A combined theoretical and molecular dynamics (MD) simulation study of the collective modes and their dispersion in a two-dimensional Yukawa system in the strongly coupled liquid state is presented. The theoretical analysis relies upon the quasilocalized charge approximation; the MD simulation generates static pair correlation functions and dynamical current-current correlation spectra.

The progressive ratio schedule requires the subject to emit an increasing number of responses for each successive reinforcement. Eventually, the response requirement becomes so large that the subject fails to respond for a period of 15 min and thereby terminates the session. This point is arbitrarily defined as the "breaking point" of the subject's performance. The measure is quantified in terms of the number of responses in the final completed (i.e., reinforced) ratio run of the session. Previous work has shown that this measure varies as a function of several motivational variables and may thus be useful as an index of reinforcement strength. The present study is an extension of that work. The subjects were four rats. In the first experiment, the effects of the size of the increment by which each ratio run increased were studied. In two additional experiments, the volume of a liquid reinforcer was varied using both large and small ratio increments. The results indicate that the number of responses in the final completed ratio run increases as a function of the size of the ratio increment. However, the number of reinforcements obtained by the animals per session declines sharply. When large ratio increments are used, the number of responses in the final ratio increases as a function of the volume of the reinforcer, but when small increments are used, progressive satiation results in a decline in performance with the larger volumes of liquid.In order to make precise comparisons between behaviors maintained by different reinforcers, an experimenter must be able to make some statement as to the relative strength of each reinforcer. This Using this index, orderly relationships have been obtained (Hodos, 1961) between the breaking point of behavior and such variables as the concentration of a liquid reinforcer and the degree of food deprivation. The purpose of the present investigation is two-fold: (1) to study the effects of variation in the size of the ratio increment on progressive ratio performance, and, (2) to extend the earlier findings by determining whether the breaking 387

Properties of two-dimensional strongly coupled Yukawa systems are explored through molecular dynamics simulations. An effective coupling coefficient gamma* for the liquid phase is introduced on the basis of the constancy of the first peak amplitude of the pair-correlation functions. Thermodynamic quantities are calculated from the pair-correlation function. The solid-liquid transition of the system is investigated through the analysis of the bond-angular order parameter. The static structure function satisfies consistency relation, attesting to the reliability of the computational method. The response is shown to be governed by the correlational part of the inverse compressibility. An analysis of the velocity autocorrelation demonstrates that this latter also exhibits a universal behavior.

Abstract.In dusty (complex) plasmas, containing mesoscopic charged grains, the grain-grain interaction in many cases can be well described through a Yukawa potential. In this Review we summarize the basics of the computational and theoretical approaches capable of describing many-particle Yukawa systems in the liquid and solid phases and discuss the properties of the dynamical density and current correlation spectra of three-and two-dimensional strongly coupled Yukawa systems, generated by molecular dynamics simulations. We show details of the ω(k) dispersion relations for the collective excitations in these systems, as obtained theoretically following the quasilocalized charge approximation, as well as from the fluctuation spectra created by simulations. The theoretical and simulation results are also compared with those obtained in complex plasma experiments.

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We determine the collective mode structure of a strongly correlated Yukawa fluid, with the purpose of analyzing wave propagation in a strongly coupled dusty plasma. We identify a longitudinal plasmon and a transverse shear mode. The dispersion is characterized by a low- k acoustic behavior, a frequency maximum well below the plasma frequency, and a high- k merging of the two modes around the Einstein frequency of localized oscillations. The damping effect of collisions between neutrals and dust grains is estimated.

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