Phase Transition Models in Atmospheric Dynamics

Abstract From both the theoretical and numerical viewpoints, we study a system of differential inclusions describing the evolution of the temperature and the specific humidity distributions in a system of moist air. We allow the so-called saturation concentration parameter to depend on the temperature, and thus we consider more general and interesting phase-change effects than the ones addressed in [2].     

On the simultaneous tridiagonalization of two symmetric matrices

We discuss congruence transformations aimed at simultaneously reducing a pair of symmetric matrices to tridiagonal–tridiagonal form under the very mild assumption that the matrix pencil is regular. We outline the general principles and propose a unified framework for the problem. This allows us to gain new insights, leading to an economical approach that only uses Gauss transformations and orthogonal Householder transformations. Numerical experiments show that the approach is numerically robust and competitive.     

A phase diagram for a stochastic reaction diffusion system

In this paper a stochastic reaction diffusion system is considered, which models the spread of a finite population reacting with a non-renewable resource in the presence of individual based noise. A two-parameter phase diagram is established to describe the large time evolution, distinguishing between certain death or possible life of the population.     

A General Palladium‐Catalyzed Method for Alkylation of Heteroarenes Using Secondary and Tertiary Alkyl Halides

A general alkylation of heterocycles using a simple palladium catalyst is reported. Most classes of heterocycles, including indoles and pyridines, efficiently coupled with unactivated secondary and tertiary alkyl halides. An alkyl radical addition to neutral heteroarenes is most likely involved.     

Infrared-infrared double resonance spectroscopy of the isomers of acetylene-HCN and cyanoacetylene-HCN in helium nanodroplets

Infrared-infrared double resonance spectroscopy is used to probe the vibrational dynamics of molecular complexes solvated in helium nanodroplets. We report results for the acetylene-HCN and cyanoacetylene-HCN binary complexes, each having two stable isomers. We find that vibrational excitation of an acetylene-HCN complex results in a population transfer to the other isomer. Photoinduced isomerization is found to be dependent on both the initially excited vibrational mode and the identity of the acetylene-HCN isomer. However, population transfer is not observed for the cyanoacetylene-HCN complexes. The results are rationalized in terms of the ab initio intermolecular potential energy surfaces for the two systems with particular emphasis on the long-range barriers to rearrangement.     

Total Synthesis of Ramonanins A–D

The first total synthesis of the ramonanin family of lignan natural products is described. The short synthesis involves a 2,5‐diaryl‐3,4‐dimethylene tetrahydrofuran intermediate, which participates in an unexpectedly facile Diels–Alder dimerization, generating all four natural products. Insights into the reactivity and stereoselectivity of the key dimerization are provided through computational studies employing B3LYP/6‐31G(d) and M06‐2X/6‐31G(d) model chemistries.     

Osmotic coefficients and activity coefficients of aqueous hydrobromic acid solutions at 25°C

The osmotic coefficients ? and activity coefficients γ_± of aqueous solutions of HBr depend largely on emf measurements utilizing the silver-silver bromide electrode. There is evidence, however, that side reactions between AgBr and bromide ion render this electrode unreliable when the HBr molality (m) exceeds 2 mol-kg^?1. It is shown, however, that the isopiestic vapor-pressure technique is capable of yielding data for HBr at higher molalities. New emf measurements of cells with hydrogen and AgBr/Ag electrodes at 25°C have been combined with literature data to recommend values for the activity coefficients of HBr in the dilute range. These have been supplemented by isopiestic measurements vs. NaCl and CaCl₂ reference solutions in the range of HBr molalities from 0.7 to 6.2m. A table of ? and γ_± at 25°C at round molalities from 0.005 to 6.0 is presented.     

Activity and osmotic coefficients oft-butylammonium chloride; Activity coefficients of HCl in mixtures with tris hydrochloride ort-butylammonium chloride at 25°C

In an earlier study, the activity coefficients of aqueous mixtures of HCl with the hydrochlorides of tris(hydroxymethyl)aminomethane (Tris) ort-butylamine (t-B) were determined at ionic strengths of 0.1, 0.5, and 1.0 mol-kg^–1. The work has been extended to ionic strengths of 2.0 and 3.0 through emf measurements with hydrogen and AgCl/Ag electrodes at 25°C. The results are considered in terms of Harned's rule and the Pitzer and Rush-Johnson-Scatchard treatments of activity coefficients in electrolyte mixtures. In order to compare ionic interaction parameters in the two systems, the activity coefficients and osmotic coefficients of t-butylammonium chloride at molalities up to saturation (7.14 mol-kg^–1) were determined by the gravimetric isopiestic method with solutions of NaCl as reference. The behavior for both systems can be accounted for satisfactorily in terms of binary (H⁺–N⁺) and ternary (H⁺–N⁺–Cl^–) interactions, where N⁺ is either Tris·H⁺ or t-B·H⁺.     

Electrochemistry and spectroelectrochemistry of heterobimetallic porphyrin-corrole dyads. Influence of the spacer, metal ion, and oxidation state on the pyridine binding ability

Combined electrochemical and UV-visible spectroelectrochemical methods were utilized to elucidate the prevailing mechanisms for electroreduction of previously synthesized porphyrin-corrole dyads of the form (PCY)H2Co and (PCY)MClCoCl where M = Fe(III) or Mn(III), PC = porphyrin-corrole, and Y is a bridging group, either biphenylenyl (B), 9,9-dimethylxanthenyl (X), anthracenyl (A), or dibenzofuranyl (O). These studies were carried out in pyridine, conditions under which the cobalt(IV) corrole in (PCY)MClCoCl is immediately reduced to its Co(III) form, thus enabling direct comparisons with the free-base porphyrin dyad, (PCY)H2Co(III) under the same solution conditions. The compounds are all reduced in multiple one-electron-transfer steps, the first of which involves the M(III)/M(II) process of the porphyrin in the case of (PCY)MClCoCl and the Co(III)/Co(II) process of the corrole in the case of (PCY)H2Co. Each metal-centered redox reaction may be accompanied by the gain or loss of pyridine axial ligands, with the exact stoichiometry of the exchange process depending upon the specific combination of metal ions in the dyad, their oxidation states, and the particular spacer in the complex. Before this study was started, it was expected that the porphyrin-corrole dyads with the largest spacers, namely, O and A, would readily accommodate the formation of cobalt(III) bis-pyridine adducts because of the larger size of the cavity while dyads with the smallest B spacer would seem to have insufficient room to add even a single pyridine within the cavity, as was structurally seen in the case of (PCB)H2Co(py). This is clearly not the case, as shown in the present study. A reversible Co(III)/Co(II) reaction is seen for (PCB)MnClCoCl at -0.62 V, which when combined with spectroscopic data, leads to the assignment of (PCB)Mn(III)(py)2Co(III)(py) as the species in pyridine. The reduction of (PCB)Mn(III)(py)2Co(III)(py) to (PCB)Mn(II)(py)Co(III)(py) is accompanied on the slower spectroelectrochemical time scale by the appearance of a 603 nm band in the UV-vis spectra and is consistent with the addition of a second pyridine ligand to the Co(III)(py) unit of the dyad