New mathematical model explains patterns of human movement by considering the costs

ScienceDaily (Oct. 13, 2011) — Using previously published data on the time-stamped locations of 100,000 anonymous cell-phone users, a researcher from Duke University has identified three distinct patterns of human mobility for short, medium, and long distance trips. In 2008, a separate research team that was not involved in the current study published a paper in which they had plotted data on cell-phone users' movements, and then fitted the data with a single, downward-sloping curve. The curve captured an intuitive relationship: the longer a trip, the less likely it was to occur.

Nicola Scafetta, however, thought deeper patterns might be hidden by the simple curve. In the AIP's journal Chaos, Scafetta proposes a finer-resolution analysis of the cell-phone data. He divided the data set up into three separate sections, one each for short (from 1 to 10 km), medium (from 10 to 300 km), and long (above 300 km) distance trips. He then fit each chunk of data with a separate curve. Surprisingly, the exponents from the three separate curve fits were simple numbers -- 1, 2 and 3 -- that illustrated a different relationship between distance and trip frequency for each zone. For all three zones, the likelihood of a trip decreases with increased distance, but the rate of decrease is faster in the higher-numbered zones.

Scafetta offers a physical and statistical explanation for this pattern. In zone one, people are running short-distance errands within an urban area, and may just consider one cost mechanism, like the time or the fuel cost of the trips, when deciding where and when to go. In the more distant zone two people are, for example, taking day-trips to nearby towns of specific interest. These trips might require travelers to consider both time and fuel costs in their decisions. And in zone three, people take multi-day trips and may consider time and fuel costs, as well as additional overnight lodging costs.

The increase in the number of considered costs for each zone could help explain the increase in the curve-fit exponent for each zone. Scafetta also rescaled the model and found that it could be used to interpret data gathered on the movements of volunteers who walked to their destinations, either in zone one (within 200 m) or zone two (from 200 to 1000 m).

The critical benefit of the alternative fitting method, Scafetta writes, is that it suggests clear physical and geographical mechanisms to explain the observations. Accurate models of human displacement have applications in traffic forecasting, urban planning, and in the study of social networks and the spread of diseases.

Recommend this story on Facebook, Twitter,
and Google +1:

Other bookmarking and sharing tools:

Story Source:

The above story is reprinted (with editorial adaptations by ScienceDaily staff) from materials provided by American Institute of Physics, via EurekAlert!, a service of AAAS.

Journal Reference:

Nicola Scafetta. Understanding the complexity of the Lévy-walk nature of human mobility with a multi-scale cost/benefit model. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2011

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here

Physicists hit on mathematical description of superfluid dynamics

ScienceDaily (June 9, 2011) — It has been 100 years since the discovery of superconductivity, a state achieved when mercury was cooled, with the help of liquid helium, to nearly the coldest temperature achievable to form a superfluid that provides no resistance to electrons as they flow through it.

During that century, scientists have struggled to find a precise mathematical explanation of why and how this strange fluid behaves as it does. Liquid helium-4 itself becomes a superfluid when cooled to within a few degrees of absolute zero on the Kelvin scale (minus 273 Celsius or minus 460 Fahrenheit), and the resulting lack of viscosity allows it to seem to defy gravity, flowing up and over the sides of a container.

Now a team led by a University of Washington physicist, using the most powerful supercomputer available for open science, has devised a theoretical framework that explains the real-time behavior of superfluids that are made of fermions -- subatomic particles such as electrons, protons and neutrons that are basic building blocks of nature.

Such superfluids are found in neutron stars, which rotate between one and 1,000 times a second. These stars, also called pulsars, have 50 percent greater mass than the sun but are packed so densely that one can occupy an area only about the size of a city such as Seattle, said Aurel Bulgac, a UW physics professor and lead author of a paper in the June 10 edition of Science that details the work.

As a neutron star rotates, the superfluid on the surface behaves quite differently than a liquid would on the surface of Earth. As the rotational speed increases the fluid opens a series of small vortices. As the vortices assemble into triangular patterns, the triangles build a lattice structure within the superfluid.

"When you reach the correct speed, you'll create one vortex in the middle," Bulgac said. "And as you increase the speed, you will increase the number of vortices. But it always occurs in steps."

Similar behavior can be recreated in a laboratory using a vacuum chamber and a laser beam to create a high-intensity electrical field that will cool a small sample, perhaps 1 million atoms, to temperatures near absolute zero. A "laser spoon" then can stir the superfluid fast enough to create vortices.

In trying to understand the odd behavior, scientists have attempted to devise descriptive equations, as they might to describe the swirling action in a cup of coffee as it is stirred, Bulgac said. But to describe the action in a superfluid made of fermions, a nearly limitless number of equations is needed. Each describes what happens if just one variable -- such as velocity, temperature or density -- is changed. Because the variables are linked, if one changes others will change as well.

The challenge, Bulgac said, was to formulate the proper mathematical problem and then find a computer that could work through the problem as the number of variable changes reached 1 trillion or more. To reach its solution, the team in the last year used the JaguarPF computer at Oak Ridge National Laboratory in Tennessee, one of the largest supercomputers in the world, for the equivalent of 70 million hours, which would require almost 8,000 years on a single-core personal computer (JaguarPF has nearly a quarter-million cores).

"This tells you the complexity of these calculations and how difficult this is," he said.

The researchers also found through their calculations that by increasing the speed at which the fluid was stirred, eventually it would lose its superfluid properties -- though not as soon as had been previously hypothesized. Video representations of the results of the massive numerical simulations are at http://www.phys.washington.edu/groups/qmbnt/UFG.

