Yr Athro Elaine Crooks

Athro

Mathematics

+44 (0) 1792 602387

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

324
Trydydd Llawr
Y Ffowndri Gyfrifiadol
Campws y Bae

Ar gael ar gyfer Goruchwyliaeth Ôl-raddedig

Dolenni Ymchwil

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

Trosolwg

Fy mhrif faes ymchwil yw dadansoddi hafaliadau differol rhannol aflinol, yn enwedig terfynau unigol PDE eliptig a pharabolig aflinol, ymddygiad asymptotig systemau adwaith-trylediad, a chyflymderau lledaenu a thaenu blaen, wedi'u hysgogi gan gymwysiadau fel newid priodweddau grisialau hylifol, trosglwyddo deunyddiau fesul cam, rhyngweithiadau cystadleuol iawn a gwahanu gofodol mewn dynameg poblogaeth, a nodweddu cyflymder lledaeniad ecolegol goresgyniadau. Diddordeb ychwanegol yw dadansoddi trawsffurfiadau amgrwm cyfadferedig a'u cymwysiadau wrth ganfod hynodwedd geometrig, a thrwy weithredu rhifiadol, canfod nodweddion mewn delweddau neu ddata, tynnu sŵn o ddelweddau, adnabod croestoriadau rhwng arwynebau, ac ati.

Meysydd Arbenigedd

Hafaliadau differol rhannol aflinol
Terfynau unigol systemau eliptig a pharabolig
Systemau adwaith-trylediad-darfudiad a thonnau sy’n teithio
Cymwysiadau PDE i fioleg
Dulliau geometrig ar gyfer prosesu delweddau

Cyhoeddiadau

Uchafbwyntiau Ymchwil

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

Holl Ymchwil

Erthyglau Cylchgronau

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

Penodau Llyfrau

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

Cynnyrch Ymchwil Arall

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

Goruchwyliaeth

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

PhD

Goruchwyliwr arall: Dr Dmitri Finkelshtein
Existence and Optimization of the Critical Speed for Travelling Front Solutions with Convection in Unbounded Cylinders (dyfarnwyd 2024)

PhD

Goruchwyliwr arall: Prof Vitaly Moroz
Analysis of reaction-diffusion equations on a time-dependent domain (dyfarnwyd 2022)

PhD

Goruchwyliwr arall: Prof Vitaly Moroz
Self-similar fast reaction limit of reaction diffusion systems with nonlinear diffusion (dyfarnwyd 2022)

PhD

Goruchwyliwr arall: Dr Carlo Mercuri

Modiwlau a Addysgir

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.

Rolau Eraill

Aelod o'r Bwrdd Cynghori Golygyddol, LMS

2009 - 2018
Aelod o'r Bwrdd Golygyddol, Mathematics , Adran `Theoretical and Mathematical Ecology'

2018 - Presennol
Aelod Cyffredinol o'r Cyngor, Cymdeithas Fathemategol Llundain

2020 - Presennol

Yr Athro Elaine Crooks

Rhif ffôn

Cyfeiriad ebost

Dolenni Ymchwil

Trosolwg

Meysydd Arbenigedd

Cyhoeddiadau

Uchafbwyntiau Ymchwil

Holl Ymchwil

Erthyglau Cylchgronau

Penodau Llyfrau

Cynnyrch Ymchwil Arall

Goruchwyliaeth

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

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

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

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

Modiwlau a Addysgir

MA-101 Introduction to Analysis 1

MA-102 Introduction to Analysis 2

MAW101 Cyflwyniad i Ddadansoddi 1

MAW102 Cyflwyniad i Ddadansoddi 2

Rolau Eraill

Aelod o'r Bwrdd Cynghori Golygyddol, LMS

Aelod o'r Bwrdd Golygyddol, Mathematics , Adran `Theoretical and Mathematical Ecology'

Aelod Cyffredinol o'r Cyngor, Cymdeithas Fathemategol Llundain