Quasipotentials for simple noisy maps with complicated dynamics

The theory of nonequilibrium potentials or quasipotentials is a physically motivated approach to small random perturbations of dynamical systems, leading to exponential estimates of invariant probabilities and mean first exit times. In the present article we develop the mathematical foundation of this theory for discrete-time systems, following and extending the work of Freidlin and Wentzell, and Kifer. We discuss strategies for calculating and estimating quasipotentials and show their application to one-dimensionalS-unimodal maps. The method proves to be especially suited for describing the noise scaling behavior of invariant probabilities, e.g., for the map occurring as the limit of the Feigenbaum period-doubling sequence. We show that the method allows statements about the scaling behavior in the case of localized noise, too, which does not originally lie within the scope of the quasipotential formalism.     

Einflu\ von Äthylendiamintetraacetat und TriÄthanolaminhydrochlorid auf die Proteinbestimmung mit der Biuret-Methode

Buffers containing triethanolamine hydrochloride and EDTA decrease the sensitivity of the protein determination by the biuret reaction. This effect is not caused by changes in the p_H but is due to an increase in the optical density (O.D. at 540 nm) of the biuret reagent by formation of a triethynolamine-copper complex. By increasing the concentration of the biuret reagent the sensitivity of the biuret method can be increased by about 33%. In the range between 0.05 and 0.23 the ionic strength of the buffers does not influence the O.D. of the biuret reagent. EDTA causes a remarkable decrease in the O.D. of the biuret reagent only at concentrations higher than 5 mM (in the buffer). This effect can be eliminated by increasing the amount of added biuret reagent.     

Labeling vibrations by light: ultrafast transient 2D-IR spectroscopy tracks vibrational modes during photoinduced charge transfer

We report on a novel ultrafast two-dimensional infrared laser experiment that correlates vibrational bands of reactant and product of a photoreaction. The possibilities of this technique are demonstrated for the metal-to-ligand charge transfer (MLCT) in [Re(CO)3Cl(dmbpy)] (dmbpy = 4,4'-dimethyl-2,2'bipyridine) where we correlated the CO vibrational modes of the ground state and the MLCT state. A distinct vibrational mode is excited in the electronic ground state by an infrared laser pulse. This vibrational label survives the subsequent electronic excitation and can be followed in the excited electronic state. It is shown that the order of the vibrational energy levels is not preserved when exciting the molecule as was commonly assumed in the literature.