ICMS

Isoperimetric problems, space-filling, and soap bubble geometry

Mar 19, 2012 - Mar 23, 2012

ICMS, 15 South College Street Edinburgh

Organisers

Name	Institution
Cox, Simon	Aberystwyth University
Morgan, Frank	Williams College
Sullivan, John	Technische Universitat Berlin

 

This workshop will address the following problems: 

• What are the main difficulties in trying to use the method of proof of the honeycomb conjecture to prove that the Kelvin cell is the least area tiling of space. Can similar tools be used to say anything about the Weaire-Phelan structure and its conjectured optimality?

• What are the optimal numerical procedures for determining conjectured minimizers for finite tilings? To what extent can they aid proofs of optimality?

• Where can this mathematics make an impact?

 The workshop will bring together experts in geometric measure theory, numerical computation, and foam structure and applications to make progress finding and proving the optimum area-minimizing cellular structures. It is anticipated that recent computational results may provide guidance in developing proofs, and results of the last 10 years will stimulate interest and further work in the area.

Each day the workshop will start with a plenary talk. Plenary speakers will be encouraged to focus on open questions to provoke discussion and debate amongst participants.  The organizers will ask participants to submit ideas for short talks on recent progress in the field to stimulate interaction and discussion. The remainder of the workshop will be made up of small group problem discussions. 

There are a limited number of spaces available at this workshop. If you would like to participate (and have not already received an invitation from ICMS by email) please apply using this application form. Completed applications must be submitted by Monday 20 February 2012 at the latest. Please note there is no financial support available from ICMS. 

A blog has been created by the workshop organisers to enable discussion in this medium ahead of the workshop. The blog can be found here.Frank Morgan also writes about the workshop here.

Photographs from the workshop can be seen on the ICMS Flickr account.

Arrangements

Venue
The workshop will take place at ICMS, 15 South College Street, Edinburgh, Scotland.

Lecture theatre facilities
The lecture theatre is fitted with data projection, visualiser (the new generation of over-head), smart-board and blackboard.  More information about the facilities are available from Helene Frossling.

Accommodation
Invited participants:
If your invitation included the offer of accommodation, then ICMS will arrange this and details will be in your letter of invitation. ICMS has reserved rooms for all delegates in University of Edinburgh en suite accommodation. All accommodation is no more than a twenty minute walk from ICMS. Please indicate on your booking form if you wish to take up the offer of these rooms or make your own arrangements. DELEGATES WILL RECEIVE INFORMATION ABOUT THEIR ACCOMMODATION IN THE FIRST WEEK OF MARCH 2012

Other participants:
ICMS cannot reserve accommodation for you. Suggestions for accommodation close to ICMS can be found here.

Meals and Refreshments
Morning and afternoon refreshments will be provided on each day of the workshop. A buffet lunch will be provided at ICMS in the Chapterhouse on the ground floor of 15 South College Street on Monday, Tuesday and Thursday. A workshop dinner will be held. The workshop grant will cover the cost of this catering.

Registration Fee and Financial Matters
A registration fee of £50 is payable by all speakers and participants. This can be paid by completing the details on this credit/debit card payment form.   As email is not secure, please print the form and return it by fax using the fax number at the top of the form.  ICMS will take your payment and a receipt will be given to you at Registration.  Alternatively, we can accept sterling cheques, made payable to Heriot-Watt University but sent to Helene Frossling , ICMS, 15 South College Street, Edinburgh, EH8 9AA.  If you have any difficulty in paying in advance, please email Helene Frossling.

Visas
ICMS asks attendees to check if they require a visa for entry to the United Kingdom. This government website gives more information. If you do require a visa ICMS will provide you with a letter in support of your application. 

Travel
Information about travel to the UK and Edinburgh is available here. Lothian buses charge 1.30 GBP for a single journey and 3.20 GBP for a day ticket. Please note that the exact fare is required and no change is given.

A taxi directly from the airport will cost approximately 18.00 to 20.00 GBP to the city centre for a one-way journey.

