The pop science of bubbles
If you look closely at the outer walls of the Beijing National Aquatic Centre, which is covered by a membrane of blue bubbles, it's easy to think the frothy design is just as 'random' as the foam in your bathtub.
But they belie a repeating mathematical pattern that scientists believe holds the secret to nature's efficient use of space.
The pattern on the centre's walls is easy to miss: the untrained eye would not guess it consists of 14-sided and 12-sided shapes in groups of eight, all cut at an odd angle to make the suds seem 'organic' rather than a mathematically rendered style that inspired the architect.
In three-dimensional form, the arrangement is called the Weaire-Phelan structure, dubbed the 'most efficient bubble foam', developed by Irish theoretical physicists Denis Weaire and Robert Phelan.
Their model is the most efficient way to partition space into equal-volume cells while minimising surface area - something soap bubbles strive to do in nature.
The scientists were pleasantly surprised when they found out about the Beijing building's design, a practical application of a structure they and their lab team at Trinity College Dublin (TCD) worked on for years and introduced in 1993.
Just last week, additional work by a team from the lab was accepted for publication in the science journal Philosophical Magazine Letters, showing how they turned their mathematical model into real foam.
'This particular work is done very much out of intellectual curiosity,' said Weaire, now emeritus professor at TCD, who has spent his life studying foam.
A single bubble in open space naturally forms a sphere because this is the least amount of surface area needed for the volume. In foam, multiple bubbles press against each other and merge to share walls - again minimising surface area.
Nature has incentives for the smart use of space. For example, bees build honeycombs with hexagonal cells, which give the maximum amount of storage space per unit so no wax is wasted.
Weaire and Phelan were not the first to grapple with the question of utilising space more efficiently. In the late 1880s, Irish physicist Lord Kelvin - who lent his name to absolute zero - experimented with foam to understand the 19th-century obsession with 'ether', then thought to be the medium through which light waves were transmitted.
Kelvin thought ether was created from an 'ideal' - which in nature often means 'most efficient' - cluster of bubbles. He proposed 14-sided polyhedrons, or 3-D polygons, but failed to mathematically prove this was the most efficient model.
More than a century later, in 1993, Weaire and Phelan used mathematician Ken Brakke's free computer program, Surface Evolver, which allows modelling of liquid surfaces, to come up with an answer to the 'Kelvin question': a unique structure with 14-sided and 12-sided polyhedrons.
This year, the team at TCD, now headed by physicist Stefan Hutzler, along with Brakke, added more than 1,500 bubbles to the Weaire-Phelan structure in their Foams and Complex Systems laboratory.
Their design is 0.3 per cent more efficient than Kelvin's, which is very significant in the mathematical world but perhaps not of practical consequence.
Such mind-bending scientific studies may seem like a child's dream ('I make bubbles at work'), but is really part of a pursuit of perfection. These physicists are on the hunt for ideal mathematical forms, even if they happen only in special conditions like their bubble structure, which took years to create in the lab.
'Cellular structures are something used in nature ... You can build very strong structures by doing that, and they are all around us,' said Hutzler. But nature isn't always ideal, he said. Cells are not always equal, and even in a honeycomb, there are defects. 'Nature is very good at coming up with different solutions, but it might not be the ultimate,' he said.
Still, the quest for ideal forms has gained many followers. One of them is Dr Ho-Kei Chan, a Hong Kong-born physicist who is a research fellow at the Dublin lab. He came up with his own packing solution, this time for hard spheres in cylindrical containers.
Think of tennis balls: It's easy enough to figure out the most efficient way of stacking them in narrow columns one by one, but what happens when the columns are wider than the ball diameter?
For Chan, the solution lies in layers of helical spheres - at least in cases when the diameter of the cylinder is 2.7013 times larger than the diameter of the sphere or less. His computer program simulated dropping balls into a cylinder one by one until the bottom layer was completely filled but putting succeeding balls where the most space was left, resulting in a spiralling shape upwards.
His work, for which he is looking for funding, and future computer simulations involving cylinders or spheres in different ratios can potentially solve all kinds of packing problems, even at the nano or micro level.
In a paper this month in Physical Review E - which complements an earlier paper in Physical Review Letters published with Weaire and Dr Adil Mughal - Chan wrote that smaller molecules, such as nano-sized buckyballs (spherical carbon molecules), also self-assemble like hard spheres. However, most of this work is only theoretical.
Both Chan and Hutzler point out there are no perfect spheres in nature.
There are also studies at the Dublin university that have real-life implications. The lab does research in econophysics, a blend of economics and physics. Recently, they've looked at how online bets people place on soccer matches are similar to stock market statistics.
These are still part of the umbrella study on complex systems, including foam, which are made up of individual components (bubbles) whose varying behaviour and formation makes each system unique (each foam formation in nature is distinct).
Everything from forest fires to freak meteorological events have been studied as complex systems, but foam formations show how small-scale systems can reflect larger realities. For example, the interactions of many bubbles that make up foam can be compared to the interaction of traders that make up a stock market. The scientists' task is not to compare these interactions, but to come up with a formula or lens by which to understand both of them.
Hutzler laments the common tendency to rely on Gaussian statistics, or bell-shaped distributions that show a world with generally stable behaviour: there are gradual dips and peaks, but no large fluctuations.
'But nature and society behave differently,' said Hutzler. 'Not everything is Gaussian ... [there may be] large events, a beautiful day one day and a thunderstorm an hour later.'
Hutzler thinks lessons learned from the physics of foam could lead to the study of other complex systems relevant to society. Though they conform to scientific rules like surface tension, bubbles, after all, can suddenly rearrange or pop quite randomly, leading to a chain reaction.
'What scientists think is that [a large event] doesn't need to have a reason; it's just part of the statistics,' Hutzler said. 'Every now and then, you have an outlier.' As every economist knows well, every now and then a bubble bursts.