Research
Students and postdocs
Current postdocs:
Current PhD students:
- Anil Cengiz
- Samantha Linn
- Tory Richardson
Former PhD students:
- Elias Clark, graduated 2023, now at Metrum Research Group
- Jacob Madrid, graduated 2023, now a postdoc at Duke University
- Claire Plunkett, graduated 2023, now at Teledyne Scientific
- Amanda Alexander, graduated 2022, now a postdoc at U of Houston
Current and former undergraduates:
- Alex Gilsoul, Fall 2023
- Guang Yang, Summer 2022
- Brian Bettinson, Fall 2021
- Noel McAllister, Spring 2021 & Summer 2021
- Elijah Counterman, Fall 2020 & Spring 2021
- Emma Coates, Fall 2020
- Taylor Yates, Fall 2019
- Hannah Choi, Fall 2017 & Spring 2018
- Chong Wang, Summer 2017
- Bo Zhu, Summer 2017
- Jacob Madrid, Summer & Fall 2016
- Daniel Armstrong, Spring 2016
- Marie Tuft, Fall 2014 & Spring 2015
- Oliver Richardson, Fall 2014 & Spring 2015
- Braden Schaer, Fall 2014 & Spring 2015
- Anand Singh, Fall 2014 & Spring 2015
- Adela Yang, Summer 2014
- Ana Martinez, Summer 2014
- Jina Yun, Summer 2013
- Andrew Gao, Summer 2013
- Charnelle Bland, Summer 2012
- Kirsten Bell, Summer 2012
- Priyanka Nadar, Summer 2011
- Molly Cinderella, Summer 2010
Funding and awards
- NSF DMS-2325258, 2023-2026: eMB: Collaborative Research: Stochasticity in ovarian aging and biotechnologies for menopause delay
- NSF DMS-1944574, 2020-2025: CAREER: How diffusion, dimension, geometry, and redundancy affect cellular dynamics.
- NSF DMS-1814832, 2018-2021: Diffusion in stochastic environments: analysis and biological applications.
- SIAM Life Sciences Early Career Prize, 2018.
- NSF DMS RTG-1148230, Co-PI 2016-2020: Research training in mathematical and computational biology.
Select research areas
Medication adherence
- 87. Incretin mimetics for weight loss forgive nonadherence
A Cengiz, CC Wu, SD Lawley
Diabetes, Obesity and Metabolism, in press (medRxiv:2025.03.22.25324451) - 85. Less frequent dosing of GLP-1 receptor agonists as a viable weight maintenance strategy
CC Wu, A Cengiz, SD Lawley
Obesity, in press - 81. How missed doses of antibiotics affect bacteria growth dynamics
HR Tung, SD Lawley
Bulletin of Mathematical Biology, 87(58), 2025 - 80. Alternative dosing regimens of GLP-1 receptor agonists may reduce costs and maintain weight loss efficacy
A Cengiz, CC Wu, SD Lawley
Diabetes, Obesity and Metabolism, 27(4), 2025 - 72. Understanding and quantifying network robustness to stochastic inputs
HR Tung, SD Lawley
Bulletin of Mathematical Biology, 86(55), 2024 - 67. How drug onset rate and duration of action affect drug forgiveness
ED Clark, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2024 - 58. Should patients skip late doses of medication? A pharmacokinetic perspective
ED Clark, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2022 - 56. A pharmacokinetic and pharmacodynamic analysis of drug forgiveness
NP McAllister, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2022 - 55. Designing drug regimens that mitigate nonadherence
ED Counterman, SD Lawley
Bulletin of Mathematical Biology, 84(20), 2022 (arXiv:2108.08358)
Awarded 2023 Lee A. Segel Best Student Paper Prize of the Society for Mathematical Biology - 52. What should patients do if they miss a dose of medication? A theoretical approach
ED Counterman, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2021 (arXiv:2102.05442)
Ovarian aging and menopause timing and delay
- 90. On modeling ovarian aging and menopause timing
SD Lawley, N Santoro, J Johnson
Submitted (bioRxiv:2025.04.07.647646) - 86. Prolonging youth or prolonging perimenopause? Beware the monkey's paw
N Santoro, SD Lawley, MD Sammel, J Johnson
Menopause, in press - 84. Modeling the extension of ovarian function after therapeutic targeting of the primordial follicle reserve
J Johnson, JW Emerson, A Smith, K Medina, EE Telfer, RA Anderson, SD Lawley
Human Reproduction Update, dmaf009, 2025 - 70. Modeling delay of age at natural menopause with planned tissue cryopreservation and autologous transplantation
J Johnson, SD Lawley, JW Emerson, K Oktay
American Journal of Obstetrics & Gynecology, 2024
Try our menopause delay calculator - 68. Mathematical recapitulation of the end stages of human ovarian aging
SD Lawley, MD Sammel, N Santoro, J Johnson
Science Advances, 10(2), 2024 - 63. Why is there an "oversupply" of human ovarian follicles?