From the airport, you can take the airport bus Airlink to the city centre. It will cost you 3.50 GBP for a single ticket, or 6.00 GBP return. More details on the airport bus Airlink is available here. The bus will take you to Waverley Bridge (next to Waverley Railway Station).

If travelling by train, please note that Edinburgh has two railway stations - Waverley Railway Station being the main station and closest to the workshop venue at ICMS and George Square. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge map. The second railway station is called Haymarket and is at the West End of the city centre.

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

Conference Co-ordinator
Helene Frossling is the conference co-ordinator for this workshop.  

 

Programme

Preliminary programme published Monday 27 February 2012. Last updated 14 March.

 

Monday 19 March

08.30 - 09.00	Registration and coffee
09.00 - 09.30	Welcome and logistics
09.30 - 10.15	Manuel Ritoré (Universidad de Granada) Geometric inequalities and soap bubbles Link to slides (pdf)
10.15 - 10.30	Discussion
10.30 - 11.00	Coffee and tea (served in the Chapterhouse), time for private discussions
11.00 - 12.00	Contributed talks (15+5 minutes each, order may change)
	Antonio Cañete (Universidad de Sevilla) The isoperimetric problem in R^n for homogeneous densities Link to slides (pdf)
	Ruggero Gabbrielli (Princeton University) Ideas for an extension to the Frank-Kasper phases
	Stefano Nardulli  (Universidade Federal do Rio de Janeiro) Isoperimetry in non-compact Riemannian manifolds
12.00 - 13.30	Lunch served in the Chapterhouse
13.30 - 14.15	Thomas Hales  (University of Pittsburgh) Computer assisted proofs and the Kelvin problem Link to slides (pdf)
14.15 - 14.30	Discussion
14.30 - 15.30	Contributed talks (15+5 minutes each, order may change)
	Aladar Heppes (Alfred Renyi Institute of Mathematics) Densest packing of translates of strings
	Aldo Pratelli  (University of Pavia) Recent existence results for the isoperimetric problem in R^N with density Link to slides (pdf)
	Miyuki Koiso (Institute of Mathematics for Industry) Bifurcation and stability for solutions of isoperimetric problems
15.30 - 16.00	Coffee and tea (served in the Chapterhouse), time for private discussions
16.00 - 17.00	Contributed talks (15+5 minutes each, order may change)
	Raymond Goldstein(University of Cambridge) A soap-film Mobius strip changes topology with a twist singularity Link to slides (pdf)
	Paul Sutcliffe (University of Durham) Domain walls and double bubbles Link to slides (pdf)
	Rafi Blumenfeld (Imperial College London & Cambridge University) Quadron tessellation, structural quantification and statistical mechanics of granular and cellular structures

Tuesday 20 March

09.30 - 10.15	Andrew Kraynik (University of Erlangen-Nuremberg) Structure of random polydisperse soap froth Link to slides (PPTX)
10.15 - 10.30	Discussion
10.30 - 11.00	Coffee and tea (served in the Chapterhouse), time for private discussions
11.00 - 12.00	Contributed talks (15+5 minutes each, order may change)
	Edwin Flikkema (Aberystwyth University) From clusters of particles to 2D bubble clusters Link to slides (PPT)
	Sepehr Ravati  (Ecole Polytechnique de Montreal) Polymer droplet clusters
	Adil Mughal   (Aberystwyth University) Phyllotactic description of hard sphere packing in cylindrical channels
12.00 - 13.30	Lunch served in the Chapterhouse
13.30 - 14.15	Robert Nurnberg  (Imperial College London) Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies Link to slides (external)
14.15 - 14.30	Discussion
14.30 - 15.30	Challenge problems: parallel session
15.30 - 16.00	Coffee and tea (served in the Chapterhouse), time for private discussions
16.00 - 17.00	Contributed talks (15+5 minutes each, order may change)
	Simon Cox   (Aberystwyth University) Enumeration of candidates to the minimal free cluster in 2D
	Emanuel Lazar (Princeton University) The "shapes" of some three-dimensional space filling patters
	Robert Nemeth (Budapest University of Technology and Economics) Pattern formation of lotus receptacles Link to slides (pdf)
18.00 - 19.00	PUBLIC LECTURE Denis Weaire (Trinity College Dublin) Me and Kelvin: how bubbles brought me to Beijing
19.00 - 19.45	Wine reception in the Chapterhouse

