Topological and geometrical disorder correlate robustly in two-dimensional foams

Simon Cox; J. Kafer; D. Rabaud; C. Quilliet; François Graner; S. Ataei Talebi

doi:10.1080/09500830802334249

Topological and geometrical disorder correlate robustly in two-dimensional foams

Simon Cox, J. Kafer, D. Rabaud, C. Quilliet, François Graner, S. Ataei Talebi

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A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is 'shuffled' (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	651-660
Cyfnodolyn	Philosophical Magazine Letters
Cyfrol	88
Rhif cyhoeddi	9-10
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1080/09500830802334249
Statws	Cyhoeddwyd - 2008

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10.1080/09500830802334249

quilliet_disorder_revised.pdfLlawysgrif a gyflwynwyd, 683 KB

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@article{d2c76fc99cbf4676beae0ea4cf812d8a,

title = "Topological and geometrical disorder correlate robustly in two-dimensional foams",

abstract = "A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is 'shuffled' (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues.",

author = "Simon Cox and J. Kafer and D. Rabaud and C. Quilliet and Fran{\c c}ois Graner and {Ataei Talebi}, S.",

note = "Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes C. Quilliet, S. Ataei Talebi, D. Rabaud, J. Kafer, S.J. Cox and F. Graner (2008) Topological and geometrical disorder correlate robustly in two-dimensional foams. Sponsorship: We thank J. Legoupil for his participation in the simulations, K. Brakke for developing and maintaining the Surface Evolver code, A.F.M. Maree for developing the Potts model code used here, M.F. Vaz for providing references, I. Cantat for critical reading of the manuscript, Y. Bella¨ıche, R. Carthew and T. Hayashi for providing pictures of biological tissues, S. Courty for their analysis, P. Ballet for help in setting up the experiment, and participants of the Foam Mechanics workshop (Grenoble, January 2008) for many discussions. S.A.T. thanks Dr Ejtehadi for hospitality at the Institute of Physics and Mathematics, Tehran (Iran). S.J.C. thanks UJF for hospitality, and CNRS, EPSRC (EP/D048397/1, EP/D071127/1) and the British Council Alliance scheme for financial support.",

year = "2008",

doi = "10.1080/09500830802334249",

language = "English",

volume = "88",

pages = "651--660",

journal = "Philosophical Magazine Letters",

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TY - JOUR

T1 - Topological and geometrical disorder correlate robustly in two-dimensional foams

AU - Cox, Simon

AU - Kafer, J.

AU - Rabaud, D.

AU - Quilliet, C.

AU - Graner, François

AU - Ataei Talebi, S.

N1 - Special Issue: Solid and Liquid Foams. In commemoration of Manuel Amaral Fortes C. Quilliet, S. Ataei Talebi, D. Rabaud, J. Kafer, S.J. Cox and F. Graner (2008) Topological and geometrical disorder correlate robustly in two-dimensional foams. Sponsorship: We thank J. Legoupil for his participation in the simulations, K. Brakke for developing and maintaining the Surface Evolver code, A.F.M. Maree for developing the Potts model code used here, M.F. Vaz for providing references, I. Cantat for critical reading of the manuscript, Y. Bella¨ıche, R. Carthew and T. Hayashi for providing pictures of biological tissues, S. Courty for their analysis, P. Ballet for help in setting up the experiment, and participants of the Foam Mechanics workshop (Grenoble, January 2008) for many discussions. S.A.T. thanks Dr Ejtehadi for hospitality at the Institute of Physics and Mathematics, Tehran (Iran). S.J.C. thanks UJF for hospitality, and CNRS, EPSRC (EP/D048397/1, EP/D071127/1) and the British Council Alliance scheme for financial support.

PY - 2008

Y1 - 2008

N2 - A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is 'shuffled' (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues.

AB - A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is 'shuffled' (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues.

U2 - 10.1080/09500830802334249

DO - 10.1080/09500830802334249

M3 - Special issue

SN - 0950-0839

VL - 88

SP - 651

EP - 660

JO - Philosophical Magazine Letters

JF - Philosophical Magazine Letters

IS - 9-10

ER -

Topological and geometrical disorder correlate robustly in two-dimensional foams

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