SD Lawley, J Johnson
Biology of Reproduction, 108(5), 2023 - 64. Slowest first passage times, redundancy, and menopause timing
SD Lawley, J Johnson
Journal of Mathematical Biology, 86(90), 2023 - 60. Recapitulating human ovarian aging using random walks
J Johnson, JW Emerson, SD Lawley
PeerJ, 10:e13941, 2022
All publications
Submitted:
- 90. On modeling ovarian aging and menopause timing
SD Lawley, N Santoro, J Johnson
Submitted (bioRxiv:2025.04.07.647646) - 89. First passage times with fast immigration
HR Tung, SD Lawley
Submitted (arXiv:2502.10915) - 88. Small fluctuations induce rapid extinction in stochastic population models
JB Madrid, JP Keener, SD Lawley
Submitted
In press:
- 87. Incretin mimetics for weight loss forgive nonadherence
A Cengiz, CC Wu, SD Lawley
Diabetes, Obesity and Metabolism, in press (medRxiv:2025.03.22.25324451) - 86. Prolonging youth or prolonging perimenopause? Beware the monkey's paw
N Santoro, SD Lawley, MD Sammel, J Johnson
Menopause, in press - 85. Less frequent dosing of GLP-1 receptor agonists as a viable weight maintenance strategy
CC Wu, A Cengiz, SD Lawley
Obesity, in press
2025:
- 84. Modeling the extension of ovarian function after therapeutic targeting of the primordial follicle reserve
J Johnson, JW Emerson, A Smith, K Medina, EE Telfer, RA Anderson, SD Lawley
Human Reproduction Update, dmaf009, 2025 - 83. Reaction kinetics of membrane receptors: a spatial modeling approach
A Cengiz, SD Lawley
Journal of Mathematical Biology, 90(57), 2025 (arXiv:2501.13837) - 82. Cover times with stochastic resetting
S Linn, SD Lawley
Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(4), 2025 (arXiv:2406.12154) - 81. How missed doses of antibiotics affect bacteria growth dynamics
HR Tung, SD Lawley
Bulletin of Mathematical Biology, 87(58), 2025 - 80. Alternative dosing regimens of GLP-1 receptor agonists may reduce costs and maintain weight loss efficacy
A Cengiz, CC Wu, SD Lawley
Diabetes, Obesity and Metabolism, 27(4), 2025
2024:
- 79. Competition of many searchers
SD Lawley
Invited chapter in Target Search Problems, editors: DS Grebenkov, R Metzler, G Oshanin (arXiv:2310.02157) - 78. A reaction network model of microscale liquid-liquid phase separation reveals effects of spatial dimension
J Kim, SD Lawley, J Kim
Journal of Chemical Physics, 161(20), 2024 - 77. Narrow escape with imperfect reactions
A Cengiz, SD Lawley
Physical Review E, 110(5), 2024
Promoted by the editors as an "Editor's Suggestion" featured article - 76. Fast decisions reflect biases; slow decisions do not
S Linn, SD Lawley, BR Karamched, ZP Kilpatrick, K Josic
Physical Review E, 110(2), 2024 (arXiv:2401.00306)
Press coverage in New Scientist - 75. Hitting probabilities for fast stochastic search
S Linn, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 57(30), 2024 (arXiv:2404.01142) - 74. Boundary homogenization for partially reactive patches
CE Plunkett, SD Lawley
Multiscale Modeling and Simulation, 22(2), 2024 (arXiv:2405.11310) - 73. First hitting time of a one-dimensional Levy flight to small targets
D Gomez, SD Lawley
SIAM Journal on Applied Mathematics, 84(3), 2024 (arXiv:2307.06274) - 72. Understanding and quantifying network robustness to stochastic inputs
HR Tung, SD Lawley
Bulletin of Mathematical Biology, 86(55), 2024 - 71. Cover times of many diffusive or subdiffusive searchers
H Kim, SD Lawley
SIAM Journal on Applied Mathematics, 84(2), 2024 (arXiv:2308.13417) - 70. Modeling delay of age at natural menopause with planned tissue cryopreservation and autologous transplantation
J Johnson, SD Lawley, JW Emerson, K Oktay
American Journal of Obstetrics & Gynecology, 2024
