Diffusion with random distribution of static traps

The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability P(c,t) as a function of the trap concentration c and the time t. Theoretical arguments are presented, based on earlier work of Donsker and Varadhan and of Rosenstock, why in two dimensions one expects a data collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both data collapses show a clear crossover from the early-time Rosenstock behavior to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure

Detection of early age-related macular degeneration using novel functional parameters of the focal cone electroretinogram

The focal cone electroretinogram is a sensitive marker for macular disease, but have we unlocked its full potential? Typically assessment of waveform parameters is subjective and focuses on a small number of locations (e.g. the a-wave). This study evaluated the discriminatory and diagnostic potential of 4 conventional and 15 novel, objectively determined, parameters in patients with early Age-related Macular Degeneration. Focal cone electroretinograms were recorded in 54 participants with early Age-related Macular Degeneration (72.9±8.2 years) and 54 healthy controls (69±7.7 years). Conventional a and b wave amplitudes and implicit times were measured and compared to novel parameters derived from both the 1st and 2nd derivatives and the frequency-domain power spectrum of the electroretinogram.Statistically significant differences between groups were shown for all conventional parameters, the majority of 1st and 2nd derivative parameters and the power spectrum at 25 and 30 Hz. Receiver operating characteristics showed that both conventional and 1st and 2nd derivative implicit times had provided the best diagnostic potential. A regression model showed a small improvement over any individual parameter investigated. The non-conventional parameters enhanced the objective evaluation of the focal electroretinogram, especially when the amplitude was low. Furthermore, the novel parameters described here allow the implicit time of the electroretinogram to be probed at points other than the peaks of the a and b waves. Consequently these novel analysis techniques could prove valuable in future electrophysiological investigation, detection and monitoring of Age-related Macular Degeneration

The Chemical Problems of To-Day.

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