Granular Impact Model as an Energy-Depth Relation

Velocity-squared drag forces are common in describing an object moving through a granular material. The resulting force law is a nonlinear differential equation, and closed-form solutions of the dynamics are typically obtained by making simplifying assumptions. Here, we consider a generalized version of such a force law which has been used in many studies of granular impact. We show that recasting the force law into an equation for the kinetic energy versus depth, K(z), yields a linear differential equation, and thus general closed-form solutions for the velocity versus depth. This approach also has several advantages in fitting such models to experimental data, which we demonstrate by applying it to data from 2D impact experiments. We also present new experimental results for this model, including shape and depth dependence of the velocity-squared drag force

An Annotated Checklist of the Freshwater Fishes of Texas, with Keys to Identification of Species

Forty-five families and 247 species of fishes are known to inhabit the freshwaters of Texas. We report on the distribution and status of these fishes and provide a key to their identification. Of the native fishes originally found in Texas, five taxa, Notropis orca (phantom shiner), Notropis simus simus (Rio Grande bluntnose shiner), Cyprinella lutrensis blairi (Maravillas red shiner), Gambusia amistadensis (Amistad gambusia) and Gambusia georgei (San Marcos gambusia) are apparently extinct, and three, Oncorhynchus clarki virginalis (Rio Grande cutthroat trout), Hybognathus amarus (Rio Grande silvery minnow) and Gambusia senilis (blotched gambusia) appear to be extirpated from the state. More than 20 percent of the remaining primary freshwater species appear to be in some need of protection.Integrative Biolog

Comparative effects of instruction, self-monitoring, and self-reinforcement on teacher attending behavior

A major purpose of the present study was to assess the relative merits of instruction in contingent teacher attention, self-monitoring, and self-reinforcement on teacher approval and disapproval to disruptive classroom students. Other objectives were to assess the reliability of teacher self-recorded data and to determine whether a relationship between the frequency of approval and disapproval occurred as a function of the experimental conditions. Five junior high school teachers in an urban school system served as subjects. Each teacher identified two students in their classes regarded as disruptive or nonparticipating. Teachers and students were observed for 55 days. Data on teacher rates of approval and disapproval to a target students and student rates of appropriate and inappropriate behaviors were collected to ascertain the effectiveness of experimental conditions. Treatments were temporally staggered to avoid simultaneous duplication across teachers. Two teachers were assigned the experimental phases of instruction, self-monitoring approval, self-monitoring disapproval and self-reinforcement. Two others were given instruction, self-monitoring approval and self-reinforcement; and one teacher was under the instruction condition only. The instruction phase involved brief teacher introduction to the rationale and techniques of contingent teacher attention for controlling disruptive classroom behaviors. During the self-monitoring approval and disapproval phases, teachers recorded their rates of approval or disapproval on small mechanical counters. The self-reinforcement condition involved teachers setting up behavioral goals and rewards contingent upon their approval of target students. Line graphs were plotted to illustrate the frequencies of teacher behaviors and percentages of appropriate student behaviors. Single subject analyses of these graphs revealed the changes in teacher and student behaviors. Tabular presentations assisted in the analysis of the relationship between the changes in rates of approval and disapproval and the reliability of self-recorded data. The results showed that instruction had little effect upon either positive teacher or student behavior. Self-monitoring approval had no clear effects on teacher approval or disapproval, although students under this condition reduced their inappropriate behavior. Teachers under the self-monitoring disapproval phase reduced their disapproval, but a decrease in approval rates and appropriate student behavior also occurred. Self-reinforcement increased teacher approval but had ambiguous effects on disapproval and student behaviors. Agreement between teacher self-recorded data was low for both approval and disapproval. Teacher rates of approval and disapproval failed to show systematic variation with respect to each other as a function of the experimental treatments