If people shared taxis with strangers, how much money could be saved? And how much could pollution and traffic be reduced? A dataset of 150 million taxi trips and a new type of mathematical analysis enabled the untapped potential of New York City’s fleet of more than 13,000 taxis to be quantified.
- Quantifying the Benefits of Vehicle Pooling With Shareability Networks (PDF) – Proceedings of the National Academy of Sciences
Dynamics of social balance
“The enemy of my enemy is my friend” – what are the mathematical consequences of playing out this logic in large social or political networks? Tools from statistical physics, graph theory, and random matrix theory bring out the surprising implications of this ancient approach to friendship and rivalry.
Dynamics of political moderation
In a simple model of a society polarized by ideological conflict, how can moderation be encouraged? Under what conditions will a committed minority of true believers eventually win everyone over to their point of view?
- Encouraging Moderation: Clues From a Simple Model of Ideological Conflict (PDF) – Physical Review Letters
Chimera states for coupled oscillators
Systems of identical oscillators with symmetrical coupling can sometimes split into two domains, one synchronized, the other desynchronized. The properties of such a “chimera state” have been elucidated by exactly solvable models.
- Chimera States for Coupled Oscillators (PDF) – Physical Review Letters
- Solvable Model for Chimera States of Coupled Oscillators (PDF) – Physical Review Letters
- Solvable Model of Spiral Wave Chimeras (PDF) – Physical Review Letters
Crowd synchronization on the Millennium Bridge
What caused London’s Millennium Bridge to wobble on its opening day? And why did the pedestrians on it inadvertently fall into step with its sideways vibrations? A model based on ideas from mathematical biology explains both effects as two sides of the same coin.
- All Together Now: Synchrony Explains Swaying – The New York Times
- Few People 'Caused' Bridge Wobble – BBC News
- Explaining Why the Millennium Bridge Wobbled – Science Daily
- Revealed: Why London's Millennium Bridge Wobbled – Reuters
- Millennium Bridge Wobbles Are Explained at Last – The Telegraph
- Millennium Bridge Wobble Explained – Financial Times
Dynamics of language death
The world’s languages are vanishing at an alarming rate. Modeling the competition between languages with the tools of population dynamics led to the first quantitative model of language decline.
Percolation on random graphs
Mathematical studies of the Internet, social networks, and the power grid have addressed the resilience of these networks to either random or targeted deletion of network nodes. Percolation models on random graphs with arbitrary degree distributions can be solved exactly to illuminate this issue of network resilience.
- Network Robustness and Fragility: Percolation on Random Graphs (PDF) – Physical Review Letters
- Random Graphs with Arbitrary Degree Distribution and Their Applications (PDF) – Physical Review E
How can all seven billion of us be just six handshakes apart? “Small-world networks,” introduced by Strogatz and his former graduate student Duncan Watts, give one possible explanation. The same math also gives insight into how epidemics spread, how brains are wired, and how blackouts propagate through the power grid.
Dynamics of Josephson junction arrays
Josephson junctions are superconducting electronic devices that obey the same governing equations as pendulums – but they swing a hundred billion times faster. When thousands of them interact, how do they behave?
- Synchronization Transitions in a Disordered Josephson Series Array (PDF) – Physical Review Letters
Sending secret messages with synchronized chaos
A pair of synchronized chaotic circuits can be used to create a new kind of communication system. Moreover, a message becomes more private when it’s cloaked in chaos.
- Synchronization of Lorenz-Based Chaotic Circuits, With Applications to Communications (PDF) – IEEE Transactions on Circuits and Systems
Dynamics of switching in charge-density waves
A charge-density wave is like a block of jello on a sticky plate. If you tug it sideways, it stays stuck in place … unless you tug it just hard enough; then it breaks loose and starts to slide. A coupled oscillator model showed that the sliding speed could depend discontinuously on the tugging force – as previously seen experimentally.
- Simple Model of Collective Transport With Phase Slippage (PDF) – Physical Review Letters
- Collective Dynamics of Coupled Oscillators With Random Pinning (PDF) – Physica D
- Delayed Switching in a Phase-Slip Model of Charge-Density Wave Transport (PDF) – Physical Review B
Synchronization of coupled oscillators
How can thousands of fireflies flash on and off in unison, all night long, without any leader or cue from the environment? More generally, how can dissimilar oscillators all come to act as one, in diverse biological, physical, and chemical systems? Over two decades of work on modeling such systems, using nonlinear dynamics, statistical physics, and computer simulations, has deepened our understanding of synchrony in our bodies and the world around us.
- Synchronization of Pulse-Coupled Biological Oscillators (PDF) – SIAM Journal on Applied Mathematics
- Coupled Oscillators and Biological Synchronization (PDF) – Scientific American
- From Kuramoto to Crawford: Exploring the Onset of Synchronization in Populations of Coupled Oscillators (PDF) – Physica D
- All Together Now (PDF) – Nature
- All Together Now (PDF) – Nature
- Step in Time (PDF) – Science News
- Flirting Male Crabs Found to Wave Claws in Unison – The New York Times
- A Mystery of Nature: Mangroves Full of Fireflies Blinking in Unison – The New York Times
Data analysis of human sleep and circadian rhythms
Studies of brave volunteers living for months in underground caves or windowless apartments have clarified how bright light shifts our circadian rhythms, why many of us like to take an afternoon nap, and why it's so hard to fall asleep two hours before your regular bedtime.
- Bright Light Resets the Human Circadian Pacemaker Independent of the Timing of the Sleep-Wake Cycle – Science
- Circadian Pacemaker Interferes With Sleep Onset at Specific Times Each Day: Role in Insomnia – American Journal of Physiology
Topology of scroll waves
Spiral waves of activity occur in thin layers of heart muscle, nerve tissue, and certain chemical reactions. Scroll waves, their three-dimensional cousins, can be twisted, linked, and knotted according to a topological exclusion principle.
- Organizing Centres for Three-Dimensional Chemical Waves (PDF) – Nature
- Yeast Oscillations, Belousov-Zhabotinsky Waves, and the Non-Retraction Theorem (PDF) – Mathematical Intelligencer
Topology of chromatin and supercoiled DNA
The linking number of DNA helps us unravel the structure of the chromatin fiber, the next level of coiling above the double helix and below the chromosome.