Preprints
1.
Prokop, B.; Gelens, L.
2023, visited: 25.08.2023.
@online{SINDy_oscillations_2023,
title = {Data-driven discovery of oscillator models using SINDy: Towards the application on experimental data in biology},
author = {Prokop, B. and Gelens, L.},
doi = {10.1101/2023.08.25.554817},
year = {2023},
date = {2023-08-25},
urldate = {2023-08-25},
keywords = {},
pubstate = {published},
tppubtype = {online}
}
2.
Frolov, N.; Bijnens, B.; Ruiz-Reynés, D.; Gelens, L.
Self-organization of microtubules: complexity analysis of emergent patterns
2023, visited: 30.04.2023.
@online{selforganization_microtubules_2023,
title = {Self-organization of microtubules: complexity analysis of emergent patterns},
author = {N. Frolov and B. Bijnens and D. Ruiz-Reynés and L. Gelens},
doi = {10.48550/arXiv.2305.00539},
year = {2023},
date = {2023-04-30},
urldate = {2023-04-30},
keywords = {},
pubstate = {published},
tppubtype = {online}
}
Journal articles
1.
Rombouts, J.; Verplaetse, S.; Gelens, L.
In: Journal of the Royal Society Interface, vol. 20, no. 203, pp. 20230123, 2023.
@article{timedelayed_oscillations_2023,
title = {The ups and downs of biological oscillators: a comparison of time-delayed negative feedback mechanisms},
author = {J. Rombouts and S. Verplaetse and L. Gelens},
url = {https://royalsocietypublishing.org/doi/abs/10.1098/rsif.2023.0123},
doi = {10.1098/rsif.2023.0123},
year = {2023},
date = {2023-06-28},
urldate = {2023-06-28},
journal = {Journal of the Royal Society Interface},
volume = {20},
number = {203},
pages = {20230123},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
2.
Prokop, B.; Gelens, L.; Pelz, P. F.; Friesen, J.
In: Physical Review E, vol. 107, iss. 6, pp. 064305, 2023.
@article{discovery_prokop_2022,
title = {Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data},
author = {B. Prokop and L. Gelens and P. F. Pelz and J. Friesen},
url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.064305},
doi = {10.1103/PhysRevE.107.064305},
year = {2023},
date = {2023-06-07},
urldate = {2023-06-07},
journal = {Physical Review E},
volume = {107},
issue = {6},
pages = {064305},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
3.
Parra-Rivas*, P.; Ruiz-Reynés*, D.; Gelens, L.
Cell cycle oscillations driven by two interlinked bistable switches
In: Molecular Biology of the Cell, vol. 34, no. 6, pp. ar56, 2023.
@article{cellcyclemodel_parrarivas_2023,
title = {Cell cycle oscillations driven by two interlinked bistable switches},
author = {P. Parra-Rivas* and D. Ruiz-Reynés* and L. Gelens},
url = {https://doi.org/10.1091/mbc.E22-11-0527},
doi = {10.1101/2023.01.26.525632},
year = {2023},
date = {2023-05-05},
urldate = {2023-02-15},
journal = {Molecular Biology of the Cell},
volume = {34},
number = {6},
pages = {ar56},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
4.
Naulaerts*, S.; Datsi*, A.; Borras*, D.; Martinez*, A. A.; Messiaen, J.; Vanmeerbeek*, I.; Sprooten, J.; Laureano, R. S.; Govaerts, J.; Panovska, D.; Derweduwe, M.; Sabel, M. C.; Rapp, M.; Ni, W.; Mackay, S.; Herck, Y. Van; Gelens, L.; Venken, T.; More, S.; Bechter, O.; Bergers, G.; Liston, A.; Vleeschouwer, S. De; Eynde, B. J. Van Den; Lambrechts, D.; Verfaillie, M.; Bosisio*, F.; Tejpar*, S.; Borst*, J.; Sorg*, R. V.; Smet*, F. De; Garg, A. D.
Multiomics and spatial mapping characterizes human CD8+ T cell states in cancer
In: Science Translational Medicine, vol. 15, iss. 691, pp. eadd1016, 2023.
@article{multiomics_tcells_2023,
title = {Multiomics and spatial mapping characterizes human CD8+ T cell states in cancer},
author = {S. Naulaerts* and A. Datsi* and D. Borras* and A. A. Martinez* and J. Messiaen and I. Vanmeerbeek* and J. Sprooten and R. S. Laureano and J. Govaerts and D. Panovska and M. Derweduwe and M. C. Sabel and M. Rapp and W. Ni and S. Mackay and Y. Van Herck and L. Gelens and T. Venken and S. More and O. Bechter and G. Bergers and A. Liston and S. De Vleeschouwer and B. J. Van Den Eynde and D. Lambrechts and M. Verfaillie and F. Bosisio* and S. Tejpar* and J. Borst* and R. V. Sorg* and F. De Smet* and A. D. Garg},
url = {https://www.science.org/doi/abs/10.1126/scitranslmed.add1016},
doi = {10.1126/scitranslmed.add1016},
year = {2023},
date = {2023-04-12},
journal = {Science Translational Medicine},
volume = {15},
issue = {691},
pages = {eadd1016},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
5.
Boeck, J. De; Rombouts, J; Gelens, L.
A modular approach for modeling the cell cycle based on functional response curves
In: PLOS Computational Biology, vol. 17, iss. 8, pp. e1009008, 2021.
@article{deboeck_modular_2021,
title = {A modular approach for modeling the cell cycle based on functional response curves},
author = {J. De Boeck and J Rombouts and L. Gelens},
url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1009008},
doi = {10.1371/journal.pcbi.1009008},
year = {2021},
date = {2021-08-01},
urldate = {2021-08-01},
journal = {PLOS Computational Biology},
volume = {17},
issue = {8},
pages = {e1009008},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
6.
Rombouts, J.; Gelens, L.
Analytical approximations for the speed of pacemaker-generated waves
In: Physical Review E, vol. 104, iss. 1, pp. 014220, 2021.
@article{rombouts_analytical_2021,
title = {Analytical approximations for the speed of pacemaker-generated waves},
author = {J. Rombouts and L. Gelens},
url = {https://link.aps.org/doi/10.1103/PhysRevE.104.014220},
doi = {10.1103/PhysRevE.104.014220},
year = {2021},
date = {2021-07-01},
urldate = {2021-07-01},
journal = {Physical Review E},
volume = {104},
issue = {1},
pages = {014220},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
7.
Nolet, F. E.; Gelens, L.
Mitotic waves in an import-diffusion model with multiple nuclei in a shared cytoplasm
In: Biosystems, vol. 208, pp. 104478, 2021, ISSN: 0303-2647.
@article{nolet_mitotic_2021,
title = {Mitotic waves in an import-diffusion model with multiple nuclei in a shared cytoplasm},
author = {F. E. Nolet and L. Gelens},
url = {https://www.sciencedirect.com/science/article/pii/S0303264721001283},
doi = {https://doi.org/10.1016/j.biosystems.2021.104478},
issn = {0303-2647},
year = {2021},
date = {2021-07-01},
urldate = {2021-07-01},
journal = {Biosystems},
volume = {208},
pages = {104478},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
8.
Kamenz, J.; Gelens, L.; Ferrell, J. E. Jr.
In: Current Biology, vol. 31, no. 4, pp. 794-808.e6, 2021, ISSN: 0960-9822.
@article{kamenz_bistable_2020b,
title = {Bistable, Biphasic Regulation of PP2A-B55 Accounts for the Dynamics of Mitotic Substrate Phosphorylation},
author = {J. Kamenz and L. Gelens and J. E. Jr. Ferrell},
url = {http://www.sciencedirect.com/science/article/pii/S0960982220317711},
doi = {10.1016/j.cub.2020.11.058},
issn = {0960-9822},
year = {2021},
date = {2021-02-01},
urldate = {2021-02-01},
journal = {Current Biology},
volume = {31},
number = {4},
pages = {794-808.e6},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
9.
Rombouts, J.; Gelens, L.
Dynamic Bistable Switches Enhance Robustness and Accuracy of Cell Cycle Transitions
In: PLOS Computational Biology, vol. 17, no. 1, pp. e1008231, 2021, ISSN: 1553-7358.
@article{rombouts_dynamic_2021,
title = {Dynamic Bistable Switches Enhance Robustness and Accuracy of Cell Cycle Transitions},
author = {J. Rombouts and L. Gelens},
url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008231},
doi = {10.1371/journal.pcbi.1008231},
issn = {1553-7358},
year = {2021},
date = {2021-01-01},
urldate = {2021-01-01},
journal = {PLOS Computational Biology},
volume = {17},
number = {1},
pages = {e1008231},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
10.
Arabí, C. Mas; Parra-Rivas, P.; Hansson, T.; Gelens, L.; Wabnitz, S.; Leo, F.
In: Optics Letters, vol. 45, no. 20, pp. 5856–5859, 2020, ISSN: 1539-4794.
@article{masarabi_localized_2020,
title = {Localized Structures Formed through Domain Wall Locking in Cavity-Enhanced Second-Harmonic Generation},
author = {C. Mas Arabí and P. Parra-Rivas and T. Hansson and L. Gelens and S. Wabnitz and F. Leo},
url = {https://www.osapublishing.org/ol/abstract.cfm?uri=ol-45-20-5856},
doi = {10.1364/OL.399658},
issn = {1539-4794},
year = {2020},
date = {2020-10-01},
urldate = {2020-10-01},
journal = {Optics Letters},
volume = {45},
number = {20},
pages = {5856--5859},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
11.
Parra-Rivas, P.; Knobloch, E.; Gelens, L.; Gomila, D.
Origin, Bifurcation Structure and Stability of Localized States in Kerr Dispersive Optical Cavities
In: IMA Journal of Applied Mathematics, vol. 86, no. 5, pp. 856-895, 2020.
@article{parra-rivas_origin_2020,
title = {Origin, Bifurcation Structure and Stability of Localized States in Kerr Dispersive Optical Cavities},
author = {P. Parra-Rivas and E. Knobloch and L. Gelens and D. Gomila},
url = {https://doi.org/10.1093/imamat/hxab031},
year = {2020},
date = {2020-10-01},
urldate = {2020-10-01},
journal = {IMA Journal of Applied Mathematics},
volume = {86},
number = {5},
pages = {856-895},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
12.
Rombouts, J.; Gelens, L.
Synchronizing an Oscillatory Medium: The Speed of Pacemaker-Generated Waves
In: Physical Review Research, vol. 2, no. 4, pp. 043038, 2020.
@article{rombouts_synchronizing_2020,
title = {Synchronizing an Oscillatory Medium: The Speed of Pacemaker-Generated Waves},
author = {J. Rombouts and L. Gelens},
url = {https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.2.043038},
doi = {10.1103/PhysRevResearch.2.043038},
year = {2020},
date = {2020-10-01},
urldate = {2020-10-01},
journal = {Physical Review Research},
volume = {2},
number = {4},
pages = {043038},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
13.
Nolet, F. E. *; Rombouts, J. *; Gelens, L.
Synchronization in Reaction-Diffusion Systems with Multiple Pacemakers
In: Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 30, no. 5, pp. 053139, 2020, ISSN: 1054-1500.
@article{nolet_synchronization_2020,
title = {Synchronization in Reaction-Diffusion Systems with Multiple Pacemakers},
author = {F. E. * Nolet and J. * Rombouts and L. Gelens},
url = {https://aip.scitation.org/doi/10.1063/5.0002251},
doi = {10.1063/5.0002251},
issn = {1054-1500},
year = {2020},
date = {2020-05-28},
urldate = {2020-05-28},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
volume = {30},
number = {5},
pages = {053139},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
14.
Nolet, F. E. *; Vandervelde, A. *; Vanderbeke, A. *; Pineros, L. *; Chang, J. B.; Gelens, L.
Nuclei determine the spatial origin of mitotic waves
In: eLife, vol. 9, pp. e52868, 2020, ISSN: 2050-084X.