Wednesday 21 March

09.30 - 10.15	Gary Lawlor (Brigham Young University) New proofs for double and triple bubbles Link to slides (PPT)
10.15 - 10.30	Discussion
10.30 - 11.00	Coffee and tea (served in the Chapterhouse), time for private discussions
	FREE AFTERNOON Schools outreach project: Frank Morgan - Soap Bubbles and Mathematics

Thursday 22 March

09.30 - 10.15	Sascha Hilgenfeldt  (University of Illinois at Urbana Champaign) Order and disorder in tissues and tilings Link to slides (pdf)
10.15 - 10.30	Discussion
10.30 - 11.00	Coffee and tea (served in the Chapterhouse), time for private discussions
11.00 - 12.00	Time for private discussions
12.00 - 13.30	Lunch served in the Chapterhouse
13.30 - 14.15	Fatima Vaz and Paulo Teixeira   Surface energy of two-dimensional finite or periodic foams Link to slides (PPT)
14.15 - 14.30	Discussion
14.30 - 15.30	Challenge problems: parallel session
15.30 - 16.00	Coffee and tea (served in the Chapterhouse), time for private discussions
16.00 - 17.00	Contributed talks (15+5 minutes each, order may change)
	TBA
	TBA
	TBA
19.00	Workshop dinner at The Magnum Restaurant

 

Friday 23 March

09.30 - 10.15	John Sullivan (Technische Universitat Berlin) Foams with small faces
10.15 - 10.30	Discussion
10.30 - 11.00	Coffee and tea (served in the Chapterhouse), time for private discussions
11.00 - 12.00	Plenary summing-up / next steps

 

Presentations:

