WHAT would the world be like if freezing were triggered by heating? Hot snow
would carpet the ground in summer and warm glaciers would glide through tropical
rainforests. You鈥檇 take ice cubes out of the oven and pop them into your coffee
to keep it steaming, and that comforting rattle of cubes in an ice-cold gin and
tonic would be a mere figment of your dreams.
Fortunately, we don鈥檛 have to face this alternative reality. In our world,
heating something means pouring energy into it, making its atoms or molecules
fly about more violently. And violence never produces more order, only less. Or
so most scientists thought until a few months ago, when a computer in Hungary
seemingly reversed the laws of nature.
When physicists Dirk Helbing, Tam谩s Vicsek and Ill茅s Farkas
trapped a few dozen computer-generated particles in a virtual box and cranked up
the 鈥渢emperature鈥� by increasing the rate at which the particles moved, they
expected to witness the usual storm of haphazard motion. After all, when you
throw a chunk of steel or ice into a furnace, it melts. Restoring crystalline
regularity means slowing the molecules down so they lock into place once more,
and that, by necessity, requires cooling. You can鈥檛 impose order by adding
energy.
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But in a subtle twist to the usual rules, Helbing, Vicsek and Farkas had
endowed their particles with the ability to move under their own power, like
simple wind-up toys. And this small difference had a terrific effect. As the
particles grew hotter and slammed together more savagely, the researchers
watched dumbfounded as they fell into a perfect crystalline array.
Freezing-by-heating.
The lesson? When particles move around under their own power, a lot of
traditional physics seems to go out of the window. Researchers such as Helbing
and his colleagues are now working through the consequences of this startling
discovery, and in doing so, they are learning some very practical lessons. After
all, it鈥檚 not just in computer simulations that self-propelled objects meet in a
confined space. Such encounters occur in all sorts of real-life settings, from
crowded hallways to busy highways.
There are even tantalising signs that intangible 鈥渙bjects鈥� like opinions and
desires are governed by the same strange rules, explaining why social relations
sometimes seize up into a deadlock of differences. One day, understanding
freezing-by-heating may avert a war.
Helbing could never have suspected as much when he started out ten years ago.
鈥淚 was interested in creating a general model for social interactions,鈥� he says,
speaking from his office at the University of Technology in Dresden, Germany. He
wanted his model to explain all sorts of things, from traders competing in stock
markets to drivers jostling on the road. To begin with, he reasoned that if a
鈥減article鈥� can be an atom or a molecule, why not an automobile or a
pedestrian?
One great difference between a person and a molecule, of course, is that
people have an inner drive that energises their activities. So Helbing started
out by trying to understand the physics of particles that move under their own
steam. It wasn鈥檛 long before some curious discoveries started to roll in.
In an empty hallway, a person can walk wherever he or she likes. Not so at
the entrance to a popular department store during the January sales, however,
where people struggle in both directions at once. In such a crowd, pedestrians
bump and bounce off one another like molecules in water, and the outcome is as
mysterious as it is ubiquitous: lanes form. Even though no one barks any orders,
coherent streams emerge to carry people smoothly in each of the opposing
directions. A decade ago, says Helbing, 鈥減eople tended to look for psychological
and social explanations鈥� of such phenomena. But in 1994, he and physicist
P茅ter Moln谩r of the University of Stuttgart found a far simpler
explanation.
They ran a series of computer simulations in which 鈥減eople鈥� moved through a
stretch of hallway, each following simple laws. The idea was to capture in a few
equations how people get where they are going without running into one another.
When Helbing and Moln谩r set the computer running, some people went left,
others right, and after mingling in chaos for a time, they fell naturally into a
set of well-organised lanes (see Diagram).
鈥淲e were surprised,鈥� says Helbing, for their computer model
contained nothing that prescribed lane formation. Each
person simply tried to avoid bumping into others. So where did the organisation
come from?
As the researchers eventually discovered, the effect is a natural consequence
of stepping sideways. When two people are on a collision course, they need to
move to the side to get past one another. So in any part of a crowd where there
are no lanes and people collide frequently, they tend to drift sideways in an
erratic fashion as they pick their way.FIG-mg22474201.JPG
But suppose a tiny lane begins to form somewhere in the crowd, even by
accident. As people drift about sideways, they will eventually hit the lane and
join it. And once they鈥檝e joined, they鈥檒l stay there. As a result, lanes always
grow.
You might think of this as the first principle of crowd physics, and not
surprisingly urban planners are beginning to take notice. 鈥淚 get calls from
architects and engineers,鈥� says Helbing. But now the models are beginning to
raise physicists鈥� eyebrows as well, thanks to the most bizarre discovery yet in
the field of self-propelled particles.
For half a dozen years, physicist Tam谩s Vicsek of the E枚tv枚s
Lor谩nd University in Budapest, Hungary, has been using mathematics to
probe the flocking habits of animals ranging from mosquitoes to zebras. Here
again, a number of 鈥減articles鈥� interact with one another while moving under
their own power. Late last year, when Helbing visited Budapest for three months,
he, Vicsek and graduate student Ill茅s Farkas tried to answer a simple
question: exactly where and under what conditions do lanes form in a crowd? They
were in for a bewildering surprise.
鈥淲e had the idea that we should introduce some noise,鈥� says Helbing. Of
course, more noise is just what you get in any solid or liquid when you heat it.
But pedestrians can experience a similar effect. When someone is walking about
they don鈥檛 always go in a perfectly straight line. They may bump into someone
else, slow down or stop, or skirt around a puddle on the pavement. In the case
of real particles, increasing the noise always leads to less organisation rather
than more, and the researchers suspected that the same would be true for
self-propelled particles. Enough noise, they thought, would annihilate the
lanes, and in this they were correct. Yet what emerged in their place was a
shock.
