Ref Levy Flight Dynamics

McCrea, W. H. and F. J. W. Whipple (1940). Random paths in two and three dimensions. Proc. R. Soc. Edinburgh 60: 281-298.

Hayot, F. (1991). Levy walk in lattice-gas hydrodynamics. Phys. Rev. A 43: 806-810.

Shlesinger, M. F., B. J. West and J. Klafter (1987). Levy dynamics of enhanced diffusion: application to turbulence. Phys. Rev. Lett. 58: 1100-1103. (These authors introduce a stochastic process called a Levy walk that is a random walk having a non-local memory that is coupled in space and in time in a scaling fashion. Levy walks enhance diffusion, i.e. diffusion that grows as ta, a > 1. Applying the idea of a Levy walk to a particle diffusing in a fluid whose flow fluctuates, this model generalizes the idea of Taylor's correlated walk to give Richardson's t3 law for the turbulent diffusion of a passive scalar in a Kolmogorov -(5/3) homogeneous turbulent flow. The model also yields the deviations from the (5/3) exponent that Mandelbrot's intermittency gives. We may extend this model to describe chemical reactions occurring in turbulent flows.)

Viswanathan, G. M. et al. (1999). Optimizing the success of random searches. Nature 401: 911-914. For foraging when targets are sparse and can be visited any number of times, an inverse square power-law distribution of steps provides an optimal strategy.

(Ref: Jacobs and Hendrickson, 1997) Jacobs, D. and J. B. Hendrickson (1997). An algorithm for two-dimensional rigidity percolation: the pebble game. J.Comput. Phys. 137:346-365. (Properties depend on the number of microscopic degrees of freedom. An algorithm is formulated as a pebble game and in the context of percolation through a rigid matrix, these authors calculate the degrees of freedom, the rigid clusters and locate the over-constrained regions.)

CHAPTER TEN: CONTROL

(Ref: Agarwal et al., 2000) Agarwal, V., M. S. Hrishikesh, S. W. Keck-ler and D. Burger (2000). Clock rate versus IPC: the end of the road for conventional microarchitectures. In: Proceedings of the 27th Annual International Symposium on Computer Architecture.

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