@article{nolet_nuclei_2020,
title = {Nuclei determine the spatial origin of mitotic waves},
author = {F. E. * Nolet and A. * Vandervelde and A. * Vanderbeke and L. * Pineros and J. B. Chang and L. Gelens},
url = {https://elifesciences.org/articles/52868},
doi = {10.7554/eLife.52868},
issn = {2050-084X},
year = {2020},
date = {2020-05-26},
urldate = {2020-05-26},
journal = {eLife},
volume = {9},
pages = {e52868},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
15.
Vet, S.; Gelens, L. *; Gonze, D. *
Mutualistic cross-feeding in microbial systems generates bistability via an Allee effect
In: Scientific Reports, vol. 10, no. 1, pp. 1–12, 2020, ISSN: 2045-2322.
@article{vet_mutualistic_2020,
title = {Mutualistic cross-feeding in microbial systems generates bistability via an Allee effect},
author = {S. Vet and L. * Gelens and D. * Gonze},
url = {http://www.nature.com/articles/s41598-020-63772-4},
doi = {10.1038/s41598-020-63772-4},
issn = {2045-2322},
year = {2020},
date = {2020-05-08},
urldate = {2020-05-08},
journal = {Scientific Reports},
volume = {10},
number = {1},
pages = {1--12},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
16.
Manzione, M. G.; Rombouts, J.; Steklov, M.; Pasquali, L.; Sablina, A.; Gelens, L.; Qian, J.; Bollen, M.
Co-regulation of the antagonistic RepoMan:Aurora-B pair in proliferating cells
In: Molecular Biology of the Cell, vol. 31, no. 6, pp. 419–438, 2020, ISSN: 1059-1524.
@article{manzione_co-regulation_2020,
title = {Co-regulation of the antagonistic RepoMan:Aurora-B pair in proliferating cells},
author = {M. G. Manzione and J. Rombouts and M. Steklov and L. Pasquali and A. Sablina and L. Gelens and J. Qian and M. Bollen},
url = {http://www.molbiolcell.org/doi/full/10.1091/mbc.E19-12-0698},
doi = {10.1091/mbc.E19-12-0698},
issn = {1059-1524},
year = {2020},
date = {2020-01-01},
urldate = {2020-01-01},
journal = {Molecular Biology of the Cell},
volume = {31},
number = {6},
pages = {419--438},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
17.
Parra-Rivas, P.; Gelens, L.; Leo, F.
Localized structures in dispersive and doubly resonant optical parametric oscillators
In: Physical Review E, vol. 100, iss. 3, pp. 032219, 2019.
@article{parra-rivas_localized_2019,
title = {Localized structures in dispersive and doubly resonant optical parametric oscillators},
author = {P. Parra-Rivas and L. Gelens and F. Leo},
url = {https://link.aps.org/doi/10.1103/PhysRevE.100.032219},
doi = {10.1103/PhysRevE.100.032219},
year = {2019},
date = {2019-09-01},
urldate = {2019-09-01},
journal = {Physical Review E},
volume = {100},
issue = {3},
pages = {032219},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
18.
Rombouts, J.; Gelens, L.; Erneux, T.
Travelling fronts in time-delayed reaction-diffusion systems
In: Phil. Trans. Roy. Soc. A, vol. 377, iss. 2153, pp. 20180127, 2019.
@article{rombouts_travelling_2019,
title = {Travelling fronts in time-delayed reaction-diffusion systems},
author = {J. Rombouts and L. Gelens and T. Erneux},
url = {https://royalsocietypublishing.org/doi/10.1098/rsta.2018.0127},
doi = {10.1098/rsta.2018.0127},
year = {2019},
date = {2019-07-01},
urldate = {2019-07-01},
journal = {Phil. Trans. Roy. Soc. A},
volume = {377},
issue = {2153},
pages = {20180127},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
19.
Gelens, L.; Santos, S. D. M.
Eternal sunshine of the spotless cycle
In: Molecular Systems Biology, vol. 14, no. 4, pp. e8864, 2019.
@article{gelens_eternal_2019,
title = {Eternal sunshine of the spotless cycle},
author = {L. Gelens and S. D. M. Santos},
url = {http://msb.embopress.org/content/15/4/e8864},
doi = {10.15252/msb.20198864},
year = {2019},
date = {2019-04-01},
urldate = {2019-04-01},
journal = {Molecular Systems Biology},
volume = {14},
number = {4},
pages = {e8864},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
20.
Parra-Rivas, P.; Gelens, L.; Hansson, T.; Wabnitz, S.; Leo, F.
In: Optics Letters, vol. 44, no. 8, pp. 2004–2007, 2019.
@article{parra-rivas_frequency_2019,
title = {Frequency comb generation through the locking of domain walls in doubly resonant dispersive optical parametric oscillators},
author = {P. Parra-Rivas and L. Gelens and T. Hansson and S. Wabnitz and F. Leo},
url = {http://ol.osa.org/abstract.cfm?URI=ol-44-8-2004},
doi = {10.1364/OL.44.002004},
year = {2019},
date = {2019-04-01},
urldate = {2019-04-01},
journal = {Optics Letters},
volume = {44},
number = {8},
pages = {2004--2007},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
21.
Qian, J.; Gelens, L.; Bollen, M.
Coordination of Timers and Sensors in Cell Signaling
In: BioEssays, vol. 41, no. 3, pp. 1800217, 2019.
@article{qian_coordination_2019,
title = {Coordination of Timers and Sensors in Cell Signaling},
author = {J. Qian and L. Gelens and M. Bollen},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/bies.201800217},
doi = {10.1002/bies.201800217},
year = {2019},
date = {2019-01-01},
urldate = {2019-01-01},
journal = {BioEssays},
volume = {41},
number = {3},
pages = {1800217},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
22.
Vet, S. *; Vandervelde, A. *; Gelens, L.
Excitable dynamics through toxin-induced mRNA cleavage in bacteria
In: PLoS One, vol. 14, no. 2, pp. 1-20, 2019.
@article{vet_excitable_2019,
title = {Excitable dynamics through toxin-induced mRNA cleavage in bacteria},
author = {S. * Vet and A. * Vandervelde and L. Gelens},
url = {https://doi.org/10.1371/journal.pone.0212288},
doi = {10.1371/journal.pone.0212288},
year = {2019},
date = {2019-01-01},
urldate = {2019-01-01},
journal = {PLoS One},
volume = {14},
number = {2},
pages = {1-20},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
23.
Hansson, T.; Parra-Rivas, P.; Bernard, M.; Leo, F.; Gelens, L.; Wabnitz, S.
Quadratic soliton combs in doubly resonant second-harmonic generation
In: Optics Letters, vol. 43, no. 24, pp. 6033–6036, 2018.
@article{hansson_quadratic_2018,
title = {Quadratic soliton combs in doubly resonant second-harmonic generation},
author = {T. Hansson and P. Parra-Rivas and M. Bernard and F. Leo and L. Gelens and S. Wabnitz},
url = {http://ol.osa.org/abstract.cfm?URI=ol-43-24-6033},
doi = {10.1364/OL.43.006033},
year = {2018},
date = {2018-12-01},
urldate = {2018-12-01},
journal = {Optics Letters},
volume = {43},
number = {24},
pages = {6033--6036},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
24.
Parra-Rivas, P.; Gomila, D.; Gelens, L.; Knobloch, E.
Bifurcation structure of periodic patterns in the Lugiato-Lefever equation with anomalous dispersion
In: Physical Review E, vol. 98, iss. 4, pp. 042212, 2018.
@article{parra-rivas_bifurcation_2018b,
title = {Bifurcation structure of periodic patterns in the Lugiato-Lefever equation with anomalous dispersion},
author = {P. Parra-Rivas and D. Gomila and L. Gelens and E. Knobloch},
url = {https://link.aps.org/doi/10.1103/PhysRevE.98.042212},
doi = {10.1103/PhysRevE.98.042212},
year = {2018},
date = {2018-10-01},
urldate = {2018-10-01},
journal = {Physical Review E},
volume = {98},
issue = {4},
pages = {042212},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
25.
D'hoe, K. *; Vet, S. *; Faust, K. *; Moens, F.; Falony, G.; Gonze, D.; Lloréns-Rico, V.; Gelens, L.; Danckaert, J.; Vuyst, L. † De; Raes, J. †
In: eLife, vol. 7, pp. e37090, 2018.
@article{dhoe_integrated_2018,
title = {Integrated culturing, modeling and transcriptomics uncovers complex interactions and emergent behavior in a three-species synthetic gut community},
author = {K. * D'hoe and S. * Vet and K. * Faust and F. Moens and G. Falony and D. Gonze and V. Lloréns-Rico and L. Gelens and J. Danckaert and L. † De Vuyst and J. † Raes},
url = {https://elifesciences.org/articles/37090},
doi = {10.7554/eLife.37090},
year = {2018},
date = {2018-10-01},
urldate = {2018-10-01},
journal = {eLife},
volume = {7},
pages = {e37090},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
26.
Vet, S.; Buyl, S.; Faust, K.; Danckaert, J.; Gonze, D.; Gelens, L.
In: PLoS One, vol. 13, no. 6, pp. 1-15, 2018.
@article{vet_bistability_2018,
title = {Bistability in a system of two species interacting through mutualism as well as competition: Chemostat vs. Lotka-Volterra equations},
author = {S. Vet and S. Buyl and K. Faust and J. Danckaert and D. Gonze and L. Gelens},
url = {https://doi.org/10.1371/journal.pone.0197462},
doi = {10.1371/journal.pone.0197462},
year = {2018},
date = {2018-06-01},
urldate = {2018-06-01},
journal = {PLoS One},
volume = {13},
number = {6},
pages = {1-15},
abstract = {We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding. In line with previous studies (Assaneo, et al., 2013; Holland, et al., 2010; Iwata, et al., 2011), we demonstrate that this system has a rich repertoire of dynamical behavior, including bistability. Standard Lotka-Volterra equations are not capable to describe this particular system, as these account for only one type of interaction (mutualistic or competitive). We show here that the different steady state solutions can be well captured by an extended Lotka-Volterra model, which better describe the density-dependent interaction (mutualism at low density and competition at high density). This two-variable model provides a more intuitive description of the dynamical behavior than the chemostat equations.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding. In line with previous studies (Assaneo, et al., 2013; Holland, et al., 2010; Iwata, et al., 2011), we demonstrate that this system has a rich repertoire of dynamical behavior, including bistability. Standard Lotka-Volterra equations are not capable to describe this particular system, as these account for only one type of interaction (mutualistic or competitive). We show here that the different steady state solutions can be well captured by an extended Lotka-Volterra model, which better describe the density-dependent interaction (mutualism at low density and competition at high density). This two-variable model provides a more intuitive description of the dynamical behavior than the chemostat equations.
27.
Nikolic*, N.; Bergmiller*, T.; Vandervelde, A.; Albanese, T. G.; Gelens, L.; Moll, I.
Autoregulation of mazEF expression underlies growth heterogeneity in bacterial populations
In: Nucleic Acids Research, vol. 46, iss. 6, pp. 2918-2931, 2018.
@article{nikolic_autoregulation_2018,
title = {Autoregulation of mazEF expression underlies growth heterogeneity in bacterial populations},
author = {N. Nikolic* and T. Bergmiller* and A. Vandervelde and T. G. Albanese and L. Gelens and I. Moll},
url = {http://dx.doi.org/10.1093/nar/gky079},
doi = {10.1093/nar/gky079},
year = {2018},
date = {2018-04-01},
urldate = {2018-04-01},
journal = {Nucleic Acids Research},
volume = {46},
issue = {6},
pages = {2918-2931},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
28.
Parra-Rivas, P.; Gomila, D.; Gelens, L.; Knobloch, E.
Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion
In: Physical Review E, vol. 97, iss. 4, pp. 042204, 2018.
@article{parra-rivas_bifurcation_2018,
title = {Bifurcation structure of localized states in the Lugiato-Lefever equation with anomalous dispersion},
author = {P. Parra-Rivas and D. Gomila and L. Gelens and E. Knobloch},
url = {https://link.aps.org/doi/10.1103/PhysRevE.97.042204},
doi = {10.1103/PhysRevE.97.042204},
year = {2018},
date = {2018-04-01},
urldate = {2018-04-01},
journal = {Physical Review E},
volume = {97},
issue = {4},
pages = {042204},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
29.