Presentation Details
Blumenfeld, Rafi
Quadron tessellation, structural quantification and statistical mechanics of granular and cellular structures
View Abstract Hide Abstract
I discuss an extension of the Edwards statistical mechanical formalism to cellular structures, based on a specialised tessellation method that puts numbers on the local micro-structure. Several results are reported, the main two of which are a numerical support for the statistical mechanics approach in 2D and the discovery of an equipartition principle in granular systems. These make possible to quantify the elusive concept of compactivity - the analogue of temperature, which characterises structural fluctuations.
Cañete, Antonio
The isoperimetric problem in R^n for homogeneous densities
View Abstract Hide Abstract
Apart from the classical isoperimetric problem in R^n, we can study the same problem but considering a density function, that is, a function modifying the usual definitions of perimeter and volume functionals. In this talk we shall focus on the particular family of homogeneous densities, giving some existence results and characterizing the stable regions in this setting.
Cox, Simon
Enumeration of candidates to the minimal free cluster in 2D
View Abstract Hide Abstract
Given N bubbles of unit areas, what is the arrangement that minimizes the total perimeter? There are some proofs for small N, but they are made difficult by not being able to assume that each bubble is connected. How much progress could we make if we assumed connectedness? Computer searches over different topologies have been made, but with no guarantee that the optimal topology has been tested. I will discuss whether it is possible to enumerate and test all candidates for each N using a combination of the graph-enumeration tool CAGE and the Surface Evolver.
Flikkema, Edwin
From clusters of particles to 2D bubble clusters
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In this presentation the analogy between 2D interacting particle systems and 2D clusters of bubbles is explored. In cluster physics a cluster is often modelled as a set of particles that interact via potentials, thus resulting in a Potential Energy Surface (PES). Minima on the PES correspond to stable cluster geometries. An important problem in cluster physics is locating low-lying minima, and more specifically the global minimum. Basing Hopping is a global optimisation method that has been particularly successful in finding the global minima of clusters such as Lennard Jones clusters. In this presentation we propose to use two-dimensional cluster geometries as starting points for finding the minimal perimeter configuration of two-dimensional clusters of bubbles. A Voronoi partition is used to turn a 2D pattern of particles into a 2D set of cells. Surface Evolver is then used to minimize the perimeter while keeping the area of each bubble equal. Free bubble clusters have been considered, as well as clusters confined to a shape such as a circle or a polygon. Various forms of the interaction potential have been compared and its success in producing good candidates for the bubble cluster problem has been monitored.
Gabbrielli, Ruggero
Ideas for an extension to the Frank-Kasper phases
View Abstract Hide Abstract
The Frank-Kasper phases contain well defined types of polyhedra with 12, 14, 15 and 16 faces each. An infinite family of structures based on A15, C15 and Z has been described by Sullivan. We report here on a few new examples and ideas for an enlargement of such a family to include the tiling by truncated octahedra.
Goldstein, Raymond E.
A soap-film Mobius strip changes topology with a twist singularity
View Abstract Hide Abstract
It is well-known that a soap film spanning a looped wire can have the topology of a Möbius strip and that deformations of the wire can induce a transformation to a two-sided film, but the process by which this transformation is achieved has remained unknown. In this talk I will disucss recent experimental and theoretical work [Goldstein, Moffatt, Pesci, and Ricca, PNAS 107, 21979 (2010)] that has uncovered the dynamics of this transition. We find that this process consists of a collapse of the film toward the boundary that produces a previously unrecognized finite-time twist singularity that changes the linking number of the film’s Plateau border and the centerline of the wire. We conjecture that it is a general feature of this type of transition that the singularity always occurs at the surface boundary. The change in linking number is shown to be a consequence of a viscous reconnection of the Plateau border at the moment of the singularity. High-speed imaging of the collapse dynamics of the film’s throat, similar to that of the central opening of a catenoid, reveals a crossover between two power laws. Far from the singularity, it is suggested that the collapse is controlled by dissipation within the fluid film surrounding the wire, whereas closer to the transition the power law has the classical form arising from a balance between air inertia and surface tension. Analytical and numerical studies of minimal surfaces and ruled surfaces are used to gain insight into the energetics underlying the transition and the twisted geometry in the neighborhood of the singularity. A number of challenging mathematical questions arising from these observations are posed.
Hales, Thomas
Computer assisted proofs and the Kelvin problem
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Without knowing the form that the solution of the Kelvin problem will eventually take, I will discuss in general terms what it might mean to give a computer assisted proof of the optimality of the Phelan-Weaire foam.
Heppes, Aladar
Densest packing of translates of strings
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In this presentation packings of disjoint translates of strings are considered, - a joint work with K. Boroczky and E. Makai - , where "string" means an equidistant set of translated copies of a convex body. In a few cases the densest packing is latticelike.
Hilgenfeldt, Sascha
Order and disorder in tissues and tilings
View Abstract Hide Abstract
Biological tissues share many morphological characteristics with foams and other cellular materials. We explore the usefulness of various concepts from physics and mathematics to describe the cell shapes and structures of epithelial tissues and find that quantitative modeling is possible with only minimal reference to biological processes. The highly ordered epithelium of the Drosophila eye can be modeled in detail using concepts of energy functional minimization including cell elasticity and cell-cell adhesion, allowing for additional insight into morphogenetic processes during tissue development. Conversely, the structure of the Drosophila wing (a disordered tiling of cells) can be described by a statistical mean-field approach derived from a version of the granocentric model. Long-standing conjectures correlating size and topology distributions in such tissues and a large class of other tilings can now be demonstrated analytically.
