Percolation Systems away from the Critical Point

This article reviews some effects of disorder in percolation systems even away from the critical density p_c. For densities below p_c, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee-Yang edge singularity problem is described. Rare compact clusters give rise to Griffiths singuraties in the free energy of diluted ferromagnets, and lead to a very slow relaxation of magnetization. In biassed diffusion on percolation clusters, trapping in dead-end branches leads to asymptotic drift velocity becoming zero for strong bias, and very slow relaxation of velocity near the critical bias field.Comment: Minor typos fixed. Submitted to Praman

“Re-Culturing” Teacher Education: Inquiry, Evidence, and Action

Currently the press to make policy and practice decisions on the basis of evidence is being coupled with recognition that real change requires shifts in organizational culture. Consequently, there are now many efforts to “re-culture” organizations by making evidence central to decision making. In this article, the authors problematize the notion of a “culture of evidence” in teacher education. Then the article identifies four key aspects involved in efforts to create a culture of evidence at one institution over a five-year period: (1) development of a portfolio of studies about processes and outcomes; (2) recognition that teacher education always poses values questions as well as empirical questions; (3) an exploratory, open-ended approach to evidence construction; and, (4) multiple structures that institutionalize evidence collection and use locally and beyond. The authors suggests that building cultures of evidence has the potential to be transformative in teacher education, but only if challenges related to sustainability, complexity, and balance are addressed

Fractal chemical kinetics: Reacting random walkers

Computer simulations on binary reactions of random walkers ( A + A → A ) on fractal spaces bear out a recent conjecture: ( ρ −1 − ρ 0 −1 ) ∞ t f , where ρ is the instantaneous walker density and ρ 0 the initial one, and f = d s /2, where d s is the spectral dimension. For the Sierpinski gaskets: d =2, 2 f =1.38 ( d s =1.365); d =3, 2 f =1.56 ( d s =1.547); biased initial random distributions are compared to unbiased ones. For site percolation: d = 2, p =0.60, 2 f = 1.35 ( d s =1.35); d=3, p =0.32, 2 f =1.37 ( d s =1.4); fractal-to-Euclidean crossovers are also observed. For energetically disordered lattices, the effective 2 f (from reacting walkers) and d s (from single walkers) are in good agreement, in both two and three dimensions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45149/1/10955_2005_Article_BF01012924.pd

A type catalog of fossil invertebrates (Cnidaria: Anthozoa) in the Yale Peabody Museum

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