Try our menopause delay calculator - 69. Cover times of many random walkers on a discrete network
H Kim, SD Lawley
Physical Review E, 109(1), 2024 (arXiv:2310.07905) - 68. Mathematical recapitulation of the end stages of human ovarian aging
SD Lawley, MD Sammel, N Santoro, J Johnson
Science Advances, 10(2), 2024 - 67. How drug onset rate and duration of action affect drug forgiveness
ED Clark, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2024
2023:
- 66. First passage times under frequent stochastic resetting
S Linn, SD Lawley
Physical Review E, 108(2), 2023 - 65. Extreme statistics of superdiffusive Levy flights and every other Levy subordinate Brownian motion
SD Lawley
Journal of Nonlinear Science, 33(53), 2023 (arXiv:2103.07851) - 64. Slowest first passage times, redundancy, and menopause timing
SD Lawley, J Johnson
Journal of Mathematical Biology, 86(90), 2023 - 63. Why is there an "oversupply" of human ovarian follicles?
SD Lawley, J Johnson
Biology of Reproduction, 108(5), 2023 - 62. Boundary homogenization for patchy surfaces trapping patchy particles
CE Plunkett, SD Lawley
Journal of Chemical Physics, 158(9), 2023
2022:
- 61. Inferences from FRAP data are model dependent: a subdiffusive analysis
AM Alexander, SD Lawley
Biophysical Journal, 121(20), 2022 - 60. Recapitulating human ovarian aging using random walks
J Johnson, JW Emerson, SD Lawley
PeerJ, 10:e13941, 2022 - 59. Extreme hitting probabilities for diffusion
S Linn, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 55(34), 2022 (arXiv:2110.11277) - 58. Should patients skip late doses of medication? A pharmacokinetic perspective
ED Clark, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2022 - 57. Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects
SD Lawley, HF Nijhout, MC Reed
Journal of Mathematical Biology, 84(40), 2022 - 56. A pharmacokinetic and pharmacodynamic analysis of drug forgiveness
NP McAllister, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2022 - 55. Designing drug regimens that mitigate nonadherence
ED Counterman, SD Lawley
Bulletin of Mathematical Biology, 84(20), 2022 (arXiv:2108.08358)
Awarded 2023 Lee A. Segel Best Student Paper Prize of the Society for Mathematical Biology
2021:
- 54. Reaction-subdiffusion equations with species-dependent movement
AM Alexander, SD Lawley
SIAM Journal on Applied Mathematics, 81(6), 2021 (arXiv:2104.11151) - 53. Singularities of invariant densities for random switching between two linear ODEs in 2D
Y Bakhtin, T Hurth, SD Lawley, JC Mattingly
SIAM Journal on Applied Dynamical Systems, 20(40), 2021 (arXiv:2009.01299) - 52. What should patients do if they miss a dose of medication? A theoretical approach
ED Counterman, SD Lawley
Journal of Pharmacokinetics and Pharmacodynamics, 2021 (arXiv:2102.05442) - 51. Revising Berg-Purcell for finite receptor kinetics
G Handy, SD Lawley
Biophysical Journal, 120(11), 2021 (arXiv:2101.05956) - 50. Extreme first passage times of piecewise deterministic Markov processes
SD Lawley
Nonlinearity, 34(5), 2021 (arXiv:1912.03438) - 49. Bimolecular binding rates for pairs of spherical molecules with small binding sites
CE Plunkett, SD Lawley
Multiscale Modeling and Simulation, 19(1), 2021 (arXiv:2002.11703) - 48. The effects of fast inactivation on conditional first passage times of mortal diffusive searchers
SD Lawley
SIAM Journal on Applied Mathematics, 81(1), 2021 (arXiv:2003.05515)
2020:
- 47. Extreme first passage times for random walks on networks
SD Lawley
Physical Review E, 102(6), 2020
Promoted by the editors as an "Editor's Suggestion" featured article - 46. Subdiffusion-limited fractional reaction-subdiffusion equations with affine reactions: solution, stochastic paths, and applications
