# Browse By Person: Simpson, Matthew

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**98**.## Journal Article

Johnston, Stuart, Baker, Ruth, & Simpson, Matthew J.
(2017)
A new and accurate continuum description of moving fronts.

*New Journal of Physics*. (In Press)
2

Zheng, Minling, Liu, Fawang, Liu, Qingxia, Burrage, Kevin, & Simpson, Matthew J.
(2017)
Numerical solution of the time fractional reaction-diffusion equation with a moving boundary.

*Journal of Computational Physics*. (In Press)

Jin, Wang, Penington, Catherine J., McCue, Scott W., & Simpson, Matthew J.
(2016)
Stochastic simulation tools and continuum models
for describing two-dimensional collective cell spreading with universal growth functions.

*Physical Biology*,*13*(5), 056003.

Andrews, Christine J., Cuttle, Leila, & Simpson, Matthew J.
(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*, pp. 542-549.
1

Ellery, Adam J., Baker, Ruth E., & Simpson, Matthew J.
(2016)
An analytical method for disentangling the roles of adhesion and crowding for random walk models on a crowded lattice.

*Physical Biology*,*13*(5), 05LT02.

Johnston, Stuart T., Ross, Joshua V., Binder, Benjamin J., McElwain, D.L. Sean, Haridas, Parvathi, & Simpson, Matthew J.
(2016)
Quantifying the effect of experimental design choices for in vitro scratch assays.

*Journal of Theoretical Biology*,*400*, pp. 19-31.

Penington, Catherine J., Baker, Ruth E., & Simpson, Matthew J.
(2016)
Exits in order: How crowding affects particle lifetimes.

*The Journal of Chemical Physics*,*144*(24), Article no. 244107.

Taylor, Paul R., Baker, Ruth E., Simpson, Matthew J., & Yates, Christian A.
(2016)
Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment
approaches.

*Journal of the Royal Society Interface*,*13*(120), Article no. 20160336.

Ellery, Adam J., Baker, Ruth E., & Simpson, Matthew J.
(2016)
Communication: Distinguishing between short-time non-Fickian diffusion and long-time Fickian diffusion for a random walk on a crowded lattice.

*The Journal of Chemical Physics*,*144*(17), Article no. 171104.

Johnston, Stuart T., Baker, Ruth E., & Simpson, Matthew J.
(2016)
Filling the gaps: A robust description of adhesive birth-death-movement processes.

*Physical Review E*,*93*, Article no. 042413.
4

Haridas, Parvathi, McGovern, Jacqui A., Kashyap, Abhishek S., McElwain, D.L. Sean, & Simpson, Matthew J.
(2016)
Standard melanoma-associated markers do not identify the MM127 metastatic melanoma cell line.

*Scientific Reports*,*6*, Article Number-24569.
9

Binder, Benjamin J. & Simpson, Matthew J.
(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*(4), pp. 3438-3446.

Jin, Wang, Shah, Esha T., Penington, Catherine J., McCue, Scott W., Chopin, Lisa K., & Simpson, Matthew J.
(2016)
Reproducibility of scratch assays is affected by the initial degree of confluence: Experiments, modelling and model selection.

*Journal of Theoretical Biology*,*390*, pp. 136-145.
3

2

Binny, Rachelle N., Haridas, Parvathi, James, Alex, Law, Richard, Simpson, Matthew, & Plank, Michael J.
(2016)
Spatial structure arising from neighbour-dependent bias in collective cell movement.

*PeerJ*,*4*, e1689.
5

1

Irons, Carolyn, Plank, Michael J., & Simpson, Matthew J.
(2016)
Lattice-free models of directed cell motility.

*Physica A: Statistical Mechanics and its Applications*,*442*, pp. 110-121.
2

Jazaei, Farhad, Simpson, Matthew J., & Clement, T. Prabhakar
(2016)
Spatial analysis of aquifer response times for radial flow processes: Nondimensional analysis and laboratory-scale tests.

*Journal of Hydrology*,*532*, pp. 1-8.
1

Ellery, Adam, Baker, Ruth, McCue, Scott W., & Simpson, Matthew
(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*, pp. 74-84.
1

2

Jazaei, Farhad, Simpson, Matthew J., & Clement, T. Prabhakar
(2016)
Understanding time scales of diffusive fluxes and the implication for steady state and steady shape conditions.

*Geophysical Research Letters*,*43*.

Ellery, Adam, Baker, Ruth, & Simpson, Matthew
(2015)
Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes.