Rombouts, J.; Vandervelde, A.; Gelens, L.
Delay models for the early embryonic cell cycle oscillator
In: PLoS One, vol. 13, no. 3, pp. 1-21, 2018.
@article{rombouts_delay_2018,
title = {Delay models for the early embryonic cell cycle oscillator},
author = {J. Rombouts and A. Vandervelde and L. Gelens},
url = {https://doi.org/10.1371/journal.pone.0194769},
doi = {10.1371/journal.pone.0194769},
year = {2018},
date = {2018-03-01},
urldate = {2018-03-01},
journal = {PLoS One},
volume = {13},
number = {3},
pages = {1-21},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
30.
Gelens, L.; Saurin, A. T.
Exploring the Function of Dynamic Phosphorylation-Dephosphorylation Cycles
In: Developmental Cell, vol. 44, no. 6, pp. 659-663, 2018, ISSN: 1534-5807.
@article{gelens_exploring_2018,
title = {Exploring the Function of Dynamic Phosphorylation-Dephosphorylation Cycles},
author = {L. Gelens and A. T. Saurin},
url = {http://www.cell.com/developmental-cell/abstract/S1534-5807(18)30189-8},
doi = {https://doi.org/10.1016/j.devcel.2018.03.002},
issn = {1534-5807},
year = {2018},
date = {2018-03-01},
urldate = {2018-03-01},
journal = {Developmental Cell},
volume = {44},
number = {6},
pages = {659-663},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
31.
Qian, J.; Garcia-Gimeno, M.; Beullens, M.; Manzione, M.; der Hoeven, G. Van; Iguala, J.; Heredia, M.; Sanz, P.; Gelens, L.; Bollen, M.
An Attachment-Independent Biochemical Timer of the Spindle Assembly Checkpoint
In: Molecular Cell, vol. 68, iss. 4, pp. 715-730, 2017, ISSN: 1097-2765.
@article{spindle_qian_2017,
title = {An Attachment-Independent Biochemical Timer of the Spindle Assembly Checkpoint},
author = {J. Qian and M. Garcia-Gimeno and M. Beullens and M. Manzione and G. Van der Hoeven and J. Iguala and M. Heredia and P. Sanz and L. Gelens and M. Bollen},
url = {https://www.sciencedirect.com/science/article/pii/S1097276517307608#undfig1},
doi = {10.1016/J.MOLCEL.2017.10.011},
issn = {1097-2765},
year = {2017},
date = {2017-11-16},
urldate = {2017-11-16},
journal = {Molecular Cell},
volume = {68},
issue = {4},
pages = {715-730},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
32.
Gelens, L.; Qian, J.; Bollen, M.; Saurin, A. T.
The Importance of Kinase–Phosphatase Integration: Lessons from Mitosis
In: Trends in Cell Biology, vol. 28, iss. 1, pp. 6-21, 2017, ISSN: 0962-8924.
@article{gelens_importance_2017,
title = {The Importance of Kinase–Phosphatase Integration: Lessons from Mitosis},
author = {L. Gelens and J. Qian and M. Bollen and A. T. Saurin},
url = {http://www.sciencedirect.com/science/article/pii/S0962892417301782},
doi = {https://doi.org/10.1016/j.tcb.2017.09.005},
issn = {0962-8924},
year = {2017},
date = {2017-11-01},
urldate = {2017-11-01},
journal = {Trends in Cell Biology},
volume = {28},
issue = {1},
pages = {6-21},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
33.
Anderson*, G. A.; Gelens*, L.; Baker, J.; Ferrell, J. E. Jr.
Desynchronizing Embryonic Cell Division Waves Reveals the Robustness of Xenopus laevis Development
In: Cell Reports, vol. 21, iss. 1, pp. 37–46, 2017, (featured on the cover).
@article{anderson_desynchronizing_2017,
title = {Desynchronizing Embryonic Cell Division Waves Reveals the Robustness of \textit{Xenopus laevis} Development},
author = {G. A. Anderson* and L. Gelens* and J. Baker and J. E. Jr. Ferrell},
url = {http://www.cell.com/cell-reports/fulltext/S2211-1247(17)31278-0},
doi = {10.1016/j.celrep.2017.09.017},
year = {2017},
date = {2017-09-01},
urldate = {2017-09-01},
journal = {Cell Reports},
volume = {21},
issue = {1},
pages = {37--46},
note = {featured on the cover},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
34.
Parra-Rivas, P.; Gomila, D.; Colet, P.; Gelens, L.
In: The European Physical Journal D, vol. 71, no. 7, pp. 198, 2017, ISSN: 1434-6079.
@article{parra-rivas_interaction_2017,
title = {Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation},
author = {P. Parra-Rivas and D. Gomila and P. Colet and L. Gelens},
url = {https://doi.org/10.1140/epjd/e2017-80127-5},
doi = {10.1140/epjd/e2017-80127-5},
issn = {1434-6079},
year = {2017},
date = {2017-07-25},
urldate = {2017-07-25},
journal = {The European Physical Journal D},
volume = {71},
number = {7},
pages = {198},
abstract = {Bound states, also called soliton molecules, can form as a result of the interaction between individual solitons. This interaction is mediated through the tails of each soliton that overlap with one another. When such soliton tails have spatial oscillations, locking or pinning between two solitons can occur at fixed distances related with the wavelength of these oscillations, thus forming a bound state. In this work, we study the formation and stability of various types of bound states in the Lugiato-Lefever equation by computing their interaction potential and by analyzing the properties of the oscillatory tails. Moreover, we study the effect of higher order dispersion and noise in the pump intensity on the dynamics of bound states. In doing so, we reveal that perturbations to the Lugiato-Lefever equation that maintain reversibility, such as fourth order dispersion, lead to bound states that tend to separate from one another in time when noise is added. This separation force is determined by the shape of the envelope of the interaction potential, as well as an additional Brownian ratchet effect. In systems with broken reversibility, such as third order dispersion, this ratchet effect continues to push solitons within a bound state apart. However, the force generated by the envelope of the potential is now such that it pushes the solitons towards each other, leading to a null net drift of the solitons.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Bound states, also called soliton molecules, can form as a result of the interaction between individual solitons. This interaction is mediated through the tails of each soliton that overlap with one another. When such soliton tails have spatial oscillations, locking or pinning between two solitons can occur at fixed distances related with the wavelength of these oscillations, thus forming a bound state. In this work, we study the formation and stability of various types of bound states in the Lugiato-Lefever equation by computing their interaction potential and by analyzing the properties of the oscillatory tails. Moreover, we study the effect of higher order dispersion and noise in the pump intensity on the dynamics of bound states. In doing so, we reveal that perturbations to the Lugiato-Lefever equation that maintain reversibility, such as fourth order dispersion, lead to bound states that tend to separate from one another in time when noise is added. This separation force is determined by the shape of the envelope of the interaction potential, as well as an additional Brownian ratchet effect. In systems with broken reversibility, such as third order dispersion, this ratchet effect continues to push solitons within a bound state apart. However, the force generated by the envelope of the potential is now such that it pushes the solitons towards each other, leading to a null net drift of the solitons.
35.
Parra-Rivas, P.; Gomila, D.; Gelens, L.
Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators
In: Physical Review A, vol. 95, iss. 5, pp. 053863, 2017.
@article{PhysRevA.95.053863,
title = {Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators},
author = {P. Parra-Rivas and D. Gomila and L. Gelens},
url = {https://link.aps.org/doi/10.1103/PhysRevA.95.053863},
doi = {10.1103/PhysRevA.95.053863},
year = {2017},
date = {2017-05-01},
urldate = {2017-05-01},
journal = {Physical Review A},
volume = {95},
issue = {5},
pages = {053863},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
36.
Parra-Rivas, P.; Matías, M. A.; Colet, P.; Gelens, L.; Walgraef, D.; Gomila, D.
Front interaction induces excitable behavior
In: Physical Review E, vol. 95, iss. 2, pp. 020201(R), 2017.
@article{parra-rivas_front_2017,
title = {Front interaction induces excitable behavior},
author = {P. Parra-Rivas and M. A. Matías and P. Colet and L. Gelens and D. Walgraef and D. Gomila},
url = {http://link.aps.org/doi/10.1103/PhysRevE.95.020201},
doi = {10.1103/PhysRevE.95.020201},
year = {2017},
date = {2017-02-01},
urldate = {2017-02-01},
journal = {Physical Review E},
volume = {95},
issue = {2},
pages = {020201(R)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
37.
Araujo, A. R.; Gelens, L.; Sheriff, R. S. M.; Santos, S. D. M.
Positive feedback keeps duration of mitosis temporally insulated from upstream cell-cycle events
In: Molecular Cell, vol. 64, no. 2, pp. 362–375, 2016, ISSN: 1097-2765.
@article{araujo_positive_2016,
title = {Positive feedback keeps duration of mitosis temporally insulated from upstream cell-cycle events},
author = {A. R. Araujo and L. Gelens and R. S. M. Sheriff and S. D. M. Santos},
url = {http://www.sciencedirect.com/science/article/pii/S1097276516305676},
doi = {10.1016/j.molcel.2016.09.018},
issn = {1097-2765},
year = {2016},
date = {2016-10-01},
urldate = {2016-10-01},
journal = {Molecular Cell},
volume = {64},
number = {2},
pages = {362--375},
abstract = {Summary
Cell division is characterized by a sequence of events by which a cell gives rise to two daughter cells. Quantitative measurements of cell-cycle dynamics in single cells showed that despite variability in G1-, S-, and G2 phases, duration of mitosis is short and remarkably constant. Surprisingly, there is no correlation between cell-cycle length and mitotic duration, suggesting that mitosis is temporally insulated from variability in earlier cell-cycle phases. By combining live cell imaging and computational modeling, we showed that positive feedback is the molecular mechanism underlying the temporal insulation of mitosis. Perturbing positive feedback gave rise to a sluggish, variable entry and progression through mitosis and uncoupled duration of mitosis from variability in cell cycle length. We show that positive feedback is important to keep mitosis short, constant, and temporally insulated and anticipate it might be a commonly used regulatory strategy to create modularity in other biological systems.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Summary
Cell division is characterized by a sequence of events by which a cell gives rise to two daughter cells. Quantitative measurements of cell-cycle dynamics in single cells showed that despite variability in G1-, S-, and G2 phases, duration of mitosis is short and remarkably constant. Surprisingly, there is no correlation between cell-cycle length and mitotic duration, suggesting that mitosis is temporally insulated from variability in earlier cell-cycle phases. By combining live cell imaging and computational modeling, we showed that positive feedback is the molecular mechanism underlying the temporal insulation of mitosis. Perturbing positive feedback gave rise to a sluggish, variable entry and progression through mitosis and uncoupled duration of mitosis from variability in cell cycle length. We show that positive feedback is important to keep mitosis short, constant, and temporally insulated and anticipate it might be a commonly used regulatory strategy to create modularity in other biological systems.
Cell division is characterized by a sequence of events by which a cell gives rise to two daughter cells. Quantitative measurements of cell-cycle dynamics in single cells showed that despite variability in G1-, S-, and G2 phases, duration of mitosis is short and remarkably constant. Surprisingly, there is no correlation between cell-cycle length and mitotic duration, suggesting that mitosis is temporally insulated from variability in earlier cell-cycle phases. By combining live cell imaging and computational modeling, we showed that positive feedback is the molecular mechanism underlying the temporal insulation of mitosis. Perturbing positive feedback gave rise to a sluggish, variable entry and progression through mitosis and uncoupled duration of mitosis from variability in cell cycle length. We show that positive feedback is important to keep mitosis short, constant, and temporally insulated and anticipate it might be a commonly used regulatory strategy to create modularity in other biological systems.
38.
Parra-Rivas, P.; Knobloch, E.; Gomila, D.; Gelens, L.
Dark solitons in the Lugiato-Lefever equation with normal dispersion
In: Physical Review A, vol. 93, no. 6, pp. 063839, 2016, ISSN: 2469-9926, 2469-9934.
