisher-Kolmogorov-Petrovsky-Piskunov equation to interpret the spreading-extinction dichotomy. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. - S.T. Vittadello, S.W. McCue, G. Gunasingh, N.K. Haass and
**M.J. Simpson**(2019). Mathematical models incorporating a multi-stage cell cycle replicate normally-hidden inherent synchronisation in cell proliferation. Journal of the Royal Society Interface. - R.E. Baker, A. Parker and
**M.J. Simpson**(2019). A free boundary model of epithelial dynamics. Journal of Theoretical Biology. - A.P. Browning, F.G. Woodhouse and
**M.J. Simpson**(2019). Reversible signal transmission in an active mechanical metamaterial. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 475, 20190146. - R.J. Murphy, P. Buenzli, R.E. Baker and
**M.J. Simpson**(2019). An individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 475, 20180838. Selected for the cover of Proceedings A. - S.W. McCue, W. Jin, T.J. Moroney, K-Y Lo, S-E Chou and
**M.J. Simpson**(2019). Hole-closing model reveals exponents for nonlinear degenerate diffusivity functions in cell biology. Physica D: Nonlinear Phenomena. 398, 130 - 140. - O.M. Matsiaka, R.E. Baker, E.T. Shah and
**M.J. Simpson**(2019). Mechanistic and experimental models of cell migration reveal the importance of intercellular interactions in cell invasion. Biomedical Physics & Engineering Express. 5, 045009. - D.J. Warne, R.E. Baker and
**M.J. Simpson**(2019). Using experimental data and information criteria to guide model selection for reaction-diffusion problems in mathematical biology. Bulletin of Mathematical Biology. 81, 1760 - 1804. - J.A. Sharp, A.P. Browning, T. Mapder, K. Burrage and
**M.J. Simpson**(2019). Optimal control of acute myeloid leukaemia. Journal of Theoretical Biology. 470, 30 - 42 - D.J. Warne, R.E. Baker and
**M.J. Simpson**(2019). Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art. Journal of the Royal Society Interface. 16, 20180943. - A.P. Browning, P. Haridas and
**M.J. Simpson**(2019). A Bayesian sequential learning framework to parameterise continuum models of melanoma invasion into human skin. Bulletin of Mathematical Biology. 81, 676 - 698. **M.J. Simpson**(2019). Mathematical models of cell invasion track spatial position and progression through the cell cycle. SIAM News. 52, 1 - 2.- E.J. Carr and
**M.J. Simpson**(2019). New homogenization approaches for stochastic transport through heterogeneous media. Journal of Chemical Physics. 150, 044104. - S. McInerney, E.J. Carr and
**M.J. Simpson**(2019). Parameterising continuum models of heat transfer in heterogeneous living skin using experimental data. International Journal of Heat and Mass Transfer. 128, 964 - 975. - W. Jin, X. Liang, A. Brooks, K. Futrega, X. Liu, M.R. Doran,
**M.J. Simpson**, M.S. Roberts and H. Wang (2018). Modelling of the SDF-1/CXCR4 regulated in vivo homing of therapeutic mesenchymal stem/stromal cells in mice. PeerJ. 6, e6072 - H. Yang, R.M. Villani, H. Wang,
**M.J. Simpson**, M.S. Roberts, M. Tang and X. Liang (2018). The role of cellular reactive oxygen species in cancer chemotherapy. Journal of Experimental & Clinical Cancer Research. 37, 266. - A. Surendran, M.J. Plank and
**M.J. Simpson**(2018). Spatial moment description of birth-death-movement processes incorporating the effects of crowding and obstacles. Bulletin of Mathematical Biology. 80, 2828 - 2855. - Z. Welsh,
**M.J. Simpson**, Md I.H. Khan and M.A. Karim (2018). Multiscale modelling of food drying: State of the art. Comprehensive Reviews in Food Science and Food Safety. 17, 1293 - 1308. - A. Parker,
**M.J. Simpson**and R.E. Baker (2018). The impact of experimental design choices on parameter inference for models of growing cell colonies. Royal Society Open Science. 5, 180384. **M.J. Simpson**, W. Jin, S.T. Vittadello, T. Tambyah, J. Ryan, G. Gunasingh, N.K. Haass and S.W. McCue (2018). Stochastic models of cell invasion with fluorescent cell cycle indicators. Physica A: Statistical Mechanics and its Applications. 