鈥淥ne afternoon in the computer room,鈥� recalls Vicsek, 鈥渨e were looking at
Ill茅s鈥檚 most recent simulations.鈥� At one point Vicsek suggested turning
up the disrupting noise to see what would happen. As expected, when the noise
became strong enough, it destroyed the lanes. Yet afterwards there was not less
order but more. The application of utterly disorganised, random
noise鈥攕omething very much like heat鈥攈ad frozen the 鈥渨alkers鈥� into a
near-perfect crystalline pattern with the organisation of a solid
(see Diagram).FIG-mg22474201.JPG
Trapped by panic
Vicsek and his colleagues suspect that this effect may be closely related to
what sometimes happens during an emergency鈥攊n a smoke-filled theatre, for
example, when the desperate efforts of panicking people prevent them from
escaping. But on a more fundamental level it raises a paradox: how can pure
noise lead to more order? Since the particles are self-propelled, the weird
solid they form doesn鈥檛 violate any laws of physics. But it does play havoc with
physicists鈥� intuitions. 鈥淔reezing-by-heating,鈥� says Gene Stanley of Boston
University, 鈥渋s one of the most intriguing things found so far in self-driven
systems.鈥� And, for the moment, it is one of the most baffling. To find out
exactly why it happens and under what conditions, says Helbing, 鈥渨e will have to
wait for more experiments.鈥� But researchers are already following up a couple of
clues.
In Helbing and his colleagues鈥� computer experiments, the particles live in
the flat space of two dimensions rather than the three occupied by real atoms
and molecules. This makes it rather harder for particles to move without running
into one other, and this may have a lot to do with the effect, according to
physicist Dov Levine of Technion, the Israel Institute of Technology in Haifa.
鈥淚 would wager a dinner,鈥� he says, 鈥渢hat you would never see crystalline
ordering in such a system in three dimensions.鈥�
Even so, Helbing and his colleagues know of three-dimensional effects that
look a lot like freezing-by-heating. For example, they have found they can bring
about freezing not only by increasing the noise, but also by a more intuitive
route鈥攕tuffing ever more particles into the system. In some ways, this
transition resembles the 鈥渏amming鈥� that takes place in real-life settings.
Pour just a few beans or grains of coffee through a chute and they will flow
quite easily. Try sending too many through at once, however, and the chute jams
as the grains get frozen in place. This jamming transition is a long-standing
headache for industry, as everything from peas to pills show a stubborn
reluctance to behave, and it has at least a rough similarity to the freezing
seen by Helbing and his colleagues. Grains moving through a chute aren鈥檛
self-propelled, but they are driven forward, either by gravity or by some other
force. But there are also some puzzling differences. Whether it鈥檚 beans or
coffee, the jammed state is irregular, with particles arranged haphazardly, and
a little extra noise helps to get things unstuck. In freezing-by-heating, on the
other hand, the jammed state is an ordered crystal and extra heating only locks
things in place more tightly.
Physicists are just beginning to explore the strange phenomena caused by
self-propelled particles. But whatever they discover will almost certainly have
some practical benefits. In 1998, for example, Helbing teamed up with Bernardo
Huberman of the Xerox Palo Alto Research Center in California in a study of how
cars and lorries move down a two-lane highway. They discovered that there really
is such a thing as a good traffic jam.
Their computer simulations showed that in light traffic, cars slip into the
passing lane whenever they need to overtake a slower lorry. But this freedom
vanishes at a certain critical density of traffic, when there are so many
vehicles that passing is hardly ever an option. At this point the cars and
lorries begin to roll down the road in a solid mass like molecules locked in a
crystal. Comparing their model to data collected on a road in the Netherlands,
Helbing and Huberman found that this 鈥渇reezing鈥� effect is very real. On the
Dutch highway, it took place whenever there were more than 25 cars and lorries
per kilometre of road.
In this state, all vehicles move at much the same speed, and lane changing
occurs some ten times less often than under other conditions. Since accidents
tend to happen when people do a lot of lane changing and when there are large
differences in vehicle speeds, Helbing believes traffic measures that promote
the frozen state could save lives. Fortunately, this peculiar traffic state also
has the highest overall throughput of vehicles, so it seems to be the most
efficient too (快猫短视频, 15 January, p 34).
This idea might eventually be taken a lot further. For as Helbing points out,
there is no reason why the particles in the simulations need refer to anything
as tangible as pedestrians or automobiles. In a wider context, he says, the
models represent any situation where there are players with opposing interests.
In addition to feet and cars, for example, people have opinions, and their
opinions interact. Think of negotiators trying to settle a dispute between two
countries, or between a company and its employees.
In such cases, each side tries to persuade the other to accept its demands,
much as the pedestrians in Helbing, Vicsek and Farkas鈥檚 simulations try to move
in opposing directions. And the similarity between the two goes further. Like
the crowd of pedestrians with lanes in which people move easily, some
negotiations benefit from fluid discussion and exchange of ideas. Other cases,
of course, are more like freezing-by-heating. Both sides push too hard, the
temperature rises and the argument gets locked into an impasse.
Do stalemates of this sort sometimes happen, not because of the stubbornness
of the negotiators or the stark conflict of their demands, but for subtler
reasons? If so, it may be possible for scientists using computers to gain a few
insights into how to avoid such debilitating deadlocks. For now, of course, it
may be enough simply to puzzle over how something can freeze when it gets
heated. But scientists plumbing the depths of that riddle may one day learn how
to make the world a more chilled-out place.