The radial distribution function provides a means of characterizing an amorphous material and is a measure of the spatial distribution of a system of particles. We introduce an experiment suitable for the undergraduate laboratory that illustrates the meaning and application of the radial distribution function to a two-dimensional system of hard spheres comprised of varying area fractions. Larger area fractions lead to an increase in the correlation length and the magnitude of the underlying particle–particle correlations.
Patterns are pervasive in nature with many examples being found in both living and inanimate systems. While researchers recognize the importance of the behavior of individuals to the structure and shape of an aggregation, a major hurdle in describing aggregated organisms has been the difficulty of tracking the movement of individuals over time. Here we present an innovative application of an analytical technique derived from statistical mechanics (a subfield of physics) to describe the spatial distribution of grouped organisms. Radial distribution and pair-correlation functions are traditionally used by physicists to describe inert particle dynamics. This novel biological application allows one to infer the behavioral characteristics of individuals within a group based solely on the spatial distribution of the aggregate population. Additionally, the method allows one to determine the correlation length, the average maximum distance over which one individual may exert an influence on another member of the aggregation. The analytical technique presented here is also important in that it minimizes two problems that typically plague studies of grouped organisms: it eliminates the need to track the movements of individuals, and it partially takes into account the presence of occluded individuals. This technique also permits quantitative comparison between aggregations formed under various environmental and/or experimental conditions. Thus, this technique may be of value to resource managers, ecologists, and others working with grouped organisms (e.g., plankton swarms, schooling fish, flocking birds, or migratory mammals) who seek to gain information about factors influencing the structure and behavior of such groups.
Extracellular recordings from the auditory midbrain, Torus semicircularis, of the leopard frog reveal a wide diversity of tuning patterns. Some cells seem to be well suited for time-based coding of signal envelope, and others for rate-based coding of signal frequency. Adaptation for ongoing stimuli plays a significant role in shaping the frequency-dependent response rate at different levels of the frog auditory system. Anuran auditory-nerve fibers are unusual in that they reveal frequency-dependent adaptation [A. L. Megela, J. Acoust. Soc. Am. 75, 1155–1162 (1984)], and therefore provide rate-based input. In order to examine the influence of these peripheral inputs on central responses, three layers of auditory neurons were modeled to examine short-term neural adaptation to pure tones and complex signals. The response of each neuron was simulated with a leaky integrate and fire model, and adaptation was implemented by means of an increasing threshold. Auditory-nerve fibers, dorsal medullary nucleus neurons, and toral cells were simulated and connected in three ascending layers. Modifying the adaptation properties of the peripheral fibers dramatically alters the response at the midbrain. [Work supported by NOHR to M.J.F.; Gustavus Presidential Scholarship to K.McA.; NIH DC05257 to A.M.S.]
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