510, 375 - 386.- P. Haridas, A.P. Browning, J.A. McGovern, D.L.S. McElwain and
**M.J. Simpson**(2018). Three-dimensional experiments and individual based simulations show that cell proliferation drives melanoma nest formation in human skin tissue. BMC Systems Biology. 12, 34. - O.M. Matsiaka, C.J. Penington, R.E. Baker and
**M.J. Simpson**(2018). Discrete and continuum approximations for collective cell migration in a scratch assay with cell size dynamics. Bulletin of Mathematical Biology. 80, 738 - 757. - D.J. Warne, R.E. Baker and
**M.J. Simpson**(2018). Multilevel rejection sampling for approximate Bayesian computation. Computational Statistics & Data Analysis. 124, 71 – 86. - W. Jin, S.W. McCue and
**M.J. Simpson**(2018). Extended logistic growth model for heterogeneous populations Journal of Theoretical Biology. 445, 51 - 61. - S.T. Vittadello, S.W. McCue, G. Gunasingh, N.K. Haass and
**M.J. Simpson**(2018). Mathematical models for cell migration with real-time cell cycle dynamics. Biophysical Journal. 114, 1241 – 1253. - E.J Carr and
**M.J. Simpson**(2018). Rapid calculation of maximum particle lifetime for diffusion in complex geometries. Journal of Chemical Physics. 148, 094113. **M.J. Simpson**(2018). Calculating groundwater response times for flow in heterogeneous porous media. Groundwater. 56, 337 - 342.- W. Jin, K-Y. Lo, S-E Chou, S.W. McCue and
**M.J. Simpson**(2018). The role of initial geometry in experimental models of wound closing. Chemical Engineering Science. 179, 221 - 226. Selected for the cover of Chemical Engineering Science. - E.J. Carr and
**M.J. Simpson**(2018). Accurate and efficient calculation of response times for groundwater flow. Journal of Hydrology. 558, 470 – 481. - A.P. Browning, S.W. McCue, R.N. Binny, M.J. Plank, E.T. Shah and
**M.J. Simpson**(2018). Inferring parameters for a lattice-free model of cell migration and proliferation using experimental data. Journal of Theoretical Biology. 437, 251 - 260. - D.J. Warne, R.E. Baker and
**M.J. Simpson**(2017). Optimal quantification of contact inhibition in cell populations . Biophysical Journal (Biophysical Letter). 113, 1920 - 1924. **M.J. Simpson**and M.J. Plank (2017). Simplified calculation of diffusivity for a lattice-based random walk with a single obstacle. Results in Physics. 7, 3346 - 3348.**M.J. Simpson**, S. McInerney, E.J. Carr and L. Cuttle (2017). Quantifying the efficacy of first aid treatments for burn injuries using mathematical modelling and in vivo porcine experiments. Scientific Reports. 7, 10925- P. Haridas, J.A. McGovern, D.L.S. McElwain and
**M.J. Simpson**(2017). Quantitative comparison of the spreading and invasion of radial growth phase and metastatic melanoma cells in a three-dimensional human skin equivalent model. PeerJ. 5, e3754. - W. Jin, C.J. Penington, S.W. McCue and
**M.J. Simpson**(2017). A computational modelling framework to quantify the effects of passaging cell lines. PLOS ONE. 12, e0181941. - A.P. Browning, S.W. McCue and
**M.J. Simpson**(2017). A Bayesian computational approach to explore the optimal duration of a cell proliferation assay. Bulletin of Mathematical Biology. 79, 1888 - 1906. - P. Haridas, C.J. Penington, J.A. McGovern, D.L.S. McElwain and
**M.J. Simpson**(2017). Quantifying rates of cell migration and cell proliferation in co-culture barrier assays reveals how skin and melanoma cells interact during melanoma spreading and invasion. Journal of Theoretical Biology. 423, 13 - 25. - O.M. Matsiaka, C.J. Penington, R.E. Baker and
**M.J. Simpson**(2017). Continuum approximations for lattice-free multi-species models of collective cell migration. Journal of Theoretical Biology. 422, 1 - 11. - W. Jin, E.T. Shah, C.J. Penington, S.W. McCue, P.K. Maini and
**M.J. Simpson**(2017). Logistic proliferation of cells in scratch assays is delayed. Bulletin of Mathematical Biology. 79, 1028 - 1050. - M. Zheng, F. Liu, Q. Liu, K. Burrage and
**M.J. Simpson**(2017). A novel numerical approximation of the time fractional reaction-diffusion equation with a moving boundary. Journal of Computational Physics. 