Koiso, Miyuki
Bifurcation and stability for solutions of isoperimetric problems
View Abstract Hide Abstract
A surface with constant mean curvature (CMC surface) is an equilibrium surface of the area functional among surfaces which enclose the same volume with given boundary condition. A CMC surface is said to be stable if the second variation of the area is nonnegative for all volume-preserving variations which satisfy the boundary condition. Choosing the mean curvature or the volume enclosed by the surface as parameter, we construct conditions under which a pitchfork bifurcation occurs. We apply our results to several interesting isoperimetric problems with free or fixed boundary conditions in the euclidean space. We also generalize the results to more general variational problems with constraint in higher dimensional spaces.
Kraynik, Andrew
Structure of random polydisperse soap froth
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The Surface Evolver is used to simulate the structure of random soap froth starting from weighted-Voronoi partitions of randomly packed spheres of known size distribution. Monodisperse, polydisperse and bidisperse foams with spatially periodic structure and up to 12^3 cells are modeled. The calculations provide a database against which to test conjectures on the topology and geometry of individual bubbles or the entire foam. The topological statistics and census of cell types for monodisperse foams are in excellent agreement with the classic experiments by Matzke. The surface area of the cells in polydisperse foams is about 10% greater than a sphere of equal volume, which inspires a simple but accurate theory for the surface area of the foam. Other geometric properties of interest include cell edge length, diffusive growth rate, and measures of cell distortion. We have evaluated rheological properties such as the shear modulus (which is in excellent agreement with measurements by Princen & Kiss) and yield stress of soap froth. These models can also be used as templates to create finite element models of open-cell solid foams to simulate crushing behavior; localized bands of crushed cells that develop and gradually spread throughout the sample closely resemble experiments.
Lawlor, Gary
New methods of proof for double and triple bubbles
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Unification is a new idea that enhances variational methods and unites other minimization methods including slicing, calibration and variations into a single approach well suited to multiple bubble problems. This talk will feature a proof by unification and the Gauss-Bonnet theorem for the double bubble in space, and an approach to planar and spacial triple bubbles. A proof for equal-volume triple bubbles in 3-space appears close to completion. Attendees may find success in applying the ideas to triple and quadruple bubbles in 2-dimensional spaces.
Lazar, Emanuel
The "shapes" of some three-dimensional space filling patters
View Abstract Hide Abstract
Although Kelvin and Weaire-Phelan cells are optimal, or at least near optimal, in some sense, most disordered foams and other cellular structures do not generally contain many of them. That being the case, what can be said about the individual cells of these structures? For example, what fraction of its cells are Kelvin or Weaire-Phelan cells? How "round" or "symmetric" are typical cells? We present a graph-theoretic technique to succinctly represent the topology of individual cells, and then use this tool to study the cells that appear in Voronoi tessellations and grain-growth microstructures. In theory, this method can also be used to study disordered foams.
Morgan, Frank
Soap bubbles and mathematics
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Soap bubbles are beautiful and have lots of applications, and they continue to fascinate and confound mathematicians. The show will include a little guessing contest with demonstrations, explanations, and prizes. Fifth grade and above welcome.
Mughal, Adil
Phyllotactic description of hard sphere packing in cylindrical channels
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We study the optimal packing of hard spheres in an infinitely long cylinder. Our simulations have yielded dozens of periodic, mechanically stable, structures as the ratio of the cylinder (D) to sphere (d) diameter is varied [1]. Up to D/d=2.715 the densest structures are composed entirely of spheres which are in contact with the cylinder. The density reaches a maximum at discrete values of D/d when a maximum number of contacts are established. These maximal contact packings are of the classic "phyllotactic" type, familiar in biology. However, between these points we observe another type of packing, termed line-slip. An analytic understanding of these rigid structures follows by recourse to a yet simpler problem: the packing of disks on a cylinder. We show that maximal contact packings correspond to the perfect wrapping of a honeycomb arrangement of disks around a cylindrical tube. While line-slip packings are inhomogeneous deformations of the honeycomb lattice modified to wrap around the cylinder (and have fewer contacts per sphere). Beyond D/d=2.715 the structures are more complex, since they incorporate internal spheres, but an analysis in terms of contacts or constraints is still illuminating. We review some relevant experiments with hard spheres and small bubbles. [1] Phyllotactic description of hard sphere packing in cylindrical channels. A. Mughal, H. K. Chan and D. Weaire, Phys. Rev. Lett, 106, 115704 (2011)
Nardulli, Stefano
Isoperimetry in non-compact Riemannian manifolds
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We will give some results about existence of isoperimetric regions in non compact Riemannian manifolds satisfying some bounded geometry assumptions.
Németh, Róbert
Pattern formation of lotus receptacles
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Receptacle of a lotus is a conical remaining part of the flower after it dries out. It contains varying number of seeds. Pattern formation of the receptacle is influenced by many different internal and external effects. We focus on two of them: the seeds must be separated by a tissue wall, and the seeds must fit into the space between these walls. Modelling the pattern formation requires the conversion of these effects into mathematical constraints. It is economical if the total wall-length is as small as possible. This constraint is similar to minimizing the perimeter of equal soap bubbles in 2D. Each seed has an approximately circular shape occupying approximately the same area. Their arrangement resembles to the packing of non-overlapping, equal circles in a closed domain in a plane. The final pattern is a result of the compromise between the packing and the bubble effects. We want to find a mathematical model to describe the pattern formation. Partial results from the numerical analysis of the pattern of specimens will be presented in the talk. This is a joint work with Tibor Tarnai, supported by OTKA Grant No.81146.
