Is Nature Self-similar and Scale-free?
Advisor: Jack Heidel
Description: There is great current scientific interest in both fractals (6) and scale-free networks (5) because they seem to describe many natural and man-made structures and phenomena such as the internet, social relationships, spread of epidemics, shape and form in biology, clouds and river basins, etc. One reaction to this rapidly expanding literature is to deny that it represents anything fundamental (1). Another reaction is to look for a fundamental theory which explains it (2,3,4,7). The purpose of this project is to investigate this important question by looking at the cited literature and other references and then to attempt to formulate and justify an answer to this question.
Prerequisites: Calculus I, II and III with good grades and clear evidence of a high degree of self-motivation.
References:
1. David Avnir et al, Is the geometry of nature fractal?, Science 279(1998), 39.
2. G.I.
Barenblatt, Scaling, Self-similarity, and
Intermediate Asymptotics,
3. Adrian Bejan, Advanced Engineering Thermodynamics, John Wiley, 2006, 3rd Edition
4. Adrian Bejan, Shape and Structure, from Engineering to Nature, Cambridge 2000.
5. Adrian Bejan and James Marden, Unifying constructal theory for scale effects in running, swimming and flying, Journal of Experimental Biology 209(2006), 238.
6. Albert-Laszlo Barabasi, Linked: the New Science of Networks, Perseus 2002.
7. Benoit Mandelbrot, The Fractal Geometry of Nature, Freeman 1983.
8. C.J.
Pennycuick,
9. Manfred Schroeder, Fractals, Chaos and Power Laws, W.H. Freeman, 1991