Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Semiclassical complex angular momentum theory and Pade reconstruction for resonances, rainbows, and reaction thresholds

A semiclassical complex angular momentum theory, used to analyze atom-diatom reactive angular distributions, is applied to several well-known potential (one-particle) problems. Examples include resonance scattering, rainbow scattering, and the Eckart threshold model. Pade reconstruction of the corresponding matrix elements from the values at physical (integral) angular momenta and properties of the Pade approximants are discussed in detail.

Sildenafil citrate improves sperm motility but causes a premature acrosome reaction in vitro

Objective: to determine if sildenafil citrate; a cyclic monophosphate specific type 5 phosphodiesterase inhibitor, influences sperm motility or the acrosome reaction. Design: laboratory analysis of sperm motility after exposure to sildenafil citrate using computer assisted semen analysis (CASA) and acrosome reaction by fluoroscein isothiocyanate labelled peanut agglutinin (FITC-PNA) staining. Setting: An ART unit Patients: 57 male patients Interventions: Sperm were divided into 90% (the best fertilizing potential used in assisted conception) and 45% (the poorer subpopulation) fractions by density centrifugation and incubated with sildenafil citrate ( 0.67uM) at 37ï?°C for up to 180 minutes. Main outcome measures: both the numbers and velocity of progressively motile sperm were significantly increased by sildenafil citrate between 15 and 135 minutes. Further, samples revealed that these effects were consistent in the 90% and 45% subpopulations of sperm. In both subpopulations, sildenafil also caused a significant increase in the proportion of acrosome reacted sperm - 22.1% compared with 11.8% in the control group of the good quality fraction (p

Quantitative analysis of the reactivity of formate species seen by DRIFTS over a Au/Ce(La)O2 water–gas shift catalyst: First unambiguous evidence of the minority role of formates as reaction intermediates

The reactivity of the species formed at the surface of a Au/Ce(La)O2 catalyst during the water������¢���¯���¿���½���¯���¿���½gas shift (WGS) reaction were investigated by operando diffuse reflectance Fourier transform spectroscopy (DRIFTS) at the chemical steady state during isotopic transient kinetic analyses (SSITKA). The exchanges of the reaction product CO2 and of formate and carbonate surface species were followed during an isotopic exchange of the reactant CO using a DRIFTS cell as a single reactor. The DRIFTS cell was a modified commercial cell that yielded identical reaction rates to that measured over a quartz plug-flow reactor. The DRIFTS signal was used to quantify the relative oncentrations of the surface species and CO2. The analysis of the formate exchange curves between 428 and 493 K showed that at least two levels of reactivity were present. ������¢���¯���¿���½���¯���¿���½Slow formates������¢���¯���¿���½���¯���¿���½ displayed an exchange rate constant 10- to 20-fold slower than that of the reaction product CO2. ������¢���¯���¿���½���¯���¿���½Fast formates������¢���¯���¿���½���¯���¿���½ were exchanged on a time scale similar to that of CO2. Multiple nonreactive readsorption of CO2 took place, accounting for the kinetics of the exchange of CO2(g) and making it impossible to determine the number of active sites through the SSITKA technique. The concentration (in mol g������¢���¯���¿���½���¯���¿���½1) of formates on the catalyst was determined through a calibration curve and allowed calculation of the specific rate of formate decomposition. The rate of CO2 formation was more than an order of magnitude higher than the rate of decomposition of formates (slow + fast species), indicating that all of the formates detected by DRIFTS could not be the main reaction intermediates in the production of CO2. This work stresses the importance of full quantitative analyses (measuring both rate constants and adsorbate concentrations) when investigating the role of adsorbates as potential reaction intermediates, and illustrates how even reactive species seen by DRIFTS may be unimportant in the overall reaction scheme.