SD Lawley
Physical Review E, 102(4), 2020 - 45. Anomalous reaction-diffusion equations for linear reactions
SD Lawley
Physical Review E, 102(3), 2020 - 44. Extreme statistics of anomalous subdiffusion following a fractional Fokker-Planck equation: Subdiffusion is faster than normal diffusion
SD Lawley
Journal of Physics A: Mathematical and Theoretical, 53(38), 2020 (arXiv:2004.14994) - 43. Competition between slow and fast regimes for extreme first passage times of diffusion
JB Madrid, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 53(33), 2020 (arXiv:2004.05414) - 42. Receptor organization determines the limits of single-cell source location detection
SD Lawley, AE Lindsay, CE Miles
Physical Review Letters, 125(1), 2020 - 41. Asymptotic and numerical analysis of a stochastic PDE model of volume transmission
SD Lawley, V Shankar
Multiscale Modeling and Simulation, 18(2), 2020 - 40. Spiracular fluttering increases oxygen uptake
SD Lawley, MC Reed, HF Nijhout
PLOS ONE, 15(5), 2020 - 39. Interaction between switching diffusivities and cellular microstructure
P Murphy, PC Bressloff, SD Lawley
Multiscale Modeling and Simulation, 18(2), 2020 - 38. Distribution of extreme first passage times of diffusion
SD Lawley
Journal of Mathematical Biology, 80(7), 2020 (arXiv:1910.12170) - 37. Effective permeability of a gap junction with age-structured switching
PC Bressloff, SD Lawley, P Murphy
SIAM Journal on Applied Mathematics, 80(1), 2020 - 36. Universal formula for extreme first passage statistics of diffusion
SD Lawley
Physical Review E, 101(1), 2020 - 35. A probabilistic approach to extreme statistics of Brownian escape times in dimensions 1, 2, and 3
SD Lawley, JB Madrid
Journal of Nonlinear Science, 2020 (arXiv:1907.07515)
2019:
- 34. Boundary homogenization for trapping patchy particles
SD Lawley
Physical Review E, 100(3), 2019 - 33. Diffusive search for diffusing targets with fluctuating diffusivity and gating
SD Lawley, CE Miles
Journal of Nonlinear Science, 29(6), 2019 - 32. How receptor surface diffusion and cell rotation increase association rates
SD Lawley, CE Miles
SIAM Journal on Applied Mathematics, 79(3), 2019 - 31. First passage time distribution of multiple impatient particles with reversible binding
SD Lawley, JB Madrid
Journal of Chemical Physics, 150(21), 2019
Promoted by the editors as an "Editor's pick" featured article - 30. Electrodiffusive flux through a stochastically gated ion channel
SD Lawley, JP Keener
SIAM Journal on Applied Mathematics, 79(2), 2019 - 29. Protein concentration gradients and switching diffusions
PC Bressloff, SD Lawley, P Murphy
Physical Review E, 99(3), 2019 - 28. Role of trap recharge time on the statistics of captured particles
G Handy, SD Lawley, A Borisyuk
Physical Review E, 99(2), 2019
2018:
- 27. Blowup from randomly switching between stable boundary conditions for the heat equation
SD Lawley
Communications in Mathematical Sciences, 16(4), 2018 - 26. Analysis of non-processive molecular motor transport using renewal reward theory
CE Miles, SD Lawley, JP Keener
SIAM Journal on Applied Mathematics, 78(5), 2018 - 25. Diffusion in an age-structured randomly switching environment
PC Bressloff, SD Lawley, P Murphy
Journal of Physics A: Mathematical and Theoretical, 51(31), 2018 - 24. A probabilistic analysis of volume transmission in the brain
SD Lawley
SIAM Journal on Applied Mathematics, 14(3), 2018 - 23. Receptor recharge time drastically reduces the number of captured particles
G Handy, SD Lawley, A Borisyuk