@article{parra-rivas_dark_2016,
title = {Dark solitons in the Lugiato-Lefever equation with normal dispersion},
author = {P. Parra-Rivas and E. Knobloch and D. Gomila and L. Gelens},
url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.063839},
doi = {10.1103/PhysRevA.93.063839},
issn = {2469-9926, 2469-9934},
year = {2016},
date = {2016-06-01},
urldate = {2016-06-01},
journal = {Physical Review A},
volume = {93},
number = {6},
pages = {063839},
abstract = {The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.
39.
Parra-Rivas, P.; Gomila, D.; Knobloch, E.; Coen, S.; Gelens, L.
Origin and stability of dark pulse Kerr combs in normal dispersion resonators
In: Optics Letters, vol. 41, no. 11, pp. 2402–2405, 2016, ISSN: 1539-4794.
@article{parra-rivas_origin_2016,
title = {Origin and stability of dark pulse Kerr combs in normal dispersion resonators},
author = {P. Parra-Rivas and D. Gomila and E. Knobloch and S. Coen and L. Gelens},
url = {http://www.osapublishing.org/abstract.cfm?uri=ol-41-11-2402},
doi = {10.1364/OL.41.002402},
issn = {1539-4794},
year = {2016},
date = {2016-06-01},
urldate = {2016-06-01},
journal = {Optics Letters},
volume = {41},
number = {11},
pages = {2402--2405},
abstract = {We analyze dark pulse Kerr frequency combs in optical resonators with normal group-velocity dispersion using the Lugiato−Lefever model. We show that in the time domain the combs correspond to interlocked switching waves between the upper and lower homogeneous states, and explain how this fact accounts for many of their experimentally observed properties. Modulational instability does not play any role in their existence. We provide a detailed map indicating for which parameters stable dark pulse Kerr combs can be found, and how they are destabilized for increasing values of frequency detuning.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We analyze dark pulse Kerr frequency combs in optical resonators with normal group-velocity dispersion using the Lugiato−Lefever model. We show that in the time domain the combs correspond to interlocked switching waves between the upper and lower homogeneous states, and explain how this fact accounts for many of their experimentally observed properties. Modulational instability does not play any role in their existence. We provide a detailed map indicating for which parameters stable dark pulse Kerr combs can be found, and how they are destabilized for increasing values of frequency detuning.
40.
Parra-Rivas, P.; Gomila, D.; Gelens, L.; Matías, M. A.; Colet, P.
Dynamics of dissipative solitons in presence of inhomogeneities and drift
In: Grelu, Philippe (Ed.): Nonlinear Optical Cavity Dynamics, pp. 107–128, Wiley-VCH Verlag GmbH & Co. KGaA, 2016, ISBN: 978-3-527-68647-6.
@incollection{parra-rivas_dynamics_2016,
title = {Dynamics of dissipative solitons in presence of inhomogeneities and drift},
author = {P. Parra-Rivas and D. Gomila and L. Gelens and M. A. Matías and P. Colet},
editor = {Philippe Grelu},
url = {http://onlinelibrary.wiley.com/doi/10.1002/9783527686476.ch5/summary},
isbn = {978-3-527-68647-6},
year = {2016},
date = {2016-01-01},
urldate = {2016-01-01},
booktitle = {Nonlinear Optical Cavity Dynamics},
pages = {107--128},
publisher = {Wiley-VCH Verlag GmbH & Co. KGaA},
abstract = {This chapter presents the general theory about how different dissipative soliton (DS) dynamics are induced by inhomogeneities and drift. For this purpose, the prototypical Swift-Hohenberg equation (SHE) is used. The chapter focuses on the mechanism that leads to excitable dynamics. It discusses the modeling of fiber cavities in terms of the Lugiato-Lefever model, and describes the effect of periodic pumping in ring cavities. In fiber cavities and microresonators, inhomogeneities and drift are unavoidable due to imperfections in the fabrication process, material properties, and higher-order chromatic light dispersion. In the context of fiber cavities and microresonators, periodic boundary conditions lead to the emission of a train of solitons from the inhomogeneity. These trains of solitons lie at the basis of Kerr frequency comb generation. Therefore, the dynamical instabilities of cavity solitons induced by imperfections of themicroresonator can be particularly relevant for applications relying on stable frequency combs.},
keywords = {},
pubstate = {published},
tppubtype = {incollection}
}
This chapter presents the general theory about how different dissipative soliton (DS) dynamics are induced by inhomogeneities and drift. For this purpose, the prototypical Swift-Hohenberg equation (SHE) is used. The chapter focuses on the mechanism that leads to excitable dynamics. It discusses the modeling of fiber cavities in terms of the Lugiato-Lefever model, and describes the effect of periodic pumping in ring cavities. In fiber cavities and microresonators, inhomogeneities and drift are unavoidable due to imperfections in the fabrication process, material properties, and higher-order chromatic light dispersion. In the context of fiber cavities and microresonators, periodic boundary conditions lead to the emission of a train of solitons from the inhomogeneity. These trains of solitons lie at the basis of Kerr frequency comb generation. Therefore, the dynamical instabilities of cavity solitons induced by imperfections of themicroresonator can be particularly relevant for applications relying on stable frequency combs.
41.
Vandervelde, A.; Loris, R.; Danckaert, J.; Gelens, L.
Computational methods to model persistence
In: Michiels, Jan; Fauvart, Maarten (Ed.): Bacterial Persistence, no. 1333, pp. 207–240, Springer New York, 2016, ISBN: 978-1-4939-2853-8, (DOI: 10.1007/978-1-4939-2854-5_17).
@incollection{michiels_computational_2016,
title = {Computational methods to model persistence},
author = {A. Vandervelde and R. Loris and J. Danckaert and L. Gelens},
editor = {Jan Michiels and Maarten Fauvart},
url = {http://dx.doi.org/10.1007/978-1-4939-2854-5_17},
isbn = {978-1-4939-2853-8},
year = {2016},
date = {2016-01-01},
urldate = {2016-01-01},
booktitle = {Bacterial Persistence},
number = {1333},
pages = {207--240},
publisher = {Springer New York},
series = {Methods in Molecular Biology},
abstract = {Bacterial persister cells are dormant cells, tolerant to multiple antibiotics, that are involved in several chronic infections. Toxin–antitoxin modules play a significant role in the generation of such persister cells. Toxin–antitoxin modules are small genetic elements, omnipresent in the genomes of bacteria, which code for an intracellular toxin and its neutralizing antitoxin. In the past decade, mathematical modeling has become an important tool to study the regulation of toxin–antitoxin modules and their relation to the emergence of persister cells. Here, we provide an overview of several numerical methods to simulate toxin–antitoxin modules. We cover both deterministic modeling using ordinary differential equations and stochastic modeling using stochastic differential equations and the Gillespie method. Several characteristics of toxin–antitoxin modules such as protein production and degradation, negative autoregulation through DNA binding, toxin–antitoxin complex formation and conditional cooperativity are gradually integrated in these models. Finally, by including growth rate modulation, we link toxin–antitoxin module expression to the generation of persister cells.},
note = {DOI: 10.1007/978-1-4939-2854-5_17},
keywords = {},
pubstate = {published},
tppubtype = {incollection}
}
Bacterial persister cells are dormant cells, tolerant to multiple antibiotics, that are involved in several chronic infections. Toxin–antitoxin modules play a significant role in the generation of such persister cells. Toxin–antitoxin modules are small genetic elements, omnipresent in the genomes of bacteria, which code for an intracellular toxin and its neutralizing antitoxin. In the past decade, mathematical modeling has become an important tool to study the regulation of toxin–antitoxin modules and their relation to the emergence of persister cells. Here, we provide an overview of several numerical methods to simulate toxin–antitoxin modules. We cover both deterministic modeling using ordinary differential equations and stochastic modeling using stochastic differential equations and the Gillespie method. Several characteristics of toxin–antitoxin modules such as protein production and degradation, negative autoregulation through DNA binding, toxin–antitoxin complex formation and conditional cooperativity are gradually integrated in these models. Finally, by including growth rate modulation, we link toxin–antitoxin module expression to the generation of persister cells.
42.
Parra-Rivas, P.; Gomila, D.; Matías, M. A.; Colet, P.; Gelens, L.
In: Physical Review E, vol. 93, no. 1, pp. 012211, 2016.
@article{parra-rivas_competition_2016,
title = {Competition between drift and spatial defects leads to oscillatory and excitable dynamics of dissipative solitons},
author = {P. Parra-Rivas and D. Gomila and M. A. Matías and P. Colet and L. Gelens},
url = {http://link.aps.org/doi/10.1103/PhysRevE.93.012211},
doi = {10.1103/PhysRevE.93.012211},
year = {2016},
date = {2016-01-01},
urldate = {2016-01-01},
journal = {Physical Review E},
volume = {93},
number = {1},
pages = {012211},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Journal articles (before DiBS Lab)
1.
Gelens, L.; Huang, K. C.; Jr., J. E. Ferrell
How does the Xenopus laevis embryonic cell cycle avoid spatial chaos?
In: Cell Reports, vol. 12, no. 5, pp. 892–900, 2015, ISSN: 2211-1247.
@article{gelens_how_2015,
title = {How does the \textit{Xenopus laevis} embryonic cell cycle avoid spatial chaos?},
author = {L. Gelens and K. C. Huang and J. E. Ferrell Jr.},
url = {http://www.sciencedirect.com/science/article/pii/S2211124715007081},
doi = {10.1016/j.celrep.2015.06.070},
issn = {2211-1247},
year = {2015},
date = {2015-08-01},
urldate = {2015-08-01},
journal = {Cell Reports},
volume = {12},
number = {5},
pages = {892--900},
abstract = {Summary
Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally, and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Summary
Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally, and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells.
Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally, and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells.
2.
Parra-Rivas, P.; Gomila, D.; Matías, M. A.; Colet, P.; Gelens, L.
In: Optics Express, vol. 22, no. 25, pp. 30943–30954, 2014, ISSN: 1094-4087.
@article{parra-rivas_effects_2014,
title = {Effects of inhomogeneities and drift on the dynamics of temporal solitons in fiber cavities and microresonators},
author = {P. Parra-Rivas and D. Gomila and M. A. Matías and P. Colet and L. Gelens},
url = {http://www.osapublishing.org/abstract.cfm?uri=oe-22-25-30943},
doi = {10.1364/OE.22.030943},
issn = {1094-4087},
year = {2014},
date = {2014-12-01},
urldate = {2014-12-01},
journal = {Optics Express},
volume = {22},
number = {25},
pages = {30943--30954},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
3.
Gelens, L.; Anderson, G. A.; Jr., J. E. Ferrell
Spatial trigger waves: positive feedback gets you a long way
In: Molecular Biology of the Cell, vol. 25, no. 22, pp. 3486–3493, 2014, ISSN: 1059-1524, 1939-4586.
@article{gelens_spatial_2014,
title = {Spatial trigger waves: positive feedback gets you a long way},
author = {L. Gelens and G. A. Anderson and J. E. Ferrell Jr.},
url = {http://www.molbiolcell.org/content/25/22/3486},
doi = {10.1091/mbc.E14-08-1306},
issn = {1059-1524, 1939-4586},
year = {2014},
date = {2014-11-01},
urldate = {2014-11-01},
journal = {Molecular Biology of the Cell},
volume = {25},
number = {22},
pages = {3486--3493},
abstract = {Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances. Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs. Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely used in physics and theoretical biology, to examine different types of trigger waves—spatial switches, pulses, and oscillations—and to show how they arise.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Trigger waves are a recurring biological phenomenon involved in transmitting information quickly and reliably over large distances. Well-characterized examples include action potentials propagating along the axon of a neuron, calcium waves in various tissues, and mitotic waves in Xenopus eggs. Here we use the FitzHugh-Nagumo model, a simple model inspired by the action potential that is widely used in physics and theoretical biology, to examine different types of trigger waves—spatial switches, pulses, and oscillations—and to show how they arise.
4.
Parra-Rivas, P.; Gomila, D.; Leo, F.; Coen, S.; Gelens, L.
