Random walk through fractal environments

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is less than 2, there is though always a finite rate of unaffected escape. Random walks through fractal sets with D less or equal 2 can thus be considered as defective Levy walks. The distribution of jump increments for D > 2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk-increments. It is shown that the particles undergo anomalous, enhanced diffusion for D_F < 2, the diffusion is dominated by the finite escape rate. Diffusion for D_F > 2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality (SOC) models give rise to enhanced diffusion. The analytical results are illustrated by Monte-Carlo simulations.Comment: 22 pages, 16 figures; in press at Phys. Rev. E, 200

Mechanistic principles and applications of resonance energy transfer

Resonance energy transfer is the primary mechanism for the migration of electronic excitation in the condensed phase. Well-known in the particular context of molecular photochemistry, it is a phenomenon whose much wider prevalence in both natural and synthetic materials has only slowly been appreciated, and for which the fundamental theory and understanding have witnessed major advances in recent years. With the growing to maturity of a robust theoretical foundation, the latest developments have led to a more complete and thorough identification of key principles. The present review first describes the context and general features of energy transfer, then focusing on its electrodynamic, optical, and photophysical characteristics. The particular role the mechanism plays in photosynthetic materials and synthetic analogue polymers is then discussed, followed by a summary of its primarily biological structure determination applications. Lastly, several possible methods are described, by the means of which all-optical switching might be effected through the control and application of resonance energy transfer in suitably fabricated nanostructures.Key words: FRET, Förster energy transfer, photophysics, fluorescence, laser