Nurnberg, Robert
Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies
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Geometric flows, in which (collections of) hypersurfaces move such that an energy, involving surface and bending terms, decreases appear in many situations in the natural sciences and in geometry. Classic examples are mean curvature, surface diffusion and Willmore flows. Computational methods to approximate such flows are based on one of three approaches (i) parametric methods, (ii) phase field methods or (iii) level set methods. The first tracks the hypersurface, whilst the other two implicitly capture the hypersurface. In this talk we present a variational formulation of the parametric approach, which leads to unconditionally stable, fully discrete finite element approximations. In addition, the schemes have very good properties with respect to the distribution of mesh points, and volume conservation. Moreover, the method naturally generalizes to surface clusters. In particular, numerical approximations of the considered gradient flows will lead to conjectured minimizers for least area partitioning problems. Here the triple junction conditions, that have to hold where three surfaces meet, are naturally approximated in the discretization of our variational formulation. We extend the approximation to anisotropic surface energies. Here the surface energy density is allowed to depend on the direction of the surface normal.
Pratelli, Aldo
Recent existence results for the isoperimetric problem in R^N with density
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We will present some recent developments about existence of isoperimetric sets in R^N with density. A number of non-existence examples is also given. We will discuss also related questions, such as the boundedness of isoperimetric sets and the increasingness of the isoperimetric function
Ritoré, Manuel
Geometric inequalities and soap bubbles
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We will discuss recent applications of soap bubble techniques to obtain geometric inequalities, specially of isoperimetric type.
Sullivan, John
Foams with small faces
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There are exactly 4761 different foams with only 3-, 4- and 5-sided faces; these fill spherical space rather than Euclidean space. Their duals are the 4761 simplicial triangulations of the three-sphere with no edges of valence more than 5. We examine these from several geometric and combinatorial points of view. In particular, each gives rise to a spherical cone metric, which in most cases can be smoothed by a curvature flow. Some of these ideas extend to TCP triangulations, where some edges of valence 6 are allowed.
Sutcliffe, Paul
Domain walls and double bubbles
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I shall present a description of double bubbles in terms of static intersecting domain wall solutions of a partial differential equation describing volume-preserving flow in a Wess-Zumino model.
Teixeira, Paulo
Surface energy of two-dimensional finite or periodic foams
View Abstract Hide Abstract
The proof of the honeycomb conjecture by Hales and the improvement made by Weaire and Phelan on the foam structure, led to an increased number of studies on the equilibrium and energy of bubble systems. Most studies deal with two-dimensional (2D) clusters, which may include free (finite) or periodic clusters. In this presentation, equations for the surface energy of two-dimensional free bubble clusters will be given and will be compared either with exact calculations and either with the results of Surface Evolver simulations. Finite clusters can be of several types namely a) a central bubble surrounded by several shells of bubbles with the same or different areas; b) finite collections of identical bubbles or two different-area bubbles; c) chain clusters which consist of periodic rows of bubbles; and d) bubble clusters with defects inside. In addition, we have also studied a subset of periodic, bi-disperse 2D foams (i.e. minimal tilings of the Euclidian plane with tiles of two different types). Surface energy results are presented for each case and the accuracy of the results is discussed. Joint talk with F. Vaz
Vaz, Fatima
Surface energy of two-dimensional finite or periodic foams
View Abstract Hide Abstract
The proof of the honeycomb conjecture by Hales and the improvement made by Weaire and Phelan on the foam structure, led to an increased number of studies on the equilibrium and energy of bubble systems. Most studies deal with two-dimensional (2D) clusters, which may include free (finite) or periodic clusters. In this presentation, equations for the surface energy of two-dimensional free bubble clusters will be given and will be compared either with exact calculations and either with the results of Surface Evolver simulations. Finite clusters can be of several types namely a) a central bubble surrounded by several shells of bubbles with the same or different areas; b) finite collections of identical bubbles or two different-area bubbles; c) chain clusters which consist of periodic rows of bubbles; and d) bubble clusters with defects inside. In addition, we have also studied a subset of periodic, bi-disperse 2D foams (i.e. minimal tilings of the Euclidian plane with tiles of two different types). Surface energy results are presented for each case and the accuracy of the results is discussed. Joint talk with P. Teixeira
Weaire, Denis
Me and Kelvin: how bubbles brought me to Beijing
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Our lecturer is an expert on how things pack together, in particular how bubbles form a foam. This a subject into which Lord Kelvin ventured in 1887, starting a debate about ideal foam structures which continues today. An important milestone was the 1994 publication of the Weaire-Phelan structure, which surpassed that of Kelvin by achieving a lower surface area. It was used as the basis of the daring design of the Water Cube aquatic centre at the Beijing Olympics. Weaire will give a light-hearted account of the fun he has enjoyed with foam, after which washing the dishes will never be quite the same...