338, 493 - 510. **M.J. Simpson**, K-Y. Lo and Y-S. Sun (2017). Quantifying the roles of random motility and directed motility using advection-diffusion theory for a 3T3 fibroblast cell migration assay stimulated with an electric field. BMC Systems Biology. 11, 39.- S.T. Johnston, R.E. Baker and
**M.J. Simpson**(2017). A new and accurate continuum description of moving fronts. New Journal of Physics. 19, 033010. - S.T. Johnston, R.E. Baker, D.L.S. McElwain and
**M.J. Simpson**(2017). Co-operation, competition and crowding: a discrete framework linking Allee kinetics, nonlinear diffusion, shocks and sharp-fronted travelling waves. Scientific Reports. 7, 42134. **M.J. Simpson**(2017). Critical time scales for morphogen gradient formation: Concentration or gradient criteria. International Journal of Heat and Mass Transfer. 106, 570 - 572.- F. Jazaei,
**M.J. Simpson**and T.P. Clement (2017). Understanding time scales of diffusive fluxes and the implication for steady state and steady shape conditions. Geophysical Research Letters. 44, 174 - 180. - W. Jin, C.J. Penington, S.W. McCue and
**M.J. Simpson**(2016). Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with universal growth functions. Physical Biology. 13, 056003. - A.J. Ellery, R.E. Baker and
**M.J. Simpson**(2016). An analytical method for disentangling the roles of adhesion and crowding for random walk models on a crowded lattice. Fast Track Letter, Physical Biology. 13, 05LT02. - P.R. Taylor, R.E. Baker,
**M.J. Simpson**and C.A. Yates (2016). Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches. Journal of the Royal Society Interface. 13, 2016336. - C.J. Penington, R.E. Baker and
**M.J. Simpson**(2016). Exits in order: how crowding affects particle lifetimes. The Journal of Chemical Physics. 144, 244107. - C.J. Andrews, L. Cuttle and
**M.J. Simpson**(2016). Quantifying the role of burn temperature, burn duration and skin thickness in an*in vivo*animal skin model of heat conduction. International Journal of Heat and Mass Transfer. 101, 542 - 549. - A.J. Ellery, R.E. Baker and
**M.J. Simpson**(2016). Distinguishing between short-time non-Fickian diffusion, and long-time Fickian diffusion for a random walk on a crowded lattice. Communication, The Journal of Chemical Physics. 144, 171104. - S.T. Johnston, R.E. Baker and
**M.J. Simpson**(2016). Filling the gaps: A robust description of adhesive birth-death-movement processes. Physical Review E. 93, 042413. - S.T. Johnston, J.V. Ross, B.J. Binder, D.L.S. McElwain, P. Haridas and
**M.J. Simpson**(2016). Quantifying the effect of experimental design choices for*in vitro*scratch assays. Journal of Theoretical Biology. 400, 19 - 31. - P. Haridas, J.A. McGovern, A.S. Kashyap, D.L.S. McElwain and
**M.J. Simpson**(2016). Standard melanoma-associated markers do not identify the MM127 metastatic melanoma cell line. Scientific Reports. 6, 24569. - R.N. Binny, P. Haridas, A. James, R. Law,
**M.J. Simpson**and M.J. Plank (2016). Spatial structure arising from neighbour-dependent bias in collective cell movement. PeerJ. 4, e1689. - B.J. Binder and
**M.J. Simpson**(2016). Cell density and cell size dynamics during*in vitro*tissue growth experiments: Implications for mathematical models of collective cell behaviour. Applied Mathematical Modelling. 40, 3438 - 3446. - A.J. Ellery, R.E. Baker, S.W. McCue and
**M.J. Simpson**(2016). Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes. Physica A: Statistical Mechanics and its Applications. 449, 74 - 84. - W. Jin, E.T. Shah, C.J. Penington, S.W. McCue, L.K. Chopin and
**M.J. Simpson**(2016). Reproducibility of scratch assays is affected by the initial degree of confluence: experiments, modelling and model selection. Journal of Theoretical Biology. 390, 136 - 145. - F. Jazaei,
**M.J. Simpson**and T.P. Clement (2016). Spatial analysis of aquifer response times for radial flow processes: Nondimensional analysis and laboratory-scale tests. Journal of Hydrology. 