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.

Differences in mitochondrial and nuclear DNA status of high-density and low-density sperm fractions after density centrifugation preparation

Background: In order to isolate the â??bestâ?? sperm for assisted conception a discontinuous two-step density gradient centrifugation is usually employed. This technique is known to isolate a subpopulation with good motility, morphology and nuclear DNA (nDNA) integrity. As yet its ability to isolate sperm with unfragmented mitochondrial DNA (mtDNA) is unknown. Methods: Semen was obtained from men (n=28) attending our Regional Fertility Centre for infertility investigations. We employed a modified long polymerase chain reaction to study mtDNA and a modified alkaline Comet assay to determine nDNA fragmentation. Results: The high- density fraction displayed significantly more wild type mtDNA (75% of samples) than that of the low- density fraction (25% of samples). In the high-density fraction, there was a higher incidence of single, rather than double or multiple deletions and the deletions were predominantly small scale (0.1-4.0kb). There was a strong correlation between nDNA fragmentation, the number of mtDNA deletions (r=0.7, p

Analytically continued generalized continuum distorted waves

The continuum distorted-wave eikonal-initial-state (CDW-EIS) theory of Crothers and McCann (Crothers DSF and McCann JF, 1983 J. Phys. B: At. Mol. Opt. Phys. 16 3229 ) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS, to incorporate the azimuthal ange dependence into the final-state wavefunction. This is accomplished by the analytic continuation of hydrogenic-like wavefunctions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 ke V u^{-1}, the total CDW-EIS ionization cross section falls off, with decreasing energy, too quickly in comparison with experimental data by Crothers and McCann. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment, by including contributions from non-zero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it.

Homocysteine is lower in the Third Trimester of Pregnancy in Women with Enhanced Folate status from continued Folic Acid Supplementation.

Background: In many countries current recommendations are that women take a daily 400ug folic acid supplement, from before conception until the end of the 12th week of gestation, for the prevention of neural tube defects. Low folate status is associated with an elevated concentration of plasma total homocysteine (tHcy), a risk factor that is associated with pregnancy complications such as pre-eclampsia. Methods: In a longitudinal study, tHcy and corresponding folate status were determined in 101 pregnant women at 12, 20 and 35 weeks of gestation, in 35 non-pregnant control subjects sampled conconcurrently, and in a subgroup (n=21 pregnant, 19 non-pregnant women) at 3 days post-partum. Results: Plasma tHcy concentrations were significantly lower throughout pregnancy compared with control subjects, with values lowest in the 2nd trimester before increasing toward non-pregnant values in the 3rd trimester. Importantly, tHcy concentrations were lower in pregnant women taking folic acid supplements compared to those not, an effect which reached significance in the 3rd trimester (5.25 umol/l v 6.89 umol/l, P <0.05). Furthermore, during the 3rd trimester, tHcy concentrations were significantly higher in pregnant women with a history of miscarriage compared to those with no previous history (7.32 umol/l v 5.62 u­mol/l, P <0.01). Conclusion: This is the first longitudinal study to show that homocysteine levels rise in late pregnancy towards non-pregnant levels; a rise which can be limited by enhancing folate status through continued folic acid supplementation. These results indicate a potential role for continued folic acid supplementation in reducing pregnancy complications associated with hyperhomocysteinaemia.

1-Ethyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}amide as solvent for the separation of aromatic and aliphatic hydrocarbons by liquid extraction - extension to C-7- and C-8-fractions

The ionic liquid 1-ethyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}amide ([C(2)mim][NTf2]) was tested as solvent for the separation of aromatic and aliphatic hydrocarbons containing 7 or 8 carbon atoms (the C-7- and C-8-fractions). The liquid-liquid equilibria (LLE) of the ternary systems (heptane + toluene + [C(2)mim][NTf2]) and (octane + ethylbenzene + [C(2)mim][NTf2]), at 25 degrees C, were experimentally determined. The performance of the ionic liquid as the solvent in such systems was evaluated by means of the calculation of the solute distribution ratio and the selectivity. The results were compared to those previously reported for the extraction of benzene from its mixtures with hexane by using the same ionic liquid, therefore analysing the influence of the size of the hydrocarbons. It was found that the ionic liquid is also good for the extraction of C-7- and C-8- fraction aromatic compounds, just a greater amount of ionic liquid being needed to perform an equivalently efficient separation than for the C-6-fraction. It is also discussed how [C(2)mim][NTf2] performs comparably better than the conventional solvent sulfolane. The original 'Non-Random Two-Liquid' (NRTL) equation was used to adequately correlate the experimental LLE data.