Third-order chromatic dispersion stabilizes Kerr frequency combs
In: Optics Letters, vol. 39, no. 10, pp. 2971–2974, 2014, ISSN: 1539-4794.
@article{parra-rivas_third-order_2014,
title = {Third-order chromatic dispersion stabilizes Kerr frequency combs},
author = {P. Parra-Rivas and D. Gomila and F. Leo and S. Coen and L. Gelens},
url = {http://www.osapublishing.org/abstract.cfm?uri=ol-39-10-2971},
doi = {10.1364/OL.39.002971},
issn = {1539-4794},
year = {2014},
date = {2014-05-01},
urldate = {2014-05-01},
journal = {Optics Letters},
volume = {39},
number = {10},
pages = {2971--2974},
abstract = {Using numerical simulations of an extended Lugiato–Lefever equation we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators, taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Using numerical simulations of an extended Lugiato–Lefever equation we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators, taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.
5.
Parra-Rivas, P.; Gomila, D.; Matías, M. A.; Coen, S.; Gelens, L.
In: Physical Review A, vol. 89, no. 4, pp. 043813, 2014.
@article{parra-rivas_dynamics_2014,
title = {Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs},
author = {P. Parra-Rivas and D. Gomila and M. A. Matías and S. Coen and L. Gelens},
url = {http://link.aps.org/doi/10.1103/PhysRevA.89.043813},
doi = {10.1103/PhysRevA.89.043813},
year = {2014},
date = {2014-04-01},
urldate = {2014-04-01},
journal = {Physical Review A},
volume = {89},
number = {4},
pages = {043813},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
6.
Colet, P.; Matías, M. A.; Gelens, L.; Gomila, D.
In: Physical Review E, vol. 89, no. 1, pp. 012914, 2014.
@article{colet_formation_2014,
title = {Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework},
author = {P. Colet and M. A. Matías and L. Gelens and D. Gomila},
url = {http://link.aps.org/doi/10.1103/PhysRevE.89.012914},
doi = {10.1103/PhysRevE.89.012914},
year = {2014},
date = {2014-01-01},
urldate = {2014-01-01},
journal = {Physical Review E},
volume = {89},
number = {1},
pages = {012914},
abstract = {The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.
7.
Colet, P.; Matías, M. A.; Gelens, L.; Gomila, D.
In: Physical Review E, vol. 89, no. 1, pp. 012914, 012915, 2014.
@article{formation_2014_parts12,
title = {Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework and II. The nonlocal Ginzburg-Landau equation},
author = {P. Colet and M. A. Matías and L. Gelens and D. Gomila},
url = {http://link.aps.org/doi/10.1103/PhysRevE.89.012914},
doi = {10.1103/PhysRevE.89.012914},
year = {2014},
date = {2014-01-01},
urldate = {2014-01-01},
journal = {Physical Review E},
volume = {89},
number = {1},
pages = {012914, 012915},
abstract = {The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.
8.
Coomans, W.; der Sande, G. Van; Gelens, L.
Oscillations and multistability in two semiconductor ring lasers coupled by a single waveguide
In: Physical Review A, vol. 88, no. 3, pp. 033813, 2013.
@article{coomans_oscillations_2013,
title = {Oscillations and multistability in two semiconductor ring lasers coupled by a single waveguide},
author = {W. Coomans and G. Van der Sande and L. Gelens},
url = {http://link.aps.org/doi/10.1103/PhysRevA.88.033813},
doi = {10.1103/PhysRevA.88.033813},
year = {2013},
date = {2013-09-01},
urldate = {2013-09-01},
journal = {Physical Review A},
volume = {88},
number = {3},
pages = {033813},
abstract = {We theoretically study the dynamical behavior of semiconductor ring lasers coupled by a single bus waveguide, both when weakly coupled and when strongly coupled. We provide a detailed analysis of the multistable landscape in the coupled system, analyze the stability of all solutions, and relate the internal dynamics in the individual lasers to the field effectively measured at the output of the waveguide. We show that coupling phases close to π/2 generally promote instabilities. Finally, our analysis enables us to discuss the advantages and disadvantages for optical memory operation of coupled semiconductor ring lasers versus solitary ones.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We theoretically study the dynamical behavior of semiconductor ring lasers coupled by a single bus waveguide, both when weakly coupled and when strongly coupled. We provide a detailed analysis of the multistable landscape in the coupled system, analyze the stability of all solutions, and relate the internal dynamics in the individual lasers to the field effectively measured at the output of the waveguide. We show that coupling phases close to π/2 generally promote instabilities. Finally, our analysis enables us to discuss the advantages and disadvantages for optical memory operation of coupled semiconductor ring lasers versus solitary ones.
9.
Gelens, L.; Hill, L.; Vandervelde, A.; Danckaert, J.; Loris, R.
A general model for toxin-antitoxin module dynamics can explain persister cell formation in E. coli
In: PLOS Computational Biology, vol. 9, no. 8, pp. e1003190, 2013, ISSN: 1553-7358.
@article{gelens_general_2013,
title = {A general model for toxin-antitoxin module dynamics can explain persister cell formation in \textit{E. coli}},
author = {L. Gelens and L. Hill and A. Vandervelde and J. Danckaert and R. Loris},
url = {http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003190},
doi = {10.1371/journal.pcbi.1003190},
issn = {1553-7358},
year = {2013},
date = {2013-08-01},
urldate = {2013-08-01},
journal = {PLOS Computational Biology},
volume = {9},
number = {8},
pages = {e1003190},
abstract = {Author Summary Bacterial persistence plays an important role in many chronic infections. Persisters are subpopulations of bacteria which are tolerant to biological stresses such as antibiotics because they are in a dormant, non-dividing state. Toxin-antitoxin (TA) modules play a pivotal role in persister generation and bacterial stress response. These small genetic loci, ubiquitous in bacterial genomes and plasmids, code for a toxin that slows down or halts bacterial metabolism and a corresponding antitoxin that regulates this activity. In order to further unravel the intricate autoregulation of TA modules and their role in persister cell formation, we built stochastic models describing the transcriptional regulation including conditional cooperativity. This is a complex mechanism in which the molar ratio between both proteins determines whether the toxin will behave as a co-repressor or as a de-repressor for the antitoxin. We found that the necessary protein production and therefore the energetic cost decreases with increased binding site number. Finally, these models allow us to simulate the formation of persister cells through rare, stochastic increases in the free toxin level. We believe that our analysis provides a fresh view and contributes to our understanding of TA regulation and how it may be related to the emergence of persisters.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Author Summary Bacterial persistence plays an important role in many chronic infections. Persisters are subpopulations of bacteria which are tolerant to biological stresses such as antibiotics because they are in a dormant, non-dividing state. Toxin-antitoxin (TA) modules play a pivotal role in persister generation and bacterial stress response. These small genetic loci, ubiquitous in bacterial genomes and plasmids, code for a toxin that slows down or halts bacterial metabolism and a corresponding antitoxin that regulates this activity. In order to further unravel the intricate autoregulation of TA modules and their role in persister cell formation, we built stochastic models describing the transcriptional regulation including conditional cooperativity. This is a complex mechanism in which the molar ratio between both proteins determines whether the toxin will behave as a co-repressor or as a de-repressor for the antitoxin. We found that the necessary protein production and therefore the energetic cost decreases with increased binding site number. Finally, these models allow us to simulate the formation of persister cells through rare, stochastic increases in the free toxin level. We believe that our analysis provides a fresh view and contributes to our understanding of TA regulation and how it may be related to the emergence of persisters.
10.
Leo, F.; Gelens, L.; Emplit, P.; Haelterman, M.; Coen, S.
Dynamics of one-dimensional Kerr cavity solitons
In: Optics Express, vol. 21, no. 7, pp. 9180–9191, 2013, ISSN: 1094-4087.
@article{leo_dynamics_2013,
title = {Dynamics of one-dimensional Kerr cavity solitons},
author = {F. Leo and L. Gelens and P. Emplit and M. Haelterman and S. Coen},
url = {http://www.osapublishing.org/abstract.cfm?uri=oe-21-7-9180},
doi = {10.1364/OE.21.009180},
issn = {1094-4087},
year = {2013},
date = {2013-04-01},
urldate = {2013-04-01},
journal = {Optics Express},
volume = {21},
number = {7},
pages = {9180--9191},
abstract = {We present an experimental observation of an oscillating Kerr cavity soliton, i.e., a time-periodic oscillating one-dimensional temporally localized structure excited in a driven nonlinear fiber cavity with a Kerr-type nonlinearity. More generally, these oscillations result from a Hopf bifurcation of a (spatially or temporally) localized state in the generic class of driven dissipative systems close to the 1 : 1 resonance tongue. Furthermore, we theoretically analyze dynamical instabilities of the one-dimensional cavity soliton, revealing oscillations and different chaotic states in previously unexplored regions of parameter space. As cavity solitons are closely related to Kerr frequency combs, we expect these dynamical regimes to be highly relevant for the field of microresonator-based frequency combs.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We present an experimental observation of an oscillating Kerr cavity soliton, i.e., a time-periodic oscillating one-dimensional temporally localized structure excited in a driven nonlinear fiber cavity with a Kerr-type nonlinearity. More generally, these oscillations result from a Hopf bifurcation of a (spatially or temporally) localized state in the generic class of driven dissipative systems close to the 1 : 1 resonance tongue. Furthermore, we theoretically analyze dynamical instabilities of the one-dimensional cavity soliton, revealing oscillations and different chaotic states in previously unexplored regions of parameter space. As cavity solitons are closely related to Kerr frequency combs, we expect these dynamical regimes to be highly relevant for the field of microresonator-based frequency combs.
11.
Mashal, L.; der Sande, G. Van; Gelens, L.; Danckaert, J.; Verschaffelt, G.
Square-wave oscillations in semiconductor ring lasers with delayed optical feedback
In: Optics Express, vol. 20, no. 20, pp. 22503–22516, 2012, ISSN: 1094-4087.
@article{mashal_square-wave_2012,
title = {Square-wave oscillations in semiconductor ring lasers with delayed optical feedback},
author = {L. Mashal and G. Van der Sande and L. Gelens and J. Danckaert and G. Verschaffelt},
url = {http://www.osapublishing.org/abstract.cfm?uri=oe-20-20-22503},
doi = {10.1364/OE.20.022503},
issn = {1094-4087},
year = {2012},
date = {2012-09-01},
urldate = {2012-09-01},
journal = {Optics Express},
volume = {20},
number = {20},
pages = {22503--22516},
abstract = {We analyze experimentally and theoretically the effects of delayed optical cross-feedback in semiconductor ring lasers. We show that under appropriate conditions, feeding of only one directional mode back into the counter-propagating mode leads to square-wave oscillations. In this regime, the laser switches regularly between the two counter-propagating modes with a period close to twice the roundtrip time in the external feedback loop. We find that these oscillations are robust and appear for a wide range of parameters as long as a small asymmetry in the linear coupling between both modes is present. We show that by increasing the feedback strength or the injection current, the square-wave oscillations gradually disappear. Due to noise, mode-hopping between stable lasing in one directional mode and square wave oscillations is observed in this transition region.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We analyze experimentally and theoretically the effects of delayed optical cross-feedback in semiconductor ring lasers. We show that under appropriate conditions, feeding of only one directional mode back into the counter-propagating mode leads to square-wave oscillations. In this regime, the laser switches regularly between the two counter-propagating modes with a period close to twice the roundtrip time in the external feedback loop. We find that these oscillations are robust and appear for a wide range of parameters as long as a small asymmetry in the linear coupling between both modes is present. We show that by increasing the feedback strength or the injection current, the square-wave oscillations gradually disappear. Due to noise, mode-hopping between stable lasing in one directional mode and square wave oscillations is observed in this transition region.
12.
Kingni, S. Takougang; der Sande, G. Van; Gelens, L.; Erneux, T.; Danckaert, J.
Direct modulation of semiconductor ring lasers: numerical and asymptotic analysis
In: JOSA B, vol. 29, no. 8, pp. 1983–1992, 2012, ISSN: 1520-8540.
