Professor Elaine Crooks

Professor

Mathematics

+44 (0) 1792 602387

e.c.m.crooks@swansea.ac.uk

Office - 324
Third Floor
Computational Foundry
Bay Campus

Available For Postgraduate Supervision

Research Links

https://orcid.org/0000-0002-9274-7528

About

My main research area is the analysis of nonlinear partial differential equations, particularly singular limits of nonlinear elliptic and parabolic PDE, asymptotic behaviour of reaction-diffusion systems, and front propagation and spreading speeds, motivated by applications such as switching properties of liquid crystals, phase transitions of materials, strongly competitive interactions and spatial segregation in population dynamics, and the characterization of the speed of spread of ecological invasions. An additional interest is the analysis of compensated convex transforms and their applications to geometric singularity detection, and, via a numerical implementation, the detection of features in images or data, removal of noise from images, identification of intersections between surfaces, etc.

Areas Of Expertise

Nonlinear partial differential equations
Singular limits of elliptic and parabolic systems
Reaction-diffusion-convection systems and travelling waves
Applications of PDE to biology
Geometric methods for image processing

Publications

Research Highlights

Cobley, R., Beggs, E., Crooks, E., Palmer, R., & Tucker, J. (2022). WORKSHOP REPORT: MASI Agenda Setting Workshop on Unconventional and Natural Computing
https://doi.org/10.23889/SURep.60483, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa60483
Orlando, A., Crooks, E., & Zhang, K. (2023). Compensated Convex-Based Transforms for Image Processing and Shape Interrogation. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging (pp. 1827-1886). Springer International Publishing
https://doi.org/10.1007/978-3-030-98661-2_106, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63730
http://dx.doi.org/10.1007/978-3-030-98661-2_106
Crooks, E. & Grinfeld, M. (2020). Minimal travelling wave speed and explicit solutions in monostable reaction-diffusion equations. Electronic Journal of Qualitative Theory of Differential Equations, 79(79), 1-9.
https://doi.org/10.14232/ejqtde.2020.1.79, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa57943
Zhang, K., Orlando, A., & Crooks, E. (2021). Compensated convexity on bounded domains, mixed Moreau envelopes and computational methods. Applied Mathematical Modelling, 94, 688-720.
https://doi.org/10.1016/j.apm.2021.01.040, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa57942
Wilson, R., Neate, A., Holton, M., Shepard, E., Scantlebury, D., Lambertucci, S., Virgilio, A., Crooks, E., Mulvenna, C., & Marks, N. (2018). Luck in Food Finding Affects Individual Performance and Population Trajectories. Current Biology, 28(23), 3871-3877.e5.
https://doi.org/10.1016/j.cub.2018.10.034, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa44868
Zhang, K., Crooks, E., & Orlando, A. (2018). Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Applications to Contour Lines, Sparse Data, and Inpainting. SIAM Journal on Imaging Sciences, 11(4), 2368-2428.
https://doi.org/10.1137/17m116152x, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43735
Crooks, E., Grinfeld, M., & McKay, G. (2018). Minimality conditions for wave speed in anisotropic smectic C∗ liquid crystals. Mathematical Methods in the Applied Sciences, 41(1), 88-102.
https://doi.org/10.1002/mma.4596, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa35136
http://onlinelibrary.wiley.com/doi/10.1002/mma.4596/full
Zhang, K., Crooks, E., & Orlando, A. (2016). Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations. SIAM Journal on Mathematical Analysis, 48(6), 4126-4154.
https://doi.org/10.1137/15m1045673, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa30572
Crooks, E. & Hilhorst, D. (2016). Self-similar fast-reaction limits for reaction–diffusion systems on unbounded domains. Journal of Differential Equations, 261(3), 2210-2250.
https://doi.org/10.1016/j.jde.2016.04.028, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa27408
Al-Kiffai, A. & Crooks, E. (2016). Lack of symmetry in linear determinacy due to convective effects in reaction-diffusion-convection problems. Tamkang Journal of Mathematics, 47(1), 51-70.
https://doi.org/10.5556/j.tkjm.47.2016.1891, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa27054
Zhang, K., Crooks, E., & Orlando, A. (2015). Compensated convexity, multiscale medial axis maps and sharp regularity of the squared distance function. SIAM Journal on Mathematical Analysis, 47(6), 4289-4331.
https://doi.org/10.1137/140993223, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22901
Zhang, K., Orlando, A., & Crooks, E. (2014). Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds. Mathematical Models and Methods in Applied Sciences, 25(5), 839-873.
https://doi.org/10.1142/S0218202515500207, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22109
http://www.worldscientific.com/doi/abs/10.1142/S0218202515500207
Zhang, K., Orlando, A., & Crooks, E. (2014). Compensated convexity and Hausdorff stable geometric singularity extractions. Mathematical Models and Methods in Applied Sciences, 25(4), 747-801.
https://doi.org/10.1142/S0218202515500189, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22108
http://www.worldscientific.com/doi/abs/10.1142/S0218202515500189
Crooks, E., Kazmierczak, B., & Lipniacki, T. (2013). A Spatially Extended Model of Kinase-Receptor Interaction. SIAM Journal on Applied Mathematics, 73(1), 374-400.
https://doi.org/10.1137/110860926, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13908
Crooks, E., Tsai, J., & Crooks, E. (2012). Front-like entire solutions for equations with convection. Journal of Differential Equations, 253(4), 1206-1249.
https://doi.org/10.1016/j.jde.2012.04.022, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa12668