PLOS Computational Biology, 14(3), 2018 - 22. Smooth invariant densities for random switching on the torus
Y Bakhtin, T Hurth, SD Lawley, JC Mattingly
Nonlinearity, 31(4), 2018 (arXiv:1708.01390)
2017:
- 21. Diffusive transport in the presence of stochastically gated absorption
PC Bressloff, BR Karamched, SD Lawley, E Levien
Physical Review E, 96(2), 2017 - 20. Rebinding in biochemical reactions on membranes
SD Lawley, JP Keener
Physical Biology, 14(5), 2017 - 19. Hybrid colored noise process with space-dependent switching rates
PC Bressloff, SD Lawley
Physical Review E, 96(1), 2017 - 18. Mean first passage times for piecewise deterministic Markov processes and the effects of critical points
PC Bressloff, SD Lawley
Journal of Statistical Mechanics: Theory and Experiment, 063202, 2017 - 17. Temporal disorder as a mechanism for spatially heterogeneous diffusion
PC Bressloff, SD Lawley
Physical Review E - Rapid Communication, 95(6), 2017 - 16. Residence times of a Brownian particle with temporal heterogeneity
PC Bressloff, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 50(19), 2017 - 15. Dynamically active compartments coupled by a stochastically-gated gap junction
PC Bressloff, SD Lawley
Journal of Nonlinear Science, 27(5), 2017
2016:
- 14. Including rebinding reactions in well-mixed models of distributive biochemical reactions
SD Lawley, JP Keener
Biophysical Journal, 111(10), 2016 - 13. Diffusion on a tree with stochastically-gated nodes
PC Bressloff, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 49(24), 2016
Named to the journal's "Highlights of 2016" collection - 12. Boundary value problems for statistics of diffusion in a randomly switching environment: PDE and SDE perspectives
SD Lawley
SIAM Journal on Applied Dynamical Systems, 15(3), 2016 - 11. Neurotransmitter concentrations in the presence of neural switching in one dimension
SD Lawley, J Best, MC Reed
Discrete and Continuous Dynamical Systems - Series B, 21(7), 2016
2015:
- 10. Stochastically gated diffusion-limited reactions for a small target in a bounded domain
PC Bressloff, SD Lawley
Physical Review E, 92(6), 2015 - 9. Escape from subcellular domains with randomly switching boundaries
PC Bressloff, SD Lawley
Multiscale Modeling and Simulation, 13(4), 2015 - 8. Coarse-graining intermittent intracellular transport: Two- and three-dimensional models
SD Lawley, M Tuft, HA Brooks
Physical Review E, 92(4), 2015 - 7. A new derivation of Robin boundary conditions through homogenization of a stochastically switching boundary
SD Lawley, JP Keener
SIAM Journal on Applied Dynamical Systems, 14(4), 2015 - 6. Escape from a potential well with a randomly switching boundary
PC Bressloff, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 48(22), 2015 - 5. Moment equations for a piecewise deterministic PDE
PC Bressloff, SD Lawley
Journal of Physics A: Mathematical and Theoretical, 48(10), 2015
Chosen by editors as "Publisher's pick" featured article - 4. Stochastic switching in infinite dimensions with applications to random parabolic PDE
SD Lawley, JC Mattingly, MC Reed
SIAM Journal on Mathematical Analysis, 47(4), 2015
2014:
- 3. Sensitivity to switching rates in stochastically switched ODEs
SD Lawley, JC Mattingly, MC Reed
Communications in Mathematical Sciences, 12(7), 2014 - 2. Mathematical modeling of the effects of glutathione on arsenic methylation
SD Lawley, J Yun, M Gamble, M Hall, MC Reed, HF Nijhout
Theoretical Biology and Medical Modelling, 11(20), 2014
2011:
- 1. Mathematical model insights into arsenic detoxification
SD Lawley, M Cinderella, M Hall, M Gamble, H F Nijhout, MC Reed
Theoretical Biology and Medical Modelling, 8(31), 2011