@article{kingni_direct_2012,
title = {Direct modulation of semiconductor ring lasers: numerical and asymptotic analysis},
author = {S. Takougang Kingni and G. Van der Sande and L. Gelens and T. Erneux and J. Danckaert},
url = {http://www.osapublishing.org/abstract.cfm?uri=josab-29-8-1983},
doi = {10.1364/JOSAB.29.001983},
issn = {1520-8540},
year = {2012},
date = {2012-08-01},
urldate = {2012-08-01},
journal = {JOSA B},
volume = {29},
number = {8},
pages = {1983--1992},
abstract = {We investigate numerically the dynamical behavior in a semiconductor ring laser (SRL) subject to a periodic modulation of the injection current. By varying the amplitude and frequency of the modulation at a fixed bias current, different dynamical states including periodic, quasi-periodic, and chaotic states are found. At frequencies comparable to the relaxation oscillation frequency, the intensities of the counterpropagating modes of the SRLs may exhibit in-phase chaotic motion similar to single mode semiconductor lasers. However, antiphase chaotic oscillations in the modal intensities are observed for modulation frequencies significantly lower than the relaxation oscillations frequency. We show that this antiphase chaotic regime does not involve carrier dynamics and is a result of the underlying symmetry of the SRL. We derive a two-dimensional asymptotic model valid on time-scales longer than the relaxation oscillations, which reproduces the observed dynamical behavior. In a further simplification, we can link this reduced set of equations to Duffing-type oscillators.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate numerically the dynamical behavior in a semiconductor ring laser (SRL) subject to a periodic modulation of the injection current. By varying the amplitude and frequency of the modulation at a fixed bias current, different dynamical states including periodic, quasi-periodic, and chaotic states are found. At frequencies comparable to the relaxation oscillation frequency, the intensities of the counterpropagating modes of the SRLs may exhibit in-phase chaotic motion similar to single mode semiconductor lasers. However, antiphase chaotic oscillations in the modal intensities are observed for modulation frequencies significantly lower than the relaxation oscillations frequency. We show that this antiphase chaotic regime does not involve carrier dynamics and is a result of the underlying symmetry of the SRL. We derive a two-dimensional asymptotic model valid on time-scales longer than the relaxation oscillations, which reproduces the observed dynamical behavior. In a further simplification, we can link this reduced set of equations to Duffing-type oscillators.
13.
Coomans, W.; Gelens, L.; der Sande, G. Van; Mezosi, G.; Sorel, M.; Danckaert, J.; Verschaffelt, G.
Semiconductor ring lasers coupled by a single waveguide
In: Applied Physics Letters, vol. 100, no. 25, pp. 251114, 2012, ISSN: 0003-6951, 1077-3118.
@article{coomans_semiconductor_2012,
title = {Semiconductor ring lasers coupled by a single waveguide},
author = {W. Coomans and L. Gelens and G. Van der Sande and G. Mezosi and M. Sorel and J. Danckaert and G. Verschaffelt},
url = {http://scitation.aip.org/content/aip/journal/apl/100/25/10.1063/1.4730615},
doi = {10.1063/1.4730615},
issn = {0003-6951, 1077-3118},
year = {2012},
date = {2012-06-01},
urldate = {2012-06-01},
journal = {Applied Physics Letters},
volume = {100},
number = {25},
pages = {251114},
abstract = {We experimentally and theoretically study the characteristics of semiconductorring lasers bidirectionally coupled by a single bus waveguide. This configuration has, e.g., been suggested for use as an optical memory and as an optical neural network motif. The main results are that the coupling can destabilize the state in which both rings lase in the same direction, and it brings to life a state with equal powers at both outputs. These are both undesirable for optical memory operation. Although the coupling between the rings is bidirectional, the destabilization occurs due to behavior similar to an optically injected laser system.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We experimentally and theoretically study the characteristics of semiconductorring lasers bidirectionally coupled by a single bus waveguide. This configuration has, e.g., been suggested for use as an optical memory and as an optical neural network motif. The main results are that the coupling can destabilize the state in which both rings lase in the same direction, and it brings to life a state with equal powers at both outputs. These are both undesirable for optical memory operation. Although the coupling between the rings is bidirectional, the destabilization occurs due to behavior similar to an optically injected laser system.
14.
Gelens, L.; Knobloch, E.
Traveling waves and defects in the complex Swift-Hohenberg equation
In: Physical Review E, vol. 84, no. 5, pp. 056203, 2011.
@article{gelens_traveling_2011,
title = {Traveling waves and defects in the complex Swift-Hohenberg equation},
author = {L. Gelens and E. Knobloch},
url = {http://link.aps.org/doi/10.1103/PhysRevE.84.056203},
doi = {10.1103/PhysRevE.84.056203},
year = {2011},
date = {2011-11-01},
urldate = {2011-11-01},
journal = {Physical Review E},
volume = {84},
number = {5},
pages = {056203},
abstract = {The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and, as such, admits solutions in the form of traveling waves. The properties of these waves are systematically analyzed and the dynamics associated with sources and sinks of such waves investigated numerically. A number of distinct dynamical regimes is identified and analyzed using appropriate phase equations describing the evolution of long-wavelength instabilities of both the homogeneous oscillating state and constant amplitude traveling waves.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and, as such, admits solutions in the form of traveling waves. The properties of these waves are systematically analyzed and the dynamics associated with sources and sinks of such waves investigated numerically. A number of distinct dynamical regimes is identified and analyzed using appropriate phase equations describing the evolution of long-wavelength instabilities of both the homogeneous oscillating state and constant amplitude traveling waves.
15.
Coomans, W.; Gelens, L.; Beri, S.; Danckaert, J.; der Sande, G. Van
Solitary and coupled semiconductor ring lasers as optical spiking neurons
In: Physical Review E, vol. 84, no. 3, pp. 036209, 2011.
@article{coomans_solitary_2011,
title = {Solitary and coupled semiconductor ring lasers as optical spiking neurons},
author = {W. Coomans and L. Gelens and S. Beri and J. Danckaert and G. Van der Sande},
url = {http://link.aps.org/doi/10.1103/PhysRevE.84.036209},
doi = {10.1103/PhysRevE.84.036209},
year = {2011},
date = {2011-09-01},
urldate = {2011-09-01},
journal = {Physical Review E},
volume = {84},
number = {3},
pages = {036209},
abstract = {We theoretically investigate the possibility of generating pulses in an excitable (asymmetric) semiconductor ring laser (SRL) using optical trigger pulses. We show that the phase difference between the injected field and the electric field inside the SRL determines the direction of the perturbation in phase space. Due to the folded shape of the excitability threshold, this has an important influence on the ability to cross it. A mechanism for exciting multiple consecutive pulses using a single trigger pulse (i.e., multipulse excitability) is revealed. We furthermore investigate the possibility of using asymmetric SRLs in a coupled configuration, which is a first step toward an all-optical neural network using SRLs as building blocks.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We theoretically investigate the possibility of generating pulses in an excitable (asymmetric) semiconductor ring laser (SRL) using optical trigger pulses. We show that the phase difference between the injected field and the electric field inside the SRL determines the direction of the perturbation in phase space. Due to the folded shape of the excitability threshold, this has an important influence on the ability to cross it. A mechanism for exciting multiple consecutive pulses using a single trigger pulse (i.e., multipulse excitability) is revealed. We furthermore investigate the possibility of using asymmetric SRLs in a coupled configuration, which is a first step toward an all-optical neural network using SRLs as building blocks.
16.
Kozyreff, G.; Gelens, L.
Cavity solitons and localized patterns in a finite-size optical cavity
In: Physical Review A, vol. 84, no. 2, pp. 023819, 2011.
@article{kozyreff_cavity_2011,
title = {Cavity solitons and localized patterns in a finite-size optical cavity},
author = {G. Kozyreff and L. Gelens},
url = {http://link.aps.org/doi/10.1103/PhysRevA.84.023819},
doi = {10.1103/PhysRevA.84.023819},
year = {2011},
date = {2011-08-01},
urldate = {2011-08-01},
journal = {Physical Review A},
volume = {84},
number = {2},
pages = {023819},
abstract = {In appropriate ranges of parameters, laser-driven nonlinear optical cavities can support a wide variety of optical patterns, which could be used to carry information. The intensity peaks appearing in these patterns are called cavity solitons and are individually addressable. Using the Lugiato-Lefever equation to model a perfectly homogeneous cavity, we show that cavity solitons can only be located at discrete points and at a minimal distance from the edges. Other localized states which are attached to the edges are identified. By interpreting these patterns in an information coding frame, the information capacity of this dynamical system is evaluated. The results are explained analytically in terms of the the tail characteristics of the cavity solitons. Finally, the influence of boundaries and of cavity imperfections on cavity solitons are compared.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In appropriate ranges of parameters, laser-driven nonlinear optical cavities can support a wide variety of optical patterns, which could be used to carry information. The intensity peaks appearing in these patterns are called cavity solitons and are individually addressable. Using the Lugiato-Lefever equation to model a perfectly homogeneous cavity, we show that cavity solitons can only be located at discrete points and at a minimal distance from the edges. Other localized states which are attached to the edges are identified. By interpreting these patterns in an information coding frame, the information capacity of this dynamical system is evaluated. The results are explained analytically in terms of the the tail characteristics of the cavity solitons. Finally, the influence of boundaries and of cavity imperfections on cavity solitons are compared.
17.
Tlidi, M.; Kockaert, P.; Gelens, L.
Dark localized structures in a cavity filled with a left-handed material
In: Physical Review A, vol. 84, no. 1, pp. 013807, 2011.
@article{tlidi_dark_2011,
title = {Dark localized structures in a cavity filled with a left-handed material},
author = {M. Tlidi and P. Kockaert and L. Gelens},
url = {http://link.aps.org/doi/10.1103/PhysRevA.84.013807},
doi = {10.1103/PhysRevA.84.013807},
year = {2011},
date = {2011-07-01},
urldate = {2011-07-01},
journal = {Physical Review A},
volume = {84},
number = {1},
pages = {013807},
abstract = {We consider a nonlinear passive optical cavity filled with left-handed and right-handed materials and driven by a coherent injected beam. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction allows us to stabilize dark localized structures in this device. These structures consist of dips in the transverse profile of the intracavity field and do not exist without high-order diffraction. We analyze the snaking bifurcation diagram associated with these structures. Finally, a realistic estimation of the model parameters is provided.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We consider a nonlinear passive optical cavity filled with left-handed and right-handed materials and driven by a coherent injected beam. We assume that both left-handed and right-handed materials possess a Kerr focusing type of nonlinearity. We show that close to the zero-diffraction regime, high-order diffraction allows us to stabilize dark localized structures in this device. These structures consist of dips in the transverse profile of the intracavity field and do not exist without high-order diffraction. We analyze the snaking bifurcation diagram associated with these structures. Finally, a realistic estimation of the model parameters is provided.
18.
Gelens, L.; Mashal, L.; Beri, S.; Coomans, W.; der Sande, G. Van; Danckaert, J.; Verschaffelt, G.
Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization
In: Physical Review A, vol. 82, no. 6, pp. 063841, 2010.
@article{gelens_excitability_2010,
title = {Excitability in semiconductor microring lasers: Experimental and theoretical pulse characterization},
author = {L. Gelens and L. Mashal and S. Beri and W. Coomans and G. Van der Sande and J. Danckaert and G. Verschaffelt},
url = {http://link.aps.org/doi/10.1103/PhysRevA.82.063841},
doi = {10.1103/PhysRevA.82.063841},
year = {2010},
date = {2010-12-01},
urldate = {2010-12-01},
journal = {Physical Review A},
volume = {82},
number = {6},
pages = {063841},
abstract = {We characterize the operation of semiconductor microring lasers in an excitable regime. Our experiments reveal a statistical distribution of the characteristics of noise-triggered optical pulses that is not observed in other excitable systems. In particular, an inverse correlation exists between the pulse amplitude and duration. Numerical simulations and an interpretation in an asymptotic phase space confirm and explain these experimentally observed pulse characteristics.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We characterize the operation of semiconductor microring lasers in an excitable regime. Our experiments reveal a statistical distribution of the characteristics of noise-triggered optical pulses that is not observed in other excitable systems. In particular, an inverse correlation exists between the pulse amplitude and duration. Numerical simulations and an interpretation in an asymptotic phase space confirm and explain these experimentally observed pulse characteristics.
