Fractal asymptotics

Recent advances in the periodic orbit theory of stochastically perturbed systems have permitted a calculation of the escape rate of a noisy chaotic map to order 64 in the noise strength. Comparison with the usual asymptotic expansions obtained from integrals and with a previous calculation of the electrostatic potential of exactly selfsimilar fractal charge distributions, suggests a remarkably accurate form for the late terms in the expansion, with parameters determined independently from the fractal repeller and the critical point of the map. Two methods give a precise meaning to the asymptotic expansion, Borel summation and Shafer approximants. These can then be compared with the escape rate as computed by alternative methods.Comment: 15 pages, 5 postscript figures incorporated into the text; v2: Quadratic Pade (Shafer) method added, also a few reference

Open circle maps: Small hole asymptotics

We consider escape from chaotic maps through a subset of phase space, the hole. Escape rates are known to be locally constant functions of the hole position and size. In spite of this, for the doubling map we can extend the current best result for small holes, a linear dependence on hole size h, to include a smooth h^2 ln h term and explicit fractal terms to h^2 and higher orders, confirmed by numerical simulations. For more general hole locations the asymptotic form depends on a dynamical Diophantine condition using periodic orbits ordered by stability.Comment: This version has a new section investigating different hole locations. Now 9 pages, 3 figure

Recent advances in open billiards with some open problems

Much recent interest has focused on "open" dynamical systems, in which a classical map or flow is considered only until the trajectory reaches a "hole", at which the dynamics is no longer considered. Here we consider questions pertaining to the survival probability as a function of time, given an initial measure on phase space. We focus on the case of billiard dynamics, namely that of a point particle moving with constant velocity except for mirror-like reflections at the boundary, and give a number of recent results, physical applications and open problems.Comment: 16 pages, 1 figure in six parts. To appear in Frontiers in the study of chaotic dynamical systems with open problems (Ed. Z. Elhadj and J. C. Sprott, World Scientific

Breaking conjugate pairing in thermostatted billiards by magnetic field

We demonstrate that in the thermostatted three-dimensional Lorentz gas the symmetry of the Lyapunov spectrum can be broken by adding to the system an external magnetic field not perpendicular to the electric field. For perpendicular field vectors, there is a Hamiltonian reformulation of the dynamics and the conjugate pairing rule still holds. This indicates that symmetric Lyapunov spectra has nothing to do with time reversal symmetry or reversibility; instead, it seems to be related to the existence of a Hamiltonian connection.Comment: 4 pages, 3 figure

Cycle expansions for intermittent diffusion

We investigate intermittent diffusion using cycle expansions, and show that a truncation based on cycle stability achieves reasonable convergence.Comment: 6 pages, revtex, 4 figure

Organic Produce: Who's Eating it? A Demographic Profile of Organic Produce Consumers

The organic market sector is one of the fastest growing food sectors in the United States with growth rates in organic food sales averaging 17 percent per year between 1998 and 2006. The largest segment within the organic market is fresh produce, comprising 34 percent of retail sales in 2006. To date, few published studies utilize consumer purchase information to understand which demographic factors influence the purchase of organic produce. This analysis focuses on household produce purchases in 2006 from the Nielsen Homescan Dataset. Assuming that household produce purchases are made in a two step process, a Heckman two-stage model is utilized to examine the factors that influence the probability a consumer will buy organic produce, and which factors influence the household share of organic produce purchased. Results show households with high levels of education and income are more likely to purchase organic pre-packaged produce, while the probability of purchasing organic fruits and vegetables decreases amongst African Americans.Food Consumption/Nutrition/Food Safety,