532: 1-8. - C. Irons, M.J. Plank and
**M.J. Simpson**(2016). Lattice-free models of directed cell motility. Physica A: Statistical Mechanics and its Applications. 442, 110-121. - A.J. Ellery, R.E. Baker and
**M.J. Simpson**(2015). Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes. Physical Biology. 12: 066010. - P.R. Taylor, C.A. Yates,
**M.J. Simpson**and R.E. Baker (2015). Reconciling transport models across scales: the role of volume exclusion. Rapid Communication, Physical Review E. 92, 040701(R). **M.J. Simpson**, J.A. Sharp, L.C. Morrow and R.E. Baker (2015). Exact solutions of coupled multispecies linear reaction-diffusion equations on a uniformly growing domain. PLOS ONE. 10, e0138894.**M.J. Simpson**and R.E. Baker (2015). Exact calculations of survival probability for diffusion on growing lines, disks and spheres: the role of dimension. The Journal of Chemical Physics. 143, 094109.- S.T. Johnston, E.T. Shah, L.K. Chopin, D.L.S. McElwain and
**M.J. Simpson**(2015). Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM assay data using the Fisher-Kolmogorov model. BMC Systems Biology. 9, 38. **M.J. Simpson**and L.C. Morrow (2015). Analytical model of reactive transport processes with spatially variable coefficients. Royal Society Open Science. 2, 140348.**M.J. Simpson**and R.E. Baker (2015). Spatial moment techniques for modelling biological processes. Bulletin of Mathematical Biology. 77, 581 - 585.- D.C. Markham,
**M.J. Simpson**and R.E. Baker (2015). Choosing an appropriate modelling framework for analysing multispecies co-culture experiments. Bulletin of Mathematical Biology. 77, 713-734. **M.J. Simpson**, J.A. Sharp and R.E. Baker (2015). Survival probability for a diffusive process on a growing domain. Physical Review E. 91, 042701.- B.N. Vo, C.C. Drovandi, A.N. Pettitt and
**M.J. Simpson**(2015). Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation. Mathematical Biosciences. 263, 133 - 142. **M.J. Simpson**(2015). Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: Criteria for successful colonization. PLOS ONE. 10, e0117949.- S.T. Johnston,
**M.J. Simpson**and R.E. Baker (2015). Modelling the movement of interacting cell populations: A moment dynamics approach. Journal of Theoretical Biology. 370, 81 - 92. - B.J Binder and
**M.J. Simpson**(2015). Spectral analysis of pair-correlation bandwidth: Application to cell biology images. Royal Society Open Science. 2, 140494. **M.J. Simpson**and S.W. McCue (2015). ANZIAM 2015. Gazette of the Australian Mathematical Society. 42, 23 - 25.- F. Jazaei,
**M.J. Simpson**and T.P. Clement (2014). An analytical framework for quantifying aquifer response time scales associated with transient boundary conditions. Journal of Hydrology. 519, 1642 - 1648. - S.T Johnston,
**M.J. Simpson**, D.L.S. McElwain, B.J. Binder and J.V. Ross (2014). Interpreting scratch assays using pair density dynamics and approximate Bayesian computation. Royal Society Open Biology. 4, 140097. - K.K. Treloar,
**M.J. Simpson**, B.J. Binder, D.L.S McElwain and R.E. Baker (2014). Assessing the role of spatial correlations during collective cell spreading. Scientific Reports. 4, 5713. - S.T. Johnston,
**M.J. Simpson**and D.L.S McElwain (2014). How much information can be obtained from tracking the position of the leading edge in a scratch assay? Journal of the Royal Society Interface. 11, 20140325. - K.K. Treloar,
**M.J. Simpson**, D.L.S McElwain and R.E Baker (2014). Are*in vitro*estimates of cell diffusivity and cell proliferation rate sensitive to assay geomentry? Journal of Theoretical Biology. 356, 71 - 84. - H.M. Young, A.J. Bergner,
**M.J. Simpson**, S.J. McKeown, M.M. Hao, C.R. Anderson and H. Enomoto (2014). Colonizing while migrating: How do individual enteric neural crest cells behave? BMC Biology. 12, 23. **M.J. Simpson**and A.J. Ellery (2014). Exact series solutions of reactive transport models with general initial conditions. Journal of Hydrology. 513, 7 - 12.