19.
Gelens, L.; Knobloch, E.
Coarsening and frozen faceted structures in the supercritical complex Swift-Hohenberg equation
In: The European Physical Journal D, vol. 59, no. 1, pp. 23–36, 2010, ISSN: 1434-6060, 1434-6079.
@article{gelens_coarsening_2010,
title = {Coarsening and frozen faceted structures in the supercritical complex Swift-Hohenberg equation},
author = {L. Gelens and E. Knobloch},
url = {http://link.springer.com/article/10.1140/epjd/e2010-00132-6},
doi = {10.1140/epjd/e2010-00132-6},
issn = {1434-6060, 1434-6079},
year = {2010},
date = {2010-05-01},
urldate = {2010-05-01},
journal = {The European Physical Journal D},
volume = {59},
number = {1},
pages = {23--36},
abstract = {. The supercritical complex Swift-Hohenberg equation models pattern formation in lasers, optical parametric oscillators and photorefractive oscillators. Simulations of this equation in one spatial dimension reveal that much of the observed dynamics can be understood in terms of the properties of exact solutions of phase-winding type. With real coefficients these states take the form of time-independent spatial oscillations with a constant phase difference between the real and imaginary parts of the order parameter and may be unstable to a longwave instability. Depending on parameters the evolution of this instability may or may not conserve phase. In the former case the system undergoes slow coarsening described by a Cahn-Hilliard equation; in the latter it undergoes repeated phase-slips leading either to a stable phase-winding state or to a faceted state consisting of an array of frozen defects connecting phase-winding states with equal and opposite phase. The transitions between these regimes are studied and their location in parameter space is determined.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
. The supercritical complex Swift-Hohenberg equation models pattern formation in lasers, optical parametric oscillators and photorefractive oscillators. Simulations of this equation in one spatial dimension reveal that much of the observed dynamics can be understood in terms of the properties of exact solutions of phase-winding type. With real coefficients these states take the form of time-independent spatial oscillations with a constant phase difference between the real and imaginary parts of the order parameter and may be unstable to a longwave instability. Depending on parameters the evolution of this instability may or may not conserve phase. In the former case the system undergoes slow coarsening described by a Cahn-Hilliard equation; in the latter it undergoes repeated phase-slips leading either to a stable phase-winding state or to a faceted state consisting of an array of frozen defects connecting phase-winding states with equal and opposite phase. The transitions between these regimes are studied and their location in parameter space is determined.
20.
Gelens, L.; Gomila, D.; der Sande, G. Van; Matías, M. A.; Colet, P.
Nonlocality-induced front-interaction enhancement
In: Physical Review Letters, vol. 104, no. 15, pp. 154101, 2010.
@article{gelens_nonlocality-induced_2010,
title = {Nonlocality-induced front-interaction enhancement},
author = {L. Gelens and D. Gomila and G. Van der Sande and M. A. Matías and P. Colet},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.104.154101},
doi = {10.1103/PhysRevLett.104.154101},
year = {2010},
date = {2010-04-01},
urldate = {2010-04-01},
journal = {Physical Review Letters},
volume = {104},
number = {15},
pages = {154101},
abstract = {We demonstrate that nonlocal coupling strongly influences the dynamics of fronts connecting two equivalent states. In two prototype models we observe a large amplification in the interaction strength between two opposite fronts increasing front velocities several orders of magnitude. By analyzing the spatial dynamics we prove that way beyond quantitative effects, nonlocal terms can also change the overall qualitative picture by inducing oscillations in the front profile. This leads to a mechanism for the formation of localized structures not present for local interactions. Finally, nonlocal coupling can induce a steep broadening of localized structures, eventually annihilating them.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We demonstrate that nonlocal coupling strongly influences the dynamics of fronts connecting two equivalent states. In two prototype models we observe a large amplification in the interaction strength between two opposite fronts increasing front velocities several orders of magnitude. By analyzing the spatial dynamics we prove that way beyond quantitative effects, nonlocal terms can also change the overall qualitative picture by inducing oscillations in the front profile. This leads to a mechanism for the formation of localized structures not present for local interactions. Finally, nonlocal coupling can induce a steep broadening of localized structures, eventually annihilating them.
21.
Gelens, L.; Beri, S.; der Sande, G. Van; Verschaffelt, G.; Danckaert, J.
Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry
In: The European Physical Journal D, vol. 58, no. 2, pp. 197–207, 2010, ISSN: 1434-6060, 1434-6079.
@article{gelens_multistable_2010,
title = {Multistable and excitable behavior in semiconductor ring lasers with broken Z2-symmetry},
author = {L. Gelens and S. Beri and G. Van der Sande and G. Verschaffelt and J. Danckaert},
url = {http://link.springer.com/article/10.1140/epjd/e2010-00042-7},
doi = {10.1140/epjd/e2010-00042-7},
issn = {1434-6060, 1434-6079},
year = {2010},
date = {2010-03-01},
urldate = {2010-03-01},
journal = {The European Physical Journal D},
volume = {58},
number = {2},
pages = {197--207},
abstract = {We study the bifurcation scenario and the evolution of the counter-propagating modes in a semiconductor ring laser when their symmetry is broken. We show how a two-dimensional asymptotic model for this asymmetric ring laser can be used to interpret and predict regions of multistability and excitability in the laser. The theoretical predictions and insights in these different dynamical regimes of the asymmetric semiconductor ring laser are confirmed and further explored experimentally in a semiconductor ring laser set-up that allows to controllably break the Z2-symmetry of the laser.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study the bifurcation scenario and the evolution of the counter-propagating modes in a semiconductor ring laser when their symmetry is broken. We show how a two-dimensional asymptotic model for this asymmetric ring laser can be used to interpret and predict regions of multistability and excitability in the laser. The theoretical predictions and insights in these different dynamical regimes of the asymmetric semiconductor ring laser are confirmed and further explored experimentally in a semiconductor ring laser set-up that allows to controllably break the Z2-symmetry of the laser.
22.
Coomans, W.; Beri, S.; der Sande, G. Van; Gelens, L.; Danckaert, J.
Optical injection in semiconductor ring lasers
In: Physical Review A, vol. 81, no. 3, pp. 033802, 2010.
@article{coomans_optical_2010,
title = {Optical injection in semiconductor ring lasers},
author = {W. Coomans and S. Beri and G. Van der Sande and L. Gelens and J. Danckaert},
url = {http://link.aps.org/doi/10.1103/PhysRevA.81.033802},
doi = {10.1103/PhysRevA.81.033802},
year = {2010},
date = {2010-03-01},
urldate = {2010-03-01},
journal = {Physical Review A},
volume = {81},
number = {3},
pages = {033802},
abstract = {We theoretically investigate optical injection in semiconductor ring lasers and disclose several dynamical regimes. Through numerical simulations and bifurcation continuation, two separate parameter regions in which two different injection-locked solutions coexist are revealed, in addition to a region in which a frequency-locked limit cycle coexists with an injection-locked solution. Finally, an antiphase chaotic regime without the involvement of any carrier dynamics is revealed. Parallels are drawn with the onset of chaos in the periodically forced Duffing oscillator.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We theoretically investigate optical injection in semiconductor ring lasers and disclose several dynamical regimes. Through numerical simulations and bifurcation continuation, two separate parameter regions in which two different injection-locked solutions coexist are revealed, in addition to a region in which a frequency-locked limit cycle coexists with an injection-locked solution. Finally, an antiphase chaotic regime without the involvement of any carrier dynamics is revealed. Parallels are drawn with the onset of chaos in the periodically forced Duffing oscillator.
23.
Tlidi, M.; Gelens, L.
High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities
In: Optics Letters, vol. 35, no. 3, pp. 306–308, 2010, ISSN: 1539-4794.
@article{tlidi_high-order_2010,
title = {High-order dispersion stabilizes dark dissipative solitons in all-fiber cavities},
author = {M. Tlidi and L. Gelens},
url = {http://www.osapublishing.org/abstract.cfm?uri=ol-35-3-306},
doi = {10.1364/OL.35.000306},
issn = {1539-4794},
year = {2010},
date = {2010-02-01},
urldate = {2010-02-01},
journal = {Optics Letters},
volume = {35},
number = {3},
pages = {306--308},
abstract = {Near a zero-dispersion wavelength, high-order dispersion effects play a central role in a photonic crystal fiber cavity. The study of such effects reveals the existence of stable dissipative dark solitons in the anomalous dispersion regime. Such dark localized structures are not present without high-order dispersion. They consist of dips in the profile of the intensity field. The number of dips and their temporal distribution are determined by the initial conditions. A snaking bifurcation diagram associated with these solutions is constructed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Near a zero-dispersion wavelength, high-order dispersion effects play a central role in a photonic crystal fiber cavity. The study of such effects reveals the existence of stable dissipative dark solitons in the anomalous dispersion regime. Such dark localized structures are not present without high-order dispersion. They consist of dips in the profile of the intensity field. The number of dips and their temporal distribution are determined by the initial conditions. A snaking bifurcation diagram associated with these solutions is constructed.
24.
Beri, S.; Mashall, L.; Gelens, L.; der Sande, G. Van; Mezosi, G.; Sorel, M.; Danckaert, J.; Verschaffelt, G.
Excitability in optical systems close to -symmetry
In: Physics Letters A, vol. 374, no. 5, pp. 739–743, 2010, ISSN: 0375-9601.
@article{beri_excitability_2010,
title = {Excitability in optical systems close to -symmetry},
author = {S. Beri and L. Mashall and L. Gelens and G. Van der Sande and G. Mezosi and M. Sorel and J. Danckaert and G. Verschaffelt},
url = {http://www.sciencedirect.com/science/article/pii/S0375960109015035},
doi = {10.1016/j.physleta.2009.11.070},
issn = {0375-9601},
year = {2010},
date = {2010-01-01},
urldate = {2010-01-01},
journal = {Physics Letters A},
volume = {374},
number = {5},
pages = {739--743},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
25.
Gelens, L.; Knobloch, E.
Faceting and coarsening dynamics in the complex Swift-Hohenberg equation
In: Physical Review E, vol. 80, no. 4, pp. 046221, 2009.
@article{gelens_faceting_2009,
title = {Faceting and coarsening dynamics in the complex Swift-Hohenberg equation},
author = {L. Gelens and E. Knobloch},
url = {http://link.aps.org/doi/10.1103/PhysRevE.80.046221},
doi = {10.1103/PhysRevE.80.046221},
year = {2009},
date = {2009-10-01},
urldate = {2009-10-01},
journal = {Physical Review E},
volume = {80},
number = {4},
pages = {046221},
abstract = {The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and finds applications in lasers, optical parametric oscillators, and photorefractive oscillators. We show that with real coefficients this equation exhibits two classes of localized states: localized in amplitude only or localized in both amplitude and phase. The latter are associated with phase-winding states in which the real and imaginary parts of the order parameter oscillate periodically but with a constant phase difference between them. The localized states take the form of defects connecting phase-winding states with equal and opposite phase lag, and can be stable over a wide range of parameters. The formation of these defects leads to faceting of states with initially spatially uniform phase. Depending on parameters these facets may either coarsen indefinitely, as described by a Cahn-Hilliard equation, or the coarsening ceases leading to a frozen faceted structure.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The complex Swift-Hohenberg equation models pattern formation arising from an oscillatory instability with a finite wave number at onset and finds applications in lasers, optical parametric oscillators, and photorefractive oscillators. We show that with real coefficients this equation exhibits two classes of localized states: localized in amplitude only or localized in both amplitude and phase. The latter are associated with phase-winding states in which the real and imaginary parts of the order parameter oscillate periodically but with a constant phase difference between them. The localized states take the form of defects connecting phase-winding states with equal and opposite phase lag, and can be stable over a wide range of parameters. The formation of these defects leads to faceting of states with initially spatially uniform phase. Depending on parameters these facets may either coarsen indefinitely, as described by a Cahn-Hilliard equation, or the coarsening ceases leading to a frozen faceted structure.