*Physical Biology*,*12*(6), 066010.
4

1

2

Simpson, Matthew, Sharp, Jesse, Morrow, Liam, & Baker, Ruth
(2015)
Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain.

*PLOS ONE*,*108*(9), e01388.
1

1

Simpson, Matthew & Baker, Ruth
(2015)
Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension.

*Journal of Chemical Physics*,*143*, 094109.
20

1

2

Taylor, Paul, Yates, Christian, Simpson, Matthew, & Baker, Ruth
(2015)
Reconciling transport models across scales: The role of volume exclusion.

*Physical Review E*,*92*, 040701.
7

2

1

Simpson, Matthew & Baker, Ruth
(2015)
Special Issue on Spatial Moment Techniques for Modelling Biological Processes.

*Bulletin of Mathematical Biology*,*77*(4), pp. 581-585.
6

1

1

Simpson, Matthew & Morrow, Liam
(2015)
Analytical model of reactive transport processes with
spatially variable coefficients.

*Royal Society Open Science*,*2*, 140348..

Vo, Brenda N., Drovandi, Christopher C., Pettitt, Anthony N., & Simpson, Matthew J.
(2015)
Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation.

*Mathematical Biosciences*,*263*, pp. 133-142.
15

3

3

Simpson, Matthew, Sharp, Jesse, & Baker, Ruth
(2015)
Survival probability for a diffusive process on a growing domain.

*Physical Review E*,*91*, 042701.
17

3

4

Simpson, Matthew & McCue, Scott W.
(2015)
ANZIAM 2015.

*Gazette of the Australian Mathematical Society*,*42*(1), pp. 23-25.
9

Markham, Deborah C., Simpson, Matthew, & Baker, Ruth
(2015)
Choosing an appropriate modelling framework for analysing multispecies co-culture cell biology experiments.

*Bulletin of Mathematical Biology*,*77*(4), pp. 713-734.
6

Johnston, Stuart, Shah, Esha Tushit, Chopin, Lisa K., McElwain, Sean, & Simpson, Matthew
(2015)
Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model.

*BMC Systems Biology*,*9*(38).
7

6

Johnston, Stuart T., Simpson, Matthew J., & Baker, Ruth E.
(2015)
Modelling the movement of interacting cell populations: A moment dynamics approach.

*Journal of Theoretical Biology*,*370*, pp. 81-92.
4

3

Simpson, Matthew
(2015)
Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization.

*PLOS ONE*,*10*(2), e0117949..
4

5

Binder, Benjamin J. & Simpson, Matthew J.
(2015)
Spectral analysis of pair-correlation bandwidth: Application to cell biology images.

*Royal Society Open Science*,*2*(140494).
5

6

6

Johnston, Stuart, Simpson, Matthew, McElwain, Sean, Binder, Benjamin J., & Ross, Joshua
(2014)
Interpreting scratch assays using pair density dynamics and approximate Bayesian computation.

*Open Biology*,*4*, pp. 140097-1.
209

8

7

Treloar, Katrina, Simpson, Matthew, McElwain, Sean, & Baker, Ruth
(2014)
Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?

*Journal of Theoretical Biology*,*356*, pp. 71-84.
51

12

11

Agnew, D.J.G., Green, J.E.F., Brown, T.M., Simpson, M.J., & Binder, B.J.
(2014)
Distinguishing between mechanisms of cell aggregation using
pair-correlation functions.

*Journal of Theoretical Biology*,*352*, pp. 16-23.
11

18

17

Markham, Deborah C., Simpson, Matthew, Maini, Philip K., Gaffney, Eamonn, & Baker, Ruth
(2014)
Comparing methods for modelling spreading cell fronts.

*Journal of Theoretical Biology*,*353*, pp. 95-103.
12

4

4

Treloar, Katrina, Simpson, Matthew, Binder, Benjamin J., McElwain, Sean, & Baker, Ruth
(2014)
Assessing the role of spatial correlations during collective cell spreading.

*Scientific Reports*,*4*, 5713-1---8.
28

11

11

Johnston, Stuart, Simpson, Matthew, & McElwain, Sean
(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*(97), p. 20140325.
39

15

14

Simpson, Matthew & Ellery, Adam
(2014)
Exact series solutions of reactive transport models with general initial conditions.

*Journal of Hydrology*,*513*, pp. 7-12.
15

4

3

Young, Heather, Bergner, Annette, Simpson, Matthew, McKeown, Sonja, Anderson, Colin, & Enomoto, Hideki
(2014)
Colonizing while migrating : how do individual enteric neural crest cells behave?

