The new work experimented with knots made in metal wires. The stiffness of those wires kept them free of sharp turns. This simplified geometry helped reveal how a knot's configuration and the forces within it are related.
The wires were made of a hyper-elastic nickel-titanium alloy known as nitonol. The researchers experimented with the simplest overhand knot, the trefoil knot, made by creating a loop in the middle of a rope and then passing one end of the rope through the loop. Passing the rope through the loop more than once leads to longer braids with more twists.
The scientists clamped one end of each braid to a table and measured the amount of force a mechanical arm used to pull the knot tight. They found that a knot with 10 twists needed roughly 1,000 times more force to close than a knot with just one.
These findings contradicted previous research from study co-author Basile Audoly, a physicist at Pierre and Marie Curie University in Paris, and his colleagues, who modeled overhand knots with just one or two twists. The new work revealed that for simple overhand knots with few twists, the effects of friction can largely be ignored. However, the more twists there are, the more friction plays a role, explaining why a knot with more twists is so much more difficult to tighten than a knot with fewer twists.
"This kind of research sometimes seems silly because it is cast in the form of tying your shoelaces," said theoretical physicist Christian Santangelo at the University of Massachusetts Amherst, who did not take part in this research. "But we know that friction isn't really well understood, especially when something complicated happens. The fact that the result is encapsulated in a single equation is downright amazing."
The model still needs work and is only the latest in the attempts to watch the spread of the disease.
Influenza is not a minor matter. A version in 1918 and 1919, called the Spanish flu, caused a pandemic that killed an estimated 50 million people or more, including 675,000 Americans. That might be as many as were killed by the Black Death in the 14th century. Indeed, the pandemic might rank as the most deadly calamity in human history outside World War II.
It was spread partly by millions of people moving across oceans and continents as World War I ended. Cities all over the world had so many deaths they had to pile bodies in massive trenches to bury them. Oddly, the young and healthy died at the highest rate, in part, it is believed, because older people had gained some immunity from an earlier epidemic. Pregnant women suffered the most.
The pandemic struck in three waves in the U.S. Public places were closed, basic services were interrupted, and people were ordered to wear masks outside.
Epidemiologists fear another flu like that one could strike.
Influenza is extremely contagious. People who come within six feet of a flu sufferer can catch the airborne virus, no cough required. The average flu sufferer infects 1.5-3 people. The disease is a family of virus types with names like H1N1, the cause of the 1918 pandemic. Those viruses are constantly evolving and mutating, churning out new versions, sometimes in a matter of months.
Every year, the World Health Organization guesses which versions of the virus are the most likely to strike that year. That educated guess is turned into a vaccine against the top three or four candidates. The vaccine takes four to six months to produce and usually requires an injection.
In some years, such as 2010, WHO guesses correctly. In some years, such as last year, it is wrong.
An earlier attempt to track the disease was made by Google, which tried to plot the disease by running algorithms of online searches, looking for words such as “flu” or “influenza,” as well as references to symptoms. That effort, the Google Flu Trends, made use of huge amounts of data and the law of large numbers, a theorem of probability theory.
In some years, it worked very well, said, Ryan Kennedy, associate professor of political science at the University of Houston. Every other year or so, it bombed, he said. Google has stopped publishing its data.
Part of the problem was that the algorithm used had trouble with search terms. Google researchers had to go into the algorithm and edit them by hand.
Riley said he hopes that his data, plus that from other sources including the Centers for Disease Control and Prevention and GFT, can help scientists prepare for the next big pandemic.
Mix these ingredients and they coalesce into dough. Water-soaked gluten expands to form a strong and flexible protein network that spans the entire dough. Starch granules occupy spaces in this gluten network. Yeast makes the dough rise by producing gas bubbles during baking.