Gas-phase rate coefficients for the reactions of O(3P), S(3P), Se(3P), and Te(3P) with alkenes: application of perturbation frontier molecular orbital theory, correlations, and structure-activity relations (SARs)

The kinetics of the reactions of the atoms O(P-3), S(P-3), Se(P-3), and Te((3)p) with a series of alkenes are examined for correlations relating the logarithms of the rate coefficients to the energies of the highest occupied molecular orbitals (HOMOs) of the alkenes. These correlations may be employed to predict rate coefficients from the calculated HOMO energy of any other alkene of interest. The rate coefficients obtained from the correlations were used to formulate structure-activity relations (SARs) for reactions of O((3)p), S(P-3), Se (P-3), and Te((3)p) with alkenes. A comparison of the values predicted by both the correlations and the SARs with experimental data where they exist allowed us to assess the reliability of our method. We demonstrate the applicability of perturbation frontier molecular orbital theory to gas-phase reactions of these atoms with alkenes. The correlations are apparently not applicable to reactions of C(P-3), Si(P-3), N(S-4), and Al(P-2) atoms with alkenes, a conclusion that could be explained in terms of a different mechanism for reaction of these atoms.

Effect of soil waterlogging on below-ground biomass allometric relations in Norway spruce

An increasing importance is assigned to the estimation and verification of carbon stocks in forests. Forestry practice has several long-established and reliable methods for the assessment of aboveground biomass; however we still miss accurate predictors of belowground biomass. A major windthrow event exposing the coarse root systems of Norway spruce trees allowed us to assess the effects of contrasting soil stone and water content on belowground allocation. Increasing stone content decreases root/shoot ratio, while soil waterlogging leads to an increase in this ratio. We constructed allometric relationships for belowground biomass prediction and were able to show that only soil waterlogging significantly impacts model parameters. We showed that diameter at breast height is a reliable predictor of belowground biomass and, once site-specific parameters have been developed, it is possible to accurately estimate belowground biomass in Norway spruce.

Temporal relations of column water vapor and tropical precipitation

Empirical studies using satellite data and radiosondes have shown that precipitation increases with column water vapor (CWV) in the tropics, and that this increase is much steeper above some critical CWV value. Here, eight years of 1-min-resolution microwave radiometer and optical gauge data at Nauru Island are analyzed to better understand the relationships among CWV, column liquid water (CLW), and precipitation at small time scales. CWV is found to have large autocorrelation times compared with CLW and precipitation. Before precipitation events, CWV increases on both a synoptic-scale time period and a subsequent shorter time period consistent with mesoscale convective activity; the latter period is associated with the highest CWV levels. Probabilities of precipitation increase greatly with CWV. Given initial high CWV, this increased probability of precipitation persists at least 10–12 h. Even in periods of high CWV, however, probabilities of initial precipitation in a 5-min period remain low enough that there tends to be a lag before the start of the next precipitation event. This is consistent with precipitation occurring stochastically within environments containing high CWV, with the latter being established by a combination of synoptic-scale and mesoscale forcing.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.