*BMC Biology*,*12*(23).
32

33

28

Ellery, Adam, Simpson, Matthew, McCue, Scott W., & Baker, Ruth
(2014)
Characterizing transport through a crowded environment with different obstacle sizes.

*Journal of Chemical Physics*,*140*(5), 054108.
48

4

9

Simpson, Matthew, Sharp, Jesse, & Baker, Ruth
(2014)
Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes.

*Physica A Statistical Mechanics and its Applications*,*395*, pp. 236-246.
13

7

6

Simpson, Matthew, Haridas, Parvathi, & McElwain, Sean
(2014)
Do pioneer cells exist?

*PLOS ONE*,*9*(1), e85488.
128

4

4

Jazaei, Farhad, Simpson, Matthew, & Clement, Prabhakar
(2014)
An analytical framework for quantifying aquifer response time scales associated with transient boundary conditions.

*Journal of Hydrology*,*519*(Part B), pp. 1642-1648.
33

4

4

Johnston, Stuart, Simpson, Matthew, & Plank, Michael
(2013)
Lattice-free descriptions of collective motion with crowding and adhesion.

*Physical Review E (PRE)*,*88*(6), pp. 1-11.
1

8

Treloar, Katrina, Simpson, Matthew, Haridas, Parvathi, Manton, Kerry, Leavesley, David I., McElwain, Sean, et al.
(2013)
Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies.

*BMC Systems Biology*,*7*(137).
20

15

14

Plank, Michael & Simpson, Matthew
(2013)
Lattice-free models of cell invasion : discrete simulations and travelling waves.

*Bulletin of Mathematical Biology*,*75*(11), pp. 2150-2166.
34

8

8

Ellery, Adam, Simpson, Matthew, McCue, Scott W., & Baker, Ruth
(2013)
A simplified approach for calculating the moments of action for linear reaction-diffusion equations.

*Physical Review E (PRE)*,*88*, 054102.
118

2

2

Bowden, Lucie, Simpson, Matthew, & Baker, Ruth
(2013)
Design and interpretation of cell trajectory assays.

*Journal of the Royal Society Interface*,*10*(88), pp. 1-12.
5

1

Simpson, Matthew, Jazaei, Farhad, & Clement, Prabhakar
(2013)
How long does it take for aquifer recharge or aquifer discharge processes to reach steady state?

*Journal of Hydrology*,*501*, pp. 241-248.
23

14

14

Binder, Benjamin J. & Simpson, Matthew
(2013)
Quantifying spatial structure in experimental observations and agent-based simulations using pair-correlation functions.

*Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*,*88*(2), pp. 1-10.
124

16

15

Simpson, Matthew, Foy, Brody, & McCue, Scott W.
(2013)
Travelling waves for a velocity–jump model of cell migration and proliferation.

*Mathematical Biosciences*,*244*(2), pp. 98-106.
76

1

Treloar, Katrina & Simpson, Matthew
(2013)
Sensitivity of edge detection methods for quantifying cell
migration assays.

*PLOS ONE*,*8*(6).
178

18

17

Markham, Deborah C., Simpson, Matthew J., & Baker, Ruth E.
(2013)
Simplified method for including spatial correlations in mean-field approximations.

*Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*,*87*(6), pp. 1-10.
87

14

16

Ellery, Adam J., Simpson, Matthew J., & McCue, Scott W.
(2013)
Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)].

*Journal of Chemical Physics*,*139*(017101), pp. 1-2.
76

3

4

Simpson, Matthew, Binder, Benjamin J., Haridas, Parvathi, Wood, Benjamin, Treloar, Katrina, McElwain, Sean, et al.
(2013)
Experimental and modelling investigation of monolayer development with clustering.

*Bulletin of Mathematical Biology*,*75*(5), pp. 871-889.
35

22

22

Simpson, Matthew J., Treloar, Katrina K., Binder, Benjamin J., Haridas, Parvathi, Manton, Kerry J., Leavesley, David I., et al.
(2013)
Quantifying the roles of cell motility and cell proliferation in a circular barrier assay.

*Journal of the Royal Society. Interface*,*10*(82).
23

36

32

Simpson, Matthew, Ellery, Adam, McCue, Scott W., & Baker, Ruth
(2013)
Critical timescales and time intervals for coupled linear processes.

*ANZIAM Journal*,*54*(3), pp. 127-142.
93

3

3

Markham, Deborah C., Simpson, Matthew, Maini, Philip K., Gaffney, Eamonn, & Baker, Ruth
(2013)
Incorporating spatial correlations into multispecies mean-field models.