- D.J.G. Agnew, J.E.F. Green, T.M. Brown,
**M.J. Simpson**and B.J. Binder (2014). Distinguishing between mechanisms of cell aggregation using pair-correlation functions. Journal of Theoretical Biology. 352, 16 - 23. - D.C. Markham,
**M.J. Simpson**, P.K. Maini, E.A. Gaffney and R.E. Baker (2014). Comparing methods for modelling spreading cell fronts. Journal of Theoretical Biology. 353, 95 - 103. - A.J. Ellery,
**M.J. Simpson**, S.W. McCue and R.E. Baker (2014). Characterizing transport through a crowded environment with different obstacle sizes. The Journal of Chemical Physics. 140, 054108. **M.J. Simpson**, P. Haridas and D.L.S. McElwain (2014). Do pioneer cells exist? PLOS ONE. 9, e85488.**M.J. Simpson**, J.A Sharp and R.E. Baker (2014). Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes. Physica A: Statistical Mechanics and its Applications. 395, 236 - 246.- K.K. Treloar,
**M.J. Simpson**, P. Haridas, K.J. Manton, D.I. Leavesley, D.L.S. McElwain and R.E. Baker (2013). Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies. BMC Systems Biology. 7, 137. - S.T. Johnston,
**M.J. Simpson**and M.J. Plank (2013). Lattice-free descriptions of collective motion with crowding and adhesion. Physical Review E. 88, 062720. - A.J. Ellery,
**M.J. Simpson**, S.W. McCue and R.E. Baker (2013). A simplified approach for calculating the moments of action for linear reaction-diffusion equations. Physical Review E. 88, 054102. - D.C. Markham,
**M.J. Simpson**, P.K. Maini, E.A. Gaffney and R.E. Baker (2013). Incorporating spatial correlations into multi-species mean-field models. Physical Review E. 88, 052713. **M.J. Simpson**, F. Jazaei and T.P. Clement (2013). How long does it take for aquifer recharge or aquifer discharge processes to reach steady state? Journal of Hydrology. 501, 241 - 248.- L.G. Bowden,
**M.J. Simpson**and R.E. Baker (2013). Design and interpretation of cell trajectory assays. Journal of the Royal Society Interface. 10, 20130630. - M.J. Plank and
**M.J. Simpson**(2013). Lattice-free models of cell invasion: discrete simulations and travelling waves. Bulletin of Mathematical Biology. 75, 2150 - 2166. - B.J. Binder and
**M.J. Simpson**(2013). Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions. Physical Review E. 88, 022705. - A.J. Ellery,
**M.J. Simpson**and S.W. McCue (2013). Comment on Local accumulation times for source, diffusion and degradation models in two and three dimensions. The Journal of Chemical Physics. 139, 017101. - D.C. Markham,
**M.J. Simpson**and R.E. Baker (2013). Simplified method for including spatial correlations in mean-field approximations. Physical Review E. 87, 062702. - K.K. Treloar and
**M.J. Simpson**(2013). Sensitivity of edge detection methods for quantifying cell migration assays. PLOS ONE. 8, e67389. **M.J. Simpson**, B.H. Foy and S.W. McCue (2013). Travelling waves for a velocity-jump model of cell migration and proliferation. Mathematical Biosciences. 244, 98 - 106.**M.J. Simpson**, B.J. Binder, P. Haridas, B.K. Wood, K.K. Treloar, D.L.S. McElwain and R.E. Baker (2013). Experimental and modelling investigations of monolayer development with clustering. Bulletin of Mathematical Biology. 75, 871 - 889.**M.J. Simpson**, K.K. Treloar, B.J. Binder, P. Haridas, K.J. Manton, D.I. Leavesley, D.L.S. McElwain and R.E. Baker (2013). Quantifying the roles of cell motility and cell proliferation in a circular barrier assay. Journal of the Royal Society Interface. 10, 20130007.- K.K. Treloar,
**M.J. Simpson**and S.W. McCue (2013). Velocity-jump processes with proliferation. Journal of Physics A: Mathematical and Theoretical. 46, 015003. Highlighted by IOP Insights. **M.J. Simpson**, A.J. Ellery, S.W. McCue and R.E. Baker (2013). Critical timescales and time intervals for coupled linear processes. ANZIAM Journal. 54, 127 - 142.- A.J. Ellery,
**M.J. Simpson**, S.W. McCue and R.E. Baker (2012). Moments of action provide insight into critical times for advection-diffusion-reaction processes. Physical Review E. 86, 031136. **M.J. Simpson**and G.N. Mercer (2012). Infectious disease modelling. ANZIAM Journal. 