simulating dynamical features of escape panic dirk helbing, illes farkas, and tamas vicsek...
TRANSCRIPT
![Page 1: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/1.jpg)
Simulating Dynamical Features of Escape Panic
Dirk Helbing, Illes Farkas, and Tamas Vicsek
Presentation by
Andrew Goodman
![Page 2: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/2.jpg)
The Problem
• Crowd stampedes can be deadly
• People act in uncoordinated and dangerous ways when panicking
• It is difficult to obtain real data on crowd panics
![Page 3: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/3.jpg)
The Solution
• Model people as self-driven particles
• Model physical and socio-psychological influences on people’s movement as forces
• Simulate crowd panics and see what happens
![Page 4: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/4.jpg)
Acceleration of Simulated People
• vi0(t) = desired speed
• ei0(t) = desired direction
• vi(t) = actual velocity
• τi = characteristic time
• mi = mass
![Page 5: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/5.jpg)
Forces from Other People
• Force from other people’s bodies being in the way
• Force of friction preventing people from sliding
• Psychological “force” of tendency to avoid each other
• Sum of forces of person j on person i is fij
![Page 6: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/6.jpg)
Total Force of Other People
• Aiexp[(rij – dij)/Bi]nij is psychological “force”
• rij is the sum of the people’s radii
• dij is the distance between their centers of mass
• nij is the normalized vector from j to i
• Ai and Bi are constants
![Page 7: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/7.jpg)
Physical Forces
• kg(rij – dij)nij is the force from other bodies
• κg(rij – dij)Δvtijtij is the force of sliding
friction
• g(x) is 0 if the people don’t touch and x if they do touch
• tij is the tangential direction
• Δvtij is the tangential velocity difference
• k and κ are constants
![Page 8: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/8.jpg)
Forces from Walls
• Forces from walls are calculated in basically the same way as forces from other people
![Page 9: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/9.jpg)
Values Used for Constants and Parameters
• Values chosen to match flows of people through an opening under non-panic conditions
• People are modeled as the same except for their radius
• Insufficient data on actual panic situations to analyze the algorithm quantitatively
![Page 10: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/10.jpg)
Simulation of Clogging
![Page 11: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/11.jpg)
Simulation of Clogging
• As desired speed increases beyond 1.5m s-1, it takes more time for people to leave
• As desired speed increases, the outflow of people becomes irregular
• Arch shaped clogging occurs around the doorway
![Page 12: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/12.jpg)
Widening Can Create Crowding
![Page 13: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/13.jpg)
Mass Behavior
• Panicking people tend to exhibit herding behavior• Herding simulated using “panic parameter” p
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Effects of Herding
![Page 15: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/15.jpg)
Injured People Block Exit
![Page 16: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/16.jpg)
A Column Can Increase Outflow
![Page 17: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/17.jpg)
Findings
• Bottlenecks cause clogging
• Asymmetrically placed columns around exits can reduce clogging and prevent build up of fatal pressures
• A mixture of herding and individual behavior is ideal
![Page 18: Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek Presentation by Andrew Goodman](https://reader035.vdocuments.pub/reader035/viewer/2022070400/56649f0e5503460f94c22897/html5/thumbnails/18.jpg)
Some Questions
• Are parameters based on non-panic situations correct for panic situations?
• How can we get quantitative data about panic situations to test simulations?
• What happens when injured people are allowed to fall over (and possibly be trampled)?