26.
Beri, S.; Gelens, L.; der Sande, G. Van; Danckaert, J.
Asymptotic approach to the analysis of mode-hopping in semiconductor ring lasers
In: Physical Review A, vol. 80, no. 1, pp. 013823, 2009.
@article{beri_asymptotic_2009,
title = {Asymptotic approach to the analysis of mode-hopping in semiconductor ring lasers},
author = {S. Beri and L. Gelens and G. Van der Sande and J. Danckaert},
url = {http://link.aps.org/doi/10.1103/PhysRevA.80.013823},
doi = {10.1103/PhysRevA.80.013823},
year = {2009},
date = {2009-07-01},
urldate = {2009-07-01},
journal = {Physical Review A},
volume = {80},
number = {1},
pages = {013823},
abstract = {We investigate the directional mode-hopping in semiconductor ring lasers in the limit of small noise intensity. We show how only long time scales are involved in the hopping process. In such limit, the initial stochastic rate equations can be reduced to an auxiliary Hamiltonian system, and the dependence of the hopping on the laser parameters can be investigated. The predictions made from the reduced model agree well with the results obtained by simulating the full rate-equation system.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We investigate the directional mode-hopping in semiconductor ring lasers in the limit of small noise intensity. We show how only long time scales are involved in the hopping process. In such limit, the initial stochastic rate equations can be reduced to an auxiliary Hamiltonian system, and the dependence of the hopping on the laser parameters can be investigated. The predictions made from the reduced model agree well with the results obtained by simulating the full rate-equation system.
27.
Gelens, L.; Beri, S.; der Sande, G. Van; Mezosi, G.; Sorel, M.; Danckaert, J.; Verschaffelt, G.
Exploring multistability in semiconductor ring lasers: Theory and experiment
In: Physical Review Letters, vol. 102, no. 19, pp. 193904, 2009.
@article{gelens_exploring_2009,
title = {Exploring multistability in semiconductor ring lasers: Theory and experiment},
author = {L. Gelens and S. Beri and G. Van der Sande and G. Mezosi and M. Sorel and J. Danckaert and G. Verschaffelt},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.102.193904},
doi = {10.1103/PhysRevLett.102.193904},
year = {2009},
date = {2009-05-01},
urldate = {2009-05-01},
journal = {Physical Review Letters},
volume = {102},
number = {19},
pages = {193904},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
28.
Gelens, L.; der Sande, G. Van; Beri, S.; Danckaert, J.
Phase-space approach to directional switching in semiconductor ring lasers
In: Physical Review E, vol. 79, no. 1, pp. 016213, 2009.
@article{gelens_phase-space_2009,
title = {Phase-space approach to directional switching in semiconductor ring lasers},
author = {L. Gelens and G. Van der Sande and S. Beri and J. Danckaert},
url = {http://link.aps.org/doi/10.1103/PhysRevE.79.016213},
doi = {10.1103/PhysRevE.79.016213},
year = {2009},
date = {2009-01-01},
urldate = {2009-01-01},
journal = {Physical Review E},
volume = {79},
number = {1},
pages = {016213},
abstract = {We show that a topological investigation of the phase space of a semiconductor ring laser can be used to devise switching schemes which are alternative to optical pulse injection of counterpropagating light. To provide physical insight in these switching mechanisms, a full bifurcation analysis and an investigation of the topology is performed on a two-dimensional asymptotic model. Numerical simulations confirm the topological predictions.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We show that a topological investigation of the phase space of a semiconductor ring laser can be used to devise switching schemes which are alternative to optical pulse injection of counterpropagating light. To provide physical insight in these switching mechanisms, a full bifurcation analysis and an investigation of the topology is performed on a two-dimensional asymptotic model. Numerical simulations confirm the topological predictions.
29.
Beri, S.; Gelens, L.; Mestre, M.; der Sande, G. Van; Verschaffelt, G.; Scirè, A.; Mezosi, G.; Sorel, M.; Danckaert, J.
Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers
In: Physical Review Letters, vol. 101, no. 9, pp. 093903, 2008.
@article{beri_topological_2008,
title = {Topological insight into the non-Arrhenius mode hopping of semiconductor ring lasers},
author = {S. Beri and L. Gelens and M. Mestre and G. Van der Sande and G. Verschaffelt and A. Scirè and G. Mezosi and M. Sorel and J. Danckaert},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.101.093903},
doi = {10.1103/PhysRevLett.101.093903},
year = {2008},
date = {2008-08-01},
urldate = {2008-08-01},
journal = {Physical Review Letters},
volume = {101},
number = {9},
pages = {093903},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
30.
Gelens, L.; Beri, S.; der Sande, G. Van; Danckaert, J.; Calabretta, N.; Dorren, H. J. S.; Nötzel, R.; Bente, E. A. J. M.; Smit, M. K.
Optical injection in semiconductor ring lasers: backfire dynamics
In: Optics Express, vol. 16, no. 15, pp. 10968–10974, 2008, ISSN: 1094-4087.
@article{gelens_optical_2008,
title = {Optical injection in semiconductor ring lasers: backfire dynamics},
author = {L. Gelens and S. Beri and G. Van der Sande and J. Danckaert and N. Calabretta and H. J. S. Dorren and R. Nötzel and E. A. J. M. Bente and M. K. Smit},
url = {http://www.osapublishing.org/abstract.cfm?uri=oe-16-15-10968},
doi = {10.1364/OE.16.010968},
issn = {1094-4087},
year = {2008},
date = {2008-07-01},
urldate = {2008-07-01},
journal = {Optics Express},
volume = {16},
number = {15},
pages = {10968--10974},
abstract = {We report on directional mode switching in semiconductor ring lasers through optical injection co-propagating with the lasing mode. The understanding of this novel feature in ring lasers is based on the particular structure of a two-dimensional asymptotic phase space. Our theoretical results are verified numerically and experimentally.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We report on directional mode switching in semiconductor ring lasers through optical injection co-propagating with the lasing mode. The understanding of this novel feature in ring lasers is based on the particular structure of a two-dimensional asymptotic phase space. Our theoretical results are verified numerically and experimentally.
31.
Gelens, L.; Gomila, D.; der Sande, G. Van; Danckaert, J.; Colet, P.; Matías, M. A.
In: Physical Review A, vol. 77, no. 3, pp. 033841, 2008.
@article{gelens_dynamical_2008,
title = {Dynamical instabilities of dissipative solitons in nonlinear optical cavities with nonlocal materials},
author = {L. Gelens and D. Gomila and G. Van der Sande and J. Danckaert and P. Colet and M. A. Matías},
url = {http://link.aps.org/doi/10.1103/PhysRevA.77.033841},
doi = {10.1103/PhysRevA.77.033841},
year = {2008},
date = {2008-03-01},
urldate = {2008-03-01},
journal = {Physical Review A},
volume = {77},
number = {3},
pages = {033841},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
32.
der Sande, G Van; Gelens, L.; Tassin, P.; Scirè, A.; Danckaert, J.
In: Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 41, no. 9, pp. 095402, 2008, ISSN: 0953-4075.
@article{sande_two-dimensional_2008,
title = {Two-dimensional phase-space analysis and bifurcation study of the dynamical behaviour of a semiconductor ring laser},
author = {G Van der Sande and L. Gelens and P. Tassin and A. Scirè and J. Danckaert},
url = {http://stacks.iop.org/0953-4075/41/i=9/a=095402},
doi = {10.1088/0953-4075/41/9/095402},
issn = {0953-4075},
year = {2008},
date = {2008-01-01},
urldate = {2008-01-01},
journal = {Journal of Physics B: Atomic, Molecular and Optical Physics},
volume = {41},
number = {9},
pages = {095402},
abstract = {A basic rate equation model of a quantum-well semiconductor ring laser is reduced to two equations using asymptotic methods. The reduced model allows for analytical expressions of the bifurcation points, which will simplify future model parameter estimations, and motivates a two-dimensional phase-space description of the dynamical behaviour. An analysis of the bifurcation scenarios in different parameter regimes is pursued. Physical conditions for the emergence of the operating regimes are assessed quantitatively in terms of saturation processes and backscattering mechanisms.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
A basic rate equation model of a quantum-well semiconductor ring laser is reduced to two equations using asymptotic methods. The reduced model allows for analytical expressions of the bifurcation points, which will simplify future model parameter estimations, and motivates a two-dimensional phase-space description of the dynamical behaviour. An analysis of the bifurcation scenarios in different parameter regimes is pursued. Physical conditions for the emergence of the operating regimes are assessed quantitatively in terms of saturation processes and backscattering mechanisms.
33.
Tassin, P.; Gelens, L.; Danckaert, J.; Veretennicoff, I.; der Sande, G. Van; Kockaert, P.; Tlidi, M.
Dissipative structures in left-handed material cavity optics
In: Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 17, no. 3, pp. 037116, 2007, ISSN: 1054-1500, 1089-7682.
@article{tassin_dissipative_2007,
title = {Dissipative structures in left-handed material cavity optics},
author = {P. Tassin and L. Gelens and J. Danckaert and I. Veretennicoff and G. Van der Sande and P. Kockaert and M. Tlidi},
url = {http://scitation.aip.org/content/aip/journal/chaos/17/3/10.1063/1.2768158},
doi = {10.1063/1.2768158},
issn = {1054-1500, 1089-7682},
year = {2007},
date = {2007-09-01},
urldate = {2007-09-01},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
volume = {17},
number = {3},
pages = {037116},
abstract = {We study the spatiotemporal dynamics of spatially extended nonlinear cavities containing a left-handed material. Such materials, which have a negative index of refraction, have been experimentally demonstrated recently, and allow for novel electromagnetic behavior. We show that the insertion of a left-handed material in an optical resonator allows for controlling the value and the sign of the diffraction coefficient in dispersive Kerr resonators and degenerate optical parametric oscillators. We give an overview of our analytical and numerical studies on the stability and formation of dissipative structures in systems with negative diffraction.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study the spatiotemporal dynamics of spatially extended nonlinear cavities containing a left-handed material. Such materials, which have a negative index of refraction, have been experimentally demonstrated recently, and allow for novel electromagnetic behavior. We show that the insertion of a left-handed material in an optical resonator allows for controlling the value and the sign of the diffraction coefficient in dispersive Kerr resonators and degenerate optical parametric oscillators. We give an overview of our analytical and numerical studies on the stability and formation of dissipative structures in systems with negative diffraction.
34.
Gelens, L.; der Sande, G. Van; Tassin, P.; Tlidi, M.; Kockaert, P.; Gomila, D.; Veretennicoff, I.; Danckaert, J.
Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures
In: Physical Review A, vol. 75, no. 6, pp. 063812, 2007.
@article{gelens_impact_2007,
title = {Impact of nonlocal interactions in dissipative systems: Towards minimal-sized localized structures},
author = {L. Gelens and G. Van der Sande and P. Tassin and M. Tlidi and P. Kockaert and D. Gomila and I. Veretennicoff and J. Danckaert},
url = {http://link.aps.org/doi/10.1103/PhysRevA.75.063812},
doi = {10.1103/PhysRevA.75.063812},
year = {2007},
date = {2007-06-01},
urldate = {2007-06-01},
journal = {Physical Review A},
volume = {75},
number = {6},
pages = {063812},
abstract = {In order to investigate the size limit of spatial localized structures in a nonlinear system, we explore the impact of linear nonlocality on their domains of existence and stability. Our system of choice is an optical microresonator containing an additional metamaterial layer in the cavity, allowing the nonlocal response of the material to become the dominating spatial process. In that case, our bifurcation analysis shows that this nonlocality imposes another limit on the width of localized structures going beyond the traditional diffraction limit.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In order to investigate the size limit of spatial localized structures in a nonlinear system, we explore the impact of linear nonlocality on their domains of existence and stability. Our system of choice is an optical microresonator containing an additional metamaterial layer in the cavity, allowing the nonlocal response of the material to become the dominating spatial process. In that case, our bifurcation analysis shows that this nonlocality imposes another limit on the width of localized structures going beyond the traditional diffraction limit.