Time-dependent effective rates for molecular processes

The concept of time-dependent effective rates for molecular processes such as luminescence, introduced in our earlier work, is developed further by obtaining two new results. One is the explicit evaluation of those rates for four initial conditions corresponding to experimentally relevant methods of excitation of the molecule. The other is a proof that the limiting values of those rates for long times or for infinitely fast relaxation are independent of the initial condition. The latter result extends the validity of the rate depression effect (whereby the long time limit of the effective rate is different from its thermalized value) to arbitrary initial conditions.On leave of absence from the Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 (permanent address)     

Nonlocal interaction effects on pattern formation in population dynamics

We consider a model for population dynamics such as for the evolution of bacterial colonies which is of the Fisher type but where the competitive interaction among individuals is nonlocal, and show that spatial structures with interesting features emerge. These features depend on the nature of the competitive interaction as well as on its range, specifically on the presence or absence of tails in, and the central curvature of, the influence function of the interaction.     

Nature of charge carriers in disordered molecular solids: are polarons compatible with observations?

Polaronic theories for charge transport in disordered organic solids, particularly molecularly doped polymers, have been plagued by issues of internal consistency related to the magnitude of physical parameters. We present a natural resolution of the problem by showing that, in the presence of correlated disorder, polaronic carriers with binding energies Delta approximately 50-500 meV and transfer integrals J approximately 1-20 meV are completely consistent with the magnitudes of field and temperature dependent mobilities observed.     

Steady-state delayed flourescence signals in ronchi ruling experiments: theory of coherence effects

Effects of coherence in triplet exciton transport are analyzed in the context of measurements of steady-sdtate delayed fluorescence signals from molecular crystals excited through Ronchi rulings.     

Generalized master equations under delocalized initial conditions

The initial condition term that must be appended to the generalized master equation (GME) when the density matrix is not initially diagonal in the representation chosen is studied and explicit expressions are obtained for several cases. The term is shown to vanish for initial occupation of a Bloch state of arbitrary wave vector if the system is a crystal and the representation is that of site states, despite the violation of the initial diagonality condition. It is pointed out how one is to use the expressions for the initial term in transport calculations.This article is dedicated to Prof. Max Dresden on the occasion of his sixtieth birthday.     

Effects of gradual spatial variation in resources on population extinction: Analytic calculations for abrupt transitions

We study bifurcations in a spatially extended nonlinear system representing population dynamics with the help of analytic calculations. The result we obtain helps in the understanding of the onset of abrupt transitions leading to the extinction of biological populations. The result is expressed in terms of Airy functions and sheds light on the behavior of bacteria in a Petri dish as well as of large animals such as rodents moving over a landscape.