The work means that researchers can "to some extent" study the properties of a neutron star using computer simulations, Bulgac said. It also opens new directions of research in cold-atom physics.

"This is a pretty major step forward in studying these dynamic processes," he said.

Co-authors are Yuan-Lung Luo of the UW, Piotr Magierski of the Warsaw University of Technology in Poland; Kenneth Roche of the Pacific Northwest National Laboratory in Richland, Wash.; and Yongle Yu of China's State Key Laboratory of Magnetic Resonance, Atomic and Molecular Physics. Magierski and Roche also have affiliate UW physics appointments.

The research was funded by the U.S. Department of Energy, the U.S. National Science Foundation, the Polish Ministry of Science and the Chinese National Science Foundation.

Story Source:

The above story is reprinted (with editorial adaptations by ScienceDaily staff) from materials provided by University of Washington. The original article was written by Vince Stricherz.

Journal Reference:

Aurel Bulgac, Yuan-Lung Luo, Piotr Magierski, Kenneth J. Roche, Yongle Yu. Real-Time Dynamics of Quantized Vortices in a Unitary Fermi Superfluid. Science, 10 June 2011: Vol. 332 no. 6035 pp. 1288-1291 DOI: 10.1126/science.1201968

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here

Physicists hit on mathematical description of superfluid dynamics

ScienceDaily (June 9, 2011) — It has been 100 years since the discovery of superconductivity, a state achieved when mercury was cooled, with the help of liquid helium, to nearly the coldest temperature achievable to form a superfluid that provides no resistance to electrons as they flow through it.

During that century, scientists have struggled to find a precise mathematical explanation of why and how this strange fluid behaves as it does. Liquid helium-4 itself becomes a superfluid when cooled to within a few degrees of absolute zero on the Kelvin scale (minus 273 Celsius or minus 460 Fahrenheit), and the resulting lack of viscosity allows it to seem to defy gravity, flowing up and over the sides of a container.

Now a team led by a University of Washington physicist, using the most powerful supercomputer available for open science, has devised a theoretical framework that explains the real-time behavior of superfluids that are made of fermions -- subatomic particles such as electrons, protons and neutrons that are basic building blocks of nature.

Such superfluids are found in neutron stars, which rotate between one and 1,000 times a second. These stars, also called pulsars, have 50 percent greater mass than the sun but are packed so densely that one can occupy an area only about the size of a city such as Seattle, said Aurel Bulgac, a UW physics professor and lead author of a paper in the June 10 edition of Science that details the work.

As a neutron star rotates, the superfluid on the surface behaves quite differently than a liquid would on the surface of Earth. As the rotational speed increases the fluid opens a series of small vortices. As the vortices assemble into triangular patterns, the triangles build a lattice structure within the superfluid.

"When you reach the correct speed, you'll create one vortex in the middle," Bulgac said. "And as you increase the speed, you will increase the number of vortices. But it always occurs in steps."

Similar behavior can be recreated in a laboratory using a vacuum chamber and a laser beam to create a high-intensity electrical field that will cool a small sample, perhaps 1 million atoms, to temperatures near absolute zero. A "laser spoon" then can stir the superfluid fast enough to create vortices.

In trying to understand the odd behavior, scientists have attempted to devise descriptive equations, as they might to describe the swirling action in a cup of coffee as it is stirred, Bulgac said. But to describe the action in a superfluid made of fermions, a nearly limitless number of equations is needed. Each describes what happens if just one variable -- such as velocity, temperature or density -- is changed. Because the variables are linked, if one changes others will change as well.

The challenge, Bulgac said, was to formulate the proper mathematical problem and then find a computer that could work through the problem as the number of variable changes reached 1 trillion or more. To reach its solution, the team in the last year used the JaguarPF computer at Oak Ridge National Laboratory in Tennessee, one of the largest supercomputers in the world, for the equivalent of 70 million hours, which would require almost 8,000 years on a single-core personal computer (JaguarPF has nearly a quarter-million cores).

"This tells you the complexity of these calculations and how difficult this is," he said.

The researchers also found through their calculations that by increasing the speed at which the fluid was stirred, eventually it would lose its superfluid properties -- though not as soon as had been previously hypothesized. Video representations of the results of the massive numerical simulations are at http://www.phys.washington.edu/groups/qmbnt/UFG.

The work means that researchers can "to some extent" study the properties of a neutron star using computer simulations, Bulgac said. It also opens new directions of research in cold-atom physics.

"This is a pretty major step forward in studying these dynamic processes," he said.

Co-authors are Yuan-Lung Luo of the UW, Piotr Magierski of the Warsaw University of Technology in Poland; Kenneth Roche of the Pacific Northwest National Laboratory in Richland, Wash.; and Yongle Yu of China's State Key Laboratory of Magnetic Resonance, Atomic and Molecular Physics. Magierski and Roche also have affiliate UW physics appointments.

The research was funded by the U.S. Department of Energy, the U.S. National Science Foundation, the Polish Ministry of Science and the Chinese National Science Foundation.

Story Source:

The above story is reprinted (with editorial adaptations by ScienceDaily staff) from materials provided by University of Washington. The original article was written by Vince Stricherz.

Journal Reference:

Aurel Bulgac, Yuan-Lung Luo, Piotr Magierski, Kenneth J. Roche, Yongle Yu. Real-Time Dynamics of Quantized Vortices in a Unitary Fermi Superfluid. Science, 10 June 2011: Vol. 332 no. 6035 pp. 1288-1291 DOI: 10.1126/science.1201968

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here