All Research

Journal Articles

Zhang, K., Orlando, A., & Crooks, E. (2021). Compensated convexity on bounded domains, mixed Moreau envelopes and computational methods. Applied Mathematical Modelling, 94, 688-720.
https://doi.org/10.1016/j.apm.2021.01.040, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa57942
Crooks, E. & Grinfeld, M. (2020). Minimal travelling wave speed and explicit solutions in monostable reaction-diffusion equations. Electronic Journal of Qualitative Theory of Differential Equations, 79(79), 1-9.
https://doi.org/10.14232/ejqtde.2020.1.79, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa57943
Wilson, R., Neate, A., Holton, M., Shepard, E., Scantlebury, D., Lambertucci, S., Virgilio, A., Crooks, E., Mulvenna, C., & Marks, N. (2018). Luck in Food Finding Affects Individual Performance and Population Trajectories. Current Biology, 28(23), 3871-3877.e5.
https://doi.org/10.1016/j.cub.2018.10.034, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa44868
Zhang, K., Crooks, E., & Orlando, A. (2018). Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Applications to Contour Lines, Sparse Data, and Inpainting. SIAM Journal on Imaging Sciences, 11(4), 2368-2428.
https://doi.org/10.1137/17m116152x, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43735
Crooks, E., Grinfeld, M., & McKay, G. (2018). Minimality conditions for wave speed in anisotropic smectic C∗ liquid crystals. Mathematical Methods in the Applied Sciences, 41(1), 88-102.
https://doi.org/10.1002/mma.4596, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa35136
http://onlinelibrary.wiley.com/doi/10.1002/mma.4596/full
Zhang, K., Crooks, E., & Orlando, A. (2016). Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations. SIAM Journal on Mathematical Analysis, 48(6), 4126-4154.
https://doi.org/10.1137/15m1045673, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa30572
Crooks, E. & Hilhorst, D. (2016). Self-similar fast-reaction limits for reaction–diffusion systems on unbounded domains. Journal of Differential Equations, 261(3), 2210-2250.
https://doi.org/10.1016/j.jde.2016.04.028, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa27408
Al-Kiffai, A. & Crooks, E. (2016). Lack of symmetry in linear determinacy due to convective effects in reaction-diffusion-convection problems. Tamkang Journal of Mathematics, 47(1), 51-70.
https://doi.org/10.5556/j.tkjm.47.2016.1891, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa27054
Zhang, K., Crooks, E., & Orlando, A. (2015). Compensated convexity, multiscale medial axis maps and sharp regularity of the squared distance function. SIAM Journal on Mathematical Analysis, 47(6), 4289-4331.
https://doi.org/10.1137/140993223, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22901
Zhang, K., Orlando, A., & Crooks, E. (2014). Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds. Mathematical Models and Methods in Applied Sciences, 25(5), 839-873.
https://doi.org/10.1142/S0218202515500207, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22109
http://www.worldscientific.com/doi/abs/10.1142/S0218202515500207
Zhang, K., Orlando, A., & Crooks, E. (2014). Compensated convexity and Hausdorff stable geometric singularity extractions. Mathematical Models and Methods in Applied Sciences, 25(4), 747-801.
https://doi.org/10.1142/S0218202515500189, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22108
http://www.worldscientific.com/doi/abs/10.1142/S0218202515500189
Crooks, E., Kazmierczak, B., & Lipniacki, T. (2013). A Spatially Extended Model of Kinase-Receptor Interaction. SIAM Journal on Applied Mathematics, 73(1), 374-400.
https://doi.org/10.1137/110860926, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13908
Crooks, E., Tsai, J., & Crooks, E. (2012). Front-like entire solutions for equations with convection. Journal of Differential Equations, 253(4), 1206-1249.
https://doi.org/10.1016/j.jde.2012.04.022, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa12668
Ball, J., Crooks, E., & Crooks, E. (2011). Local minimizers and planar interfaces in a phase-transition model with interfacial energy. Calculus of Variations and Partial Differential Equations, 40(3-4), 501-538.
https://doi.org/10.1007/s00526-010-0349-8, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1052
Crooks, E., Dancer, E., & Crooks, E. (2011). Competition systems with strong interaction on a subdomain. Topological Methods in Nonlinear Analysis, 37(1), 37-53.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1055
Crooks, E., Dancer, E., & Crooks, E. (2010). Highly nonlinear large-competition limits of elliptic systems. Nonlinear Analysis: Theory, Methods & Applications, 73(5), 1447-1457.
https://doi.org/10.1016/j.na.2010.05.008, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1053
Crooks, E. & Crooks, E. (2010). Front profiles in the vanishing-diffusion limit for monostable reaction-diffusion-convection equations. Differential and Integral Equations, 23(5-6), 495-512.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1054

