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# White Shark Physics

Predation Math
by

## Ryan McKinzie

on 1 August 2013

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#### Transcript of White Shark Physics

Physics of the Great White Shark
Lévy Flight and Brownian Walk
Modeling Predatory Motion
Snell Windo
Velocity of the Great White Shark jumping out of the water
Image source: "Sharks, the S&P 500, and Lévy Flights." seeingcomplexity.wordpress.com.
Brownian Motion: describes random movement of particles
Lévy flight: model of random motion in short and long bursts; most efficient pattern for random searching
Shark hunting patterns predicted by Lévy/Brownian models
Calculating escape velocity, given:
Angle of exit = 45 deg.
maximum height = 2.4m
Snell Widow:
Index of refraction
Snell Widow is a manifest as a bright circle directly overhead while the shark is under water .

The Snell Widow process is based in refraction that is the bending of the path of a light wave as it passes from one material into another material.The refraction occurs at the boundary and is cause by a change in the speed of the light wave upon crossing the boundary.
The index of refraction essentially measure how much the medium in question bends light.

Using the geometries above, here is Snell's Law:

ni Sin Qi = nr Sin Qr
Sources
Brunnschweiler, Juerg M. "Water-escape Velocities in Jumping Blacktip Sharks" J. R. Soc. Interface (2005): 389-391
Humphries, et al. "Environmental Context Explains Levy and Brownian Movement Patterns Among Ocean Predators." Nature 465 (2010): 1066-9.
Force
"Snell's Window." Wikipedia.
Full transcript