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.     

A femtosecond study of the infrared-driven cis-trans isomerization of nitrous acid (HONO)

We investigate the dynamics and mechanism of the IR-driven cis-trans isomerization of nitrous acid (HONO) in a low-temperature krypton matrix applying ultrafast time resolved IR spectroscopy. After excitation of the OH-stretching mode the trans HONO state decays biexponentially on a 8 and 260 ps time scale. The initially excited cis HONO state decays on a 20 ps time scale. Cis HONO isomerizes with 10% quantum yield on a 20 ps time scale to trans HONO. The quantum yield we observe is significantly smaller than the previously reported 100%, which could imply that additional, much slower reaction channels exist. We furthermore developed a four-dimensional model of the system, which includes the three proton intramolecular degrees of freedom of HONO fully quantum mechanically and one intermolecular translational degree of freedom of the molecule in the crystal cage. We find that cis-trans isomerization necessarily is accompanied by a translation of the molecule as a whole in the crystal cage. The translational degree of freedom tunes the intramolecular proton states of HONO with respect to each other. When resonances occur, the proton states might couple and transfer population. We suggest a possible reaction pathway, where the cis OH-stretch excited state first couples to a high cis torsional mode, which then may transfer almost instantaneously to the trans side. The model qualitatively explains all experimental observations.     

Femtosecond study of self-trapped vibrational excitons in crystalline acetanilide

Femtosecond IR spectroscopy of delocalized NH excitations of crystalline acetanilide confirms that self-trapping in hydrogen-bonded peptide units exists and does stabilize the excitation. Two phonons with frequencies of 48 and 76 cm (-1) are identified as the major degrees of freedom that mediate self-trapping. After selective excitation of the free exciton, self-trapping occurs within a few 100 fs. Excitation of the self-trapped states disappears from the spectral window of this investigation on a 1 ps time scale, followed by a slow ground state recovery of the hot ground state within 18 ps.     

Investigation on the feasibility of using an Ulbricht sphere for the absolute calibration of an ICP or other source at specific wavelengths

The short term and long term stability of an Ulbricht sphere was investigated by comparing its radiation at four Balmer wavelengths with those of two Sylvania projector lamps. A slight positive trend in the radiation intensity of the Ulbricht sphere was observed. This was attributed to a change in the molecular structure of the paint used to cover the inside of the sphere. However, the radiance varied less than 3% for 14 h burning time. The uncertainty in the primary calibration of the Tungsten standard lamp was given as ±3% in the wavelength range 400–600 nm. It was hence concluded that the sphere is suitable for spectral calibration purposes for a period of 14 h operational time without being recalibrated.     

Active phase stabilization in Fourier-transform two-dimensional infrared spectroscopy

A scheme for active phase stabilization and absolute positioning in Fourier-transform two-dimensional (2D) IR spectroscopy is presented. The position accuracy is better than 20 nm(rms) corresponding to lambda/250 at 5 microm, which significantly improves the quality of Fourier-transform 2D IR spectra. Phase stabilization is added to a standard photon echo setup in a way that does not impair the flexibility of the experiment and the control over IR pulse parameters.     

A determination of the Cabibbo-Kobayashi-Maskawa parameter |V us| using KL decays

We present a determination of the Cabibbo-Kobayashi-Maskawa parameter |V(us)| based on new measurements of the six largest K(L) branching fractions and semileptonic form factors by the KTeV (E832) experiment at Fermilab. We find |V(us)|=0.2252+/-0.0008(KTeV)+/-0.0021(ext), where the errors are from KTeV measurements and from external sources. We also use the measured branching fractions to determine the CP violation parameter |eta(+-)|=(2.228+/-0.005(KTeV)+/-0.009(ext))x10(-3).     

Measurements of the Decay KL-->e+ e- mu+ mu-

The KTeV experiment at Fermilab has isolated a total of 132 events from the rare decay K(L)-->e+ e- mu+ mu-, with an estimated background of 0.8 events. The branching ratio of this mode is determined to be [2.69+/-0.24(stat)+/-0.12(syst)]x10(-9), with a radiative cutoff of M(2)(ee mu mu)/M(2)(K)>0.95. The first measurement using this mode of the parameter alpha from the D'Ambrosio-Isidori-Portolès (DIP) model of the K(L)gamma*gamma* vertex yields a result of -1.59+/-0.37, consistent with values obtained from other decay modes. Because of the limited statistics, no sensitivity is found to the DIP parameter beta. We use this decay mode to set limits on CP and lepton violation.     

A Comparison of Concrete and Virtual Manipulative Use in Third‐ and Fourth‐Grade Mathematics

The primary purpose of this classroom experiment was to examine the effectiveness of concrete (hands‐on) manipulatives as compared with virtual (computer‐based) manipulatives on student review of fraction concepts in third grade and introduction of symmetry concepts in fourth grade. A pretest–posttest design was employed with a sample of 91 third‐grade students and 54 fourth‐grade students who were randomly assigned to complete a lesson using either concrete or virtual manipulatives. Students used a variety of manipulative materials during the lessons. Results of the posttest suggest that student learning was unchanged by lesson condition.