# Research

I am a mathematical biologist specializing in both the analysis of stochastic processes and their application to biological problems.

### Students

##### Current PhD students:

- Amanda Alexander
- Elias Clark
- Jacob Madrid
- Claire Plunkett

##### Current and former undergraduates:

- 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-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.

### Publications

##### Submitted:

- 58.
*Extreme hitting probabilities for diffusion*

S Linn, SD Lawley

Submitted (arXiv:2110.11277) - 57.
*Designing drug regimens that mitigate nonadherence*

ED Counterman, SD Lawley

Submitted (arXiv:2108.08358) - 56.
*Spiracular fluttering decouples oxygen uptake and water loss: a stochastic PDE model of respiratory water loss in insects*

SD Lawley, HF Nijhout, MC Reed

Submitted - 55.
*Extreme statistics of superdiffusive Levy flights and every other Levy subordinate Brownian motion*

SD Lawley

Submitted (arXiv:2103.07851)

##### In press:

- 54.
*Reaction-subdiffusion equations with species-dependent movement*

AM Alexander, SD Lawley

SIAM Journal on Applied Mathematics, in press (arXiv:2104.11151)

##### 2021:

- 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