*Physical Review E*,*88*(5), 052713-1-052713-9.
25

9

8

Treloar, Katrina, Simpson, Matthew, & McCue, Scott W.
(2013)
Velocity jump processes with proliferation.

*Journal of Physics A : Mathematical and General*,*46*(1), pp. 1-17.
77

1

1

Simpson, Matthew & Mercer, Geoff
(2012)
Editorial : infectious disease modelling.

*ANZIAM Journal*,*54*(1-2).
171

Binder, Benjamin J., Ross, Joshua, & Simpson, Matthew
(2012)
A hybrid model for studying spatial aspects of infectious diseases.

*ANZIAM Journal*,*54*(1-2), pp. 37-49.
263

2

2

Ellery, Adam, Simpson, Matthew, McCue, Scott W., & Baker, Ruth
(2012)
Moments of action provide insight into critical times for advection–diffusion–reaction processes.

*Physical Review E (PRE)*,*86*(3).
67

10

11

Simpson, Matthew & Ellery, Adam
(2012)
An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell.

*Applied Mathematical Modelling*,*36*(7), pp. 3329-3334.
195

8

7

Johnston, Stuart, Simpson, Matthew, & Baker, Ruth
(2012)
Mean-field descriptions of collective migration with strong adhesion.

*Physical Review E*,*85*(5), 051922-1 .
67

24

24

Plank, Michael & Simpson, Matthew
(2012)
Models of collective cell behaviour with crowding effects :
comparing lattice-based and lattice-free approaches.

*Journal of the Royal Society Interface*.
36

28

28

Ellery, Adam, Simpson, Matthew, McCue, Scott W., & Baker, Ruth
(2012)
Critical time scales for advection–diffusion–reaction processes.

*Physical Review E*,*85*(4).
185

12

12

Baker, Ruth & Simpson, Matthew
(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*(14), pp. 3729-3750.
57

9

10

Chang, Sun Woo, Clement, T. Prabhakar, Simpson, Matthew J., & Lee, Kang-Kun
(2011)
Does sea-level rise have an impact on saltwater intrusion?

*Advances in Water Resources*,*34*(10), pp. 1283-1291.
442

41

48

Simpson, Matthew & Baker, Ruth
(2011)
Corrected mean-field models for spatially-dependent
advection-diffusion-reaction phenomena.

*Physical Review E*,*83*(5), 051922-1--051922-15.
78

32

32

Simpson, Matthew, Baker, Ruth, & McCue, Scott W.
(2011)
Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models.

*Physical Review E (PRE)*,*83*, 021901-1 .
122

26

29

Treloar, Katrina, Simpson, Matthew, & McCue, Scott W.
(2011)
Velocity-jump models with crowding effects.

*Physical Review E*,*84*(6), 061920-1.
142

5

5

Ellery, Adam & Simpson, Matthew
(2011)
An analytical method to solve a general class of nonlinear reactive transport models.

*Chemical Engineering Journal*,*169*(1-3), pp. 313-318.
262

15

11

Simpson, Matthew, Towne, Chris L., McElwain, Sean, & Upton, Zee
(2010)
Migration of breast cancer cells : understanding the roles of volume exclusion and cell-to-cell adhesion.

*Physical Review E (PRE)*,*82*(4), 041901-1---41901-9.
156

29

29

Baker, Ruth & Simpson, Matthew
(2010)
Correcting mean-field approximations for birth-death-movement processes.

*Physical Review E (PRE)*,*82*(4), 041905-1---41905-12.
100

35

35

Simpson, Matthew, Landman, Kerry A., & Hughes, Barry
(2010)
Cell invasion with proliferation mechanisms motivated by
time-lapse data.

*Physica A : Statistical Mechanics and its Applications*,*389*(18), pp. 3779-3790.
104

44

45

Fernando, Anthony, Landman, Kerry A., & Simpson, Matthew
(2010)
Nonlinear diffusion and exclusion processes with contact interactions.

*Physical Review E (PRE)*,*81*(1), 011903-1---11903-11.
32

34

Simpson, Matthew, Landman, Kerry A., Hughes, Barry, & Fernando, Anthony
(2010)
A model for mesoscale patterns in motile populations.

*Physica A: Statistical Mechanics and its Applications*,*389*(7), pp. 1412-1424.
69

28

29

Simpson, Matthew
(2009)
Depth-averaging errors in reactive transport modeling.

*Water Resources Research*,*45*, pp. 1-8.
3

3

Simpson, Matthew, Hughes, Barry, & Landman, Kerry
(2009)
Diffusing populations: Ghosts or folks.

