Some Isoperimetric Inequalities in Electrochemistry and Hele Shaw Flows

Isoperimetric inequalities are applied to a moving-boundaryproblem for doubly-connected domains. This problem occurs forexample in electrochemistry, in which case the domains in questionare the electrolyte of an electrolytic cell. The two electrodessurrounding the electrolyte are assumed to grow or dissolve,at different rates in general, by electrochemical reaction.We obtain optimal estimates showing, for example, that the leastchange in volume of each electrode always occurs in sphericalsymmetry.     

Modulation of electron transfer kinetics by protein conformational fluctuations during early-stage photosynthesis

The kinetics of electron transfer during the early stages of the photosynthetic reaction cycle has recently been shown in transient absorption experiments carried out by Wang et al. [Science 316, 747 (2007)] to be strongly influenced by fluctuations in the conformation of the surrounding protein. A model of electron transfer rates in polar solvents developed by Sumi and Marcus using a reaction-diffusion formalism [J. Chem. Phys. 84, 4894 (1986)] was found to be successful in fitting the experimental absorption curves over a roughly 200 ps time interval. The fits were achieved using an empirically determined time-dependent function that described protein conformational relaxation. In the present paper, a microscopic model of this function is suggested, and it is shown that the function can be identified with the dynamic autocorrelation function of intersegment distance fluctuations that occur in a harmonic potential of mean force under the action of fractional Gaussian noise.     

Structural relaxation in complex liquids: non-Markovian dynamics in a bistable potential

The time correlation function C(t) identical with of the distance fluctuations of a particle moving in a bistable potential under the action of fractional Gaussian noise (fGn) is calculated from a Smoluchowski-type equation derived from a generalized Langevin equation (GLE). The time derivative of this function, dC(t)dt, is compared with data from optical Kerr effect measurements of liquid crystal dynamics in the vicinity of the isotropic-to-nematic transition, which are related to the time derivative of an orientational correlation function. A number of characteristic features of the experimental decay curves, including short and intermediate time power law behavior and long time exponential relaxation, are qualitatively reproduced by the analytical calculations, even though the latter do not explicitly treat orientational degrees of freedom. The GLE formalism with fGn was, in fact, originally proposed as a model of protein conformational fluctuations, so the present results suggest that it may also serve more generally as a model of structural relaxation in complex condensed phase media.