54, 1 - 2.- B.J. Binder, J.V. Ross and
**M.J. Simpson**(2012). A hybrid model for studying spatial aspects of infectious diseases. ANZIAM Journal. 54, 37 - 49. - S.T. Johnston,
**M.J. Simpson**and R.E. Baker (2012). Mean-field descriptions of collective migration with strong adhesion. Physical Review E. 85, 051922. - M.J. Plank and
**M.J. Simpson**(2012). Models of collective cell behaviour with crowding effects: comparing lattice-based and lattice-free approaches. Journal of the Royal Society Interface. 9, 2983 - 2996. - A.J. Ellery,
**M.J. Simpson**, S.W. McCue and R.E. Baker (2012). Critical timescales for advection–diffusion–reaction processes. Physical Review E. 85, 041135. - R.E. Baker and
**M.J. Simpson**(2012). Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation and travelling waves. Physica A: Statistical Mechanics and its Applications. 391, 3729 - 3750. **M.J. Simpson**and A.J. Ellery (2012). An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell. Applied Mathematical Modelling. 36, 3329 - 3334.- K.K. Treloar,
**M.J. Simpson**and S.W. McCue (2011). Velocity-jump models with crowding effects. Physical Review E. 84, 061920. - S.W. Chang, T.P. Clement,
**M.J. Simpson**and K-K. Lee (2011). Does sea-level rise have an impact on saltwater intrusion? Advances in Water Resources. 34, 1283 - 1291. **M.J. Simpson**and R.E. Baker (2011). Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena. Physical Review E. 83, 051922.- A.J. Ellery and
**M.J. Simpson**(2011). An analytical method to solve a general class of nonlinear reactive transport models. Chemical Engineering Journal. 169, 313 - 318. **M.J. Simpson**, R.E. Baker and S.W. McCue (2011). Models of collective cell spreading with variable cell aspect ratio: A motivation for degenerate diffusion models. Physical Review E. 83, 021901.**M.J. Simpson**, C. Towne, D.L.S. McElwain and Z. Upton (2010). Migration of breast cancer cells: Understanding the roles of volume exclusion and cell-to-cell adhesion. Physical Review E. 82, 041901.- R.E. Baker and
**M.J. Simpson**(2010). Correcting mean-field approximations for birth-death-movement processes. Physical Review E. 82, 041905. **M.J. Simpson**, K.A. Landman and B.D. Hughes (2010). Cell invasion with proliferation mechanisms motivated by time-lapse data. Physica A: Statistical Mechanics and its Applications. 389, 3779 - 3790.- A.E. Fernando, K.A. Landman and
**M.J. Simpson**(2010). Nonlinear diffusion and exclusion processes. Physical Review E. 81, 011903. **M.J. Simpson**, K.A. Landman, B.D. Hughes and A.E. Fernando (2010). A model for mesoscale patterns in motile populations. Physica A: Statistical Mechanics and its Applications. 389, 1412 - 1424.**M.J. Simpson**, B.D. Hughes and K.A. Landman (2009). Diffusing populations: Ghosts or Folks? Australasian Journal of Engineering Education. 15, 59 - 68.**M.J. Simpson**, K.A. Landman and B.D. Hughes (2009). Pathlines in exclusion processes. Physical Review E. 79, 031920.**M.J. Simpson**(2009). Depth-averaging errors in reactive transport modelling. Water Resources Research. 45, W02505.**M.J. Simpson**, K.A. Landman and B.D. Hughes (2009). Distinguishing between directed and undirected cell motility within an invading cell population. Bulletin of Mathematical Biology. 71, 781 - 799.**M.J. Simpson**, K.A. Landman and B.D. Hughes (2009). Multi-species simple exclusion processes. Physica A: Statistical Mechanics and its Applications. 388, 399 - 406.- B.J. Binder, K.A. Landman,
**M.J. Simpson**, M. Mariani and D.F. Newgreen (2008). Modeling proliferative tissue growth: a general approach and an avian case study. Physical Review E. 78, 031912. - K.A. Landman,
**M.J. Simpson**and G.J. Pettet (2008). Tactically-driven nonmonotone travelling waves. Physica D: Nonlinear Phenomena. 237, 678 - 691. **M.J. Simpson**and K.A. Landman (2008). Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms. Mathematics and Computers in Simulation. 