Calculation of the frequency-dependent photoconductivity of organic molecular crystals

The frequency dependent photoconductivity of charge carriers in organic molecular crystals is derived using general connections of the velocity autocorrelation function to the mean-square-displacement of the charge carriers and to the memory function of generalized master equations. The dynamics of the charge carriers is described by a stochastic Liouville equation, in one case in the usual Markovian form and in the other in a generalized non-Markovian form.     

Master equation techniques for exciton motion,relaxation, capture,and annihilation

Techniques developed recently for the study of exciton dynamics in molecular solids are discussed. They include master equation methods for the analysis of prerelaxation energy transfer, the generalized master equation approach to coherence in exciton motion, and the defect technique as applied to exciton trapping and annihilation.     

Theory of coherence effects in time-dependent delayed fluorescence. II. Application to two- and three-dimensional crystals

A recently developed theory of the effects of transport coherence of triplet excitons on the time dependence of delayed fluorescence in molecular crystals is applied to two- and three-dimensional crystals. Manifestations of anisotropy are studied for arbitrary coherence and it is shown that the mean-square-velocity tensor can be extracted explicitly in the coherent limit.     

Hurst exponents for interacting random walkers obeying nonlinear Fokker-Planck equations

Anomalous diffusion of random walks has been extensively studied for the case of non-interacting particles. Here we study the evolution of nonlinear partial differential equations by interpreting them as Fokker-Planck equations arising from interactions among random walkers. We extend the formalism of generalized Hurst exponents to the study of nonlinear evolution equations and apply it to several illustrative examples. They include an analytically solvable case of a nonlinear diffusion constant and three nonlinear equations which are not analytically solvable: the usual Fisher equation which contains a quadratic nonlinearity, a generalization of the Fisher equation with density-dependent diffusion constant, and the Nagumo equation which incorporates a cubic rather than a quadratic nonlinearity. We estimate the generalized Hurst exponents.     

Maturation of auditory temporal integration and inhibition assessed with event-related potentials (ERPs)

Background

We examined development of auditory temporal integration and inhibition by assessing electrophysiological responses to tone pairs separated by interstimulus intervals (ISIs) of 25, 50, 100, 200, 400, and 800 ms in 28 children aged 7 to 9 years, and 15 adults.

Results

In adults a distinct neural response was elicited to tones presented at ISIs of 25 ms or longer, whereas in children this was only seen in response to tones presented at ISIs above 100 ms. In adults, late N1 amplitude was larger for the second tone of the tone pair when separated by ISIs as short as 100 ms, consistent with the perceptual integration of successive stimuli within the temporal window of integration. In contrast, children showed enhanced negativity only when tone pairs were separated by ISIs of 200 ms. In children, the amplitude of the P1 component was attenuated at ISIs below 200 ms, consistent with a refractory process.

Conclusions

These results indicate that adults integrate sequential auditory information into smaller temporal segments than children. These results suggest that there are marked maturational changes from childhood to adulthood in the perceptual processes underpinning the grouping of incoming auditory sensory information, and that electrophysiological measures provide a sensitive, non-invasive method allowing further examination of these changes.     

Lithium hexamethyldisilazide-mediated ketone enolization: the influence of hindered dialkyl ethers and isostructural dialkylamines on reaction rates and mechanisms

Mechanistic studies of the enolization of 2-methylcyclohexanone mediated by lithium hexamethyldisilazide (LiHMDS; TMS(2)NLi) solvated by hindered dialkyl ethers (ROR') are described. Rate studies using in situ IR spectroscopy show that enolizations in the presence of i-Pr(2)O, 2,2,5,5-tetramethyltetrahydrofuran, and cineole proceed via dimer-based transition structures [(TMS(2)NLi)(2)(ROR')(ketone)]. Comparing the relative solvation energies and the corresponding solvent-dependent activation energies shows that the highly substituted ethers accelerate the enolizations by sterically destabilizing the reactants and stabilizing the transition structures. Comparisons of hindered dialkyl ethers with their isostructural dialkylamines reveal that the considerably higher rates elicited by the amines derive from an analogous relative destabilization of the reactants and relative stabilization of the transition structures.     

Study of transients in the propagation of nonlinear waves in some reaction diffusion systems

We study the transient dynamics of single species reaction diffusion systems whose reaction terms f(u) vary nonlinearly near u ≈ 0, specifically as f(u) ≈ u² and f(u) ≈ u³. We consider three cases, calculate their traveling wave fronts and speeds analytically and solve the equations numerically with different initial conditions to study the approach to the asymptotic front shape and speed. Observed time evolution is found to be quite sensitive to initial conditions and to display in some cases nonmonotonic behavior, ascribable to the disparity in time scales between the evolution of the front interior and the front tail.     

Generalization of a nonlinear friction relation for a dimer sliding on a periodic substrate

An atomic cluster moving along a solid surface can undergo dissipation of its translational energy through a direct mode, involving the coupling of the center-of-mass motion to thermal excitations of the substrate, and an indirect mode, due to damping of the internal motion of the cluster, to which the center-of-mass motion can be coupled as a result of surface potential. Focussing only on the less well understood indirect mode, on the basis of numerical solutions, we present, departures from a recently reported simple relationship between the force and velocity of nonlinear friction. A generalization of the analytic considerations that earlier led to that relationship is carried out and shown to explain the departures satisfactorily. Our generalization treats for the system considered (dimer sliding over a periodic substrate) the complete dependence on several of the key parameters, specifically internal dissipation, natural frequency, substrate corrugation, and length ratio. Further predictions from our generalizations are found to agree with new simulations. The system analyzed is relevant to nanostructures moving over crystal surfaces.