*Australasian Journal of Engineering Education*,*15*(2), pp. 59-68.

Simpson, Matthew, Landman, Kerry, & Hughes, Barry
(2009)
Distinguishing between directed and undirected cell motility within an invading cell population.

*Bulletin of Mathematical Biology*,*71*(4), pp. 781-799.
5

5

Simpson, Matthew, Landman, Kerry, & Hughes, Barry
(2009)
Multi-species simple exclusion processes.

*Physica A: Statistical Mechanics and its Applications*,*388*(4), pp. 399-406.
57

62

Simpson, Matthew, Landman, Kerry, & Hughes, Barry
(2009)
Pathlines in exclusion processes.

*Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*,*79*(3), pp. 1-5.
14

16

Binder, Benjamin, Landman, Kerry, Simpson, Matthew, Mariani, Michael, & Newgreen, Don
(2008)
Modeling proliferative tissue growth: A general approach and an avian case study.

*Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*,*78*(3), pp. 1-13.
38

39

Landman, Kerry, Simpson, Matthew, & Pettet, Graeme J.
(2008)
Tactically-driven nonmonotone travelling waves.

*Physica D Nonlinear Phenomena*,*237*(5), pp. 678-691.
64

7

7

Simpson, Matthew & Landman, Kerry
(2008)
Theoretical analysis and physical interpretation of temporal truncation errors in operator split algorithms.

*Mathematics and Computers in Simulation*,*77*(1), pp. 9-21.
2

3

Simpson, Matthew & Landman, Kerry
(2007)
Analysis of split operator methods applied to reactive transport with Monod kinetics.

*Advances in Water Resources*,*30*(9), pp. 2026-2033.
19

18

Simpson, Matthew, Zhang, Dong, Mariani, Michael, Landman, Kerry, & Newgreen, Don
(2007)
Cell proliferation drives neural crest cell invasion of the intestine.

*Developmental Biology*,*302*(2), pp. 553-568.
121

109

Simpson, Matthew, Landman, Kerry, & Bhaganagarapu, Kaushik
(2007)
Coalescence of interacting cell populations.

*Journal of Theoretical Biology*,*247*(3), pp. 525-543.
7

7

Landman, Kerry, Simpson, Matthew, & Newgreen, Don
(2007)
Mathematical and experimental insights into the development of the enteric nervous system and Hirschsprung's Disease.

*Development, Growth and Differentiation*,*49*(4), pp. 277-286.
36

34

Simpson, Matthew & Landman, Kerry
(2007)
Nonmonotone chemotactic invasion: High-resolution simulations, phase plane analysis and new benchmark problems.

*Journal of Computational Physics*,*225*(1), pp. 6-12.
3

3

Simpson, Matthew, Merrifield, Alistair, Landman, Kerry, & Hughes, Barry
(2007)
Simulating invasion with cellular automata: Connecting cell-scale and population-scale properties.

*Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)*,*76*(2), pp. 1-11.
63

56

Simpson, Matthew & Landman, Kerry
(2006)
Characterizing and minimizing the operator split error for Fisher's equation.

*Applied Mathematics Letters*,*19*(7), pp. 604-612.
4

1

Simpson, Matthew, Landman, Kerry, & Newgreen, Don
(2006)
Chemotactic and diffusive migration on a nonuniformly growing domain: numerical algorithm development and applications.

*Journal of Computational and Applied Mathematics*,*192*(2), pp. 282-300.
26

25

Simpson, Matthew, Landman, Kerry, Hughes, Barry, & Newgreen, Don
(2006)
Looking inside an invasion wave of cells using continuum models: Proliferation is the key.

*Journal of Theoretical Biology*,*243*(3), pp. 343-360.
49

46

Simpson, Matthew, Landman, Kerry, & Clement, T. Prabhakar
(2005)
Assessment of a non-traditional operator split algorithm for simulation of reactive transport.

*Mathematics and Computers in Simulation*,*70*(1), pp. 44-60.
23

20

Simpson, Matthew
(2005)
Computing residence times for flow towards a pumping well: nomograph solution and validity of the small draw-down approximation.

*Hydrogeology Journal*,*13*(5-6), pp. 889-894.
4

4

Landman, Kerry, Simpson, Matthew, Slater, Jennifer, & Newgreen, Don
(2005)
Diffusive and chemotactic cellular migration: Smooth and discontinuous traveling wave solutions.

*SIAM Journal on Applied Mathematics*,*65*(4), pp. 1420-1442.
24

25