77, 9 - 21.**M.J. Simpson**(2008). Discussion of Direct and split operator approaches with ELLAM for reactive transport equations. AIChE Journal. 54, 588 - 588.**M.J. Simpson**, A. Merrifield, K.A. Landman and B.D. Hughes (2007). Simulating invasion with cellular automata: connecting cell-scale and population-scale properties. Physical Review E. 76, 021918.**M.J. Simpson**and K.A. Landman (2007). Nonmonotone chemotactic invasion: High-resolution simulations, phase plane analysis and new benchmark problems. Journal of Computational Physics. 225, 6-12.**M.J. Simpson**and K.A. Landman (2007). Analysis of split operator methods applied to reactive transport with Monod kinetics. Advances in Water Resources. 30, 2026 - 2033.**M.J. Simpson**, K.A. Landman and K. Bhaganagarapu (2007). Coalescence of interacting cell populations. Journal of Theoretical Biology. 247, 525 - 543.- K.A. Landman,
**M.J. Simpson**and D.F. Newgreen (2007). Mathematical and experimental insight into the development of the enteric nervous system and Hirschsprung's Disease. Development, Growth and Differentiation. 49, 277 - 286. **M.J. Simpson**, D.C. Zhang, M. Mariani, K.A. Landman and D.F. Newgreen (2007). Cell proliferation drives neural crest cell invasion of the intestine. Developmental Biology. 302, 553 - 568. Selected for the cover of Developmental Biology.**M.J. Simpson**(2007). Reply to comment on Computing residence times for flow towards a pumping well: Nomograph solution and validity of the small draw-down approximation. Hydrogeology Journal. 15, 431 - 432.**M.J. Simpson**, K.A. Landman, B.D. Hughes and D.F. Newgreen (2006). Looking inside an invasion wave of cells using continuum models: Proliferation is the key. Journal of Theoretical Biology. 243, 343 - 360.**M.J. Simpson**, K.A. Landman and D.F. Newgreen (2006). Chemotactic and diffusive migration on a non-uniformly growing domain: Numerical algorithm development and applications. Journal of Computational and Applied Mathematics. 192, 282 - 300.**M.J. Simpson**and K.A. Landman (2006). Characterizing and minimizing the operator split error for Fisher's equation. Applied Mathematics Letters. 19, 604 - 612.**M.J. Simpson**, T.P. Clement and F.E. Yeomans (2006). Erratum, Analytical model for computing residence times near a pumping well. Groundwater. 44, 509 - 510.**M.J. Simpson**, K.A. Landman and T.P. Clement (2005). Assessment of a non-traditional operator split algorithm for simulation of reactive transport. Mathematics and Computers in Simulation. 70, 44 - 60.**M.J. Simpson**(2005). Computing residence times for flow towards a pumping well: Nomograph solution and validity of the small draw-down approximation. Hydrogeology Journal. 13, 889 - 894.- K.A. Landman,
**M.J. Simpson**, J.L. Slater and D.F. Newgreen (2005). Diffusive and chemotactic cellular migration: smooth and discontinuous travelling wave solutions. SIAM Journal on Applied Mathematics. 65, 1420 - 1442. **M.J. Simpson**(2004). SEAWAT-2000: Variable-density flow processes and integrated MT3DMS transport processes. Groundwater. 42, 642 - 645.**M.J. Simpson**and T.P. Clement (2004). Improving the worthiness of the Henry problem as a benchmark for density-dependent ground water flow problems. Water Resources Research. 40, W01504.**M.J. Simpson**, T.P. Clement and F.E. Yeomans (2003). Analytical model for computing residence times near a pumping well. Groundwater. 41, 351 - 354.**M.J. Simpson**, T.P. Clement and T.A. Gallop (2003). Laboratory and numerical investigation of flow and transport near a seepage-face boundary. Groundwater. 41, 690 - 700.**M.J. Simpson**and T.P. Clement (2003). A theoretical analysis of the worthiness of Henry and Elder problems as benchmarks of density-dependent groundwater flow models. Advances in Water Resources. 26, 17 - 31.**M.J. Simpson**and T.P. Clement (2003). Comparison of finite difference and finite element solutions to the variably saturated flow equation. Journal of Hydrology. 270, 49 - 64.