Book Chapters

Orlando, A., Crooks, E., & Zhang, K. (2023). Compensated Convex-Based Transforms for Image Processing and Shape Interrogation. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging (pp. 1827-1886). Springer International Publishing
https://doi.org/10.1007/978-3-030-98661-2_106, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63730
http://dx.doi.org/10.1007/978-3-030-98661-2_106

Other Research Outputs

Cobley, R., Beggs, E., Crooks, E., Palmer, R., & Tucker, J. (2022). WORKSHOP REPORT: MASI Agenda Setting Workshop on Unconventional and Natural Computing
https://doi.org/10.23889/SURep.60483, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa60483

Supervision

Mathematical modelling of brain formation to map species variation and developmental malformations. (current)

PhD

Other supervisor: Dr Dmitri Finkelshtein
Existence and Optimization of the Critical Speed for Travelling Front Solutions with Convection in Unbounded Cylinders (awarded 2024)

PhD

Other supervisor: Prof Vitaly Moroz
Analysis of reaction-diffusion equations on a time-dependent domain (awarded 2022)

PhD

Other supervisor: Prof Vitaly Moroz
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion (awarded 2022)

PhD

Other supervisor: Dr Carlo Mercuri

Taught Modules

MA-101 Introduction to Analysis 1

The module introduces basic concepts such as sets, functions, completeness, sequences and series.
MA-102 Introduction to Analysis 2

The module introduces fundamental concepts such as limits, continuity, differentiability and integrability.
MAW101 Cyflwyniad i Ddadansoddi 1

The module introduces basic concepts such as sets, functions, completeness, sequences and series.
MAW102 Cyflwyniad i Ddadansoddi 2

The module introduces fundamental concepts such as limits, continuity, differentiability and integrability.

Other Roles

Editorial Advisory Board member,, LMS

2009 - 2018
Editorial Board Member, Mathematics : `Theoretical and Mathematical Ecology' Section

2018 - Present
Member-at-Large of Council, London Mathematical Society

2020 - Present

Professor Elaine Crooks

Telephone number

Email address

Research Links

About

Areas Of Expertise

Publications

Research Highlights

All Research

Journal Articles

Book Chapters

Other Research Outputs

Supervision

Mathematical modelling of brain formation to map species variation and developmental malformations. (current)

Existence and Optimization of the Critical Speed for Travelling Front Solutions with Convection in Unbounded Cylinders (awarded 2024)

Analysis of reaction-diffusion equations on a time-dependent domain (awarded 2022)

Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion (awarded 2022)

Taught Modules

MA-101 Introduction to Analysis 1

MA-102 Introduction to Analysis 2

MAW101 Cyflwyniad i Ddadansoddi 1

MAW102 Cyflwyniad i Ddadansoddi 2

Other Roles

Editorial Advisory Board member,, LMS

Editorial Board Member, Mathematics : `Theoretical and Mathematical Ecology' Section

Member-at-Large of Council, London Mathematical Society