Surface Scaling Analysis of a Frustrated Spring-network Model for Surfactant-templated Hydrogels

We propose and study a simplified model for the surface and bulk structures of crosslinked polymer gels, into which voids are introduced through templating by surfactant micelles. Such systems were recently studied by Atomic Force Microscopy [M. Chakrapani et al., e-print cond-mat/0112255]. The gel is represented by a frustrated, triangular network of nodes connected by springs of random equilibrium lengths. The nodes represent crosslinkers, and the springs correspond to polymer chains. The boundaries are fixed at the bottom, free at the top, and periodic in the lateral direction. Voids are introduced by deleting a proportion of the nodes and their associated springs. The model is numerically relaxed to a representative local energy minimum, resulting in an inhomogeneous, ``clumpy'' bulk structure. The free top surface is defined at evenly spaced points in the lateral (x) direction by the height of the topmost spring, measured from the bottom layer, h(x). Its scaling properties are studied by calculating the root-mean-square surface width and the generalized increment correlation functions C_q(x)= . The surface is found to have a nontrivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales. As the vacancy concentration approaches the site-percolation limit, both the crossover length and the saturation value of the surface width diverge in a manner that appears to be proportional to the bulk connectivity length. This suggests that a percolation transition in the bulk also drives a similar divergence observed in surfactant templated polyacrylamide gels at high surfactant concentrations.Comment: 17 pages RevTex4, 10 imbedded eps figures. Expanded discussion of multi-affinit

Temporal estimation with two moving objects: overt and covert pursuit

The current study examined temporal estimation in a prediction motion task where participants were cued to overtly pursue one of two moving objects, which could either arrive first, i.e., shortest [time to contact (TTC)] or second (i.e., longest TTC) after a period of occlusion. Participants were instructed to estimate TTC of the first-arriving object only, thus making it necessary to overtly pursue the cued object while at the same time covertly pursuing the other (non-cued) object. A control (baseline) condition was also included in which participants had to estimate TTC of a single, overtly pursued object. Results showed that participants were able to estimate the arrival order of the two objects with very high accuracy irrespective of whether they had overtly or covertly pursued the first-arriving object. However, compared to the single-object baseline, participants’ temporal estimation of the covert object was impaired when it arrived 500 ms before the overtly pursued object. In terms of eye movements, participants exhibited significantly more switches in gaze location during occlusion from the cued to the non-cued object but only when the latter arrived first. Still, comparison of trials with and without a switch in gaze location when the non-cued object arrived first indicated no advantage for temporal estimation. Taken together, our results indicate that overt pursuit is sufficient but not necessary for accurate temporal estimation. Covert pursuit can enable representation of a moving object’s trajectory and thereby accurate temporal estimation providing the object moves close to the overt attentional focus