Participants

Name	Institution
Blumenfeld, Rafi	Imperial College London & Cambridge University
Cañete, Antonio	Universidad de Sevilla
Cinti, Eleonora	Università di Pavia
Cox, Simon	Aberystwyth University
Flikkema, Edwin	Aberystwyth University
Gabbrielli, Ruggero	Princeton University
Goldstein, Raymond E.	University of Cambridge
Hales, Thomas	University of Pittsburgh
Heppes, Aladar	Alfred Renyi Institute of Mathematics
Hilgenfeldt, Sascha	University of Illinois at Urbana Champaign
Koiso, Miyuki	Kyushu University
Kraynik, Andrew	University of Erlangen-Nuremberg
Lawlor, Gary	Brigham Young University
Lazar, Emanuel	Institute for Advanced Study
Morgan, Frank	Williams College
Mughal, Adil	Aberystwyth University
Nardulli, Stefano	Universidade Federal do Rio de Janeiro
Németh, Róbert	Budapest University of Technology and Economics
Neumann-Chun, Nicholas	Williams College
Nurnberg, Robert	Imperial College London
Oudet, Edouard	LJK, Universite Joseph Fourier
Pesci, Adriana	University of Cambridge
Pratelli, Aldo	University of Pavia
Ravati, Sepehr	Ecole Polytechnique de Montreal
Ritoré, Manuel	Universidad de Granada
Sullivan, John	Technische Universitat Berlin
Sutcliffe, Paul	Durham University
Taylor, Jean	Courant Institute, NYU
Teixeira, Paulo	Lisbon Polytechnic Institute and CFTC-UL
Tibor, Tarnai	Budapest University of Technology and Economics
Vaz, Fatima	ICEMS and Instituto Superior Tecnico, UTL
Vernadakis, Efstratios	University of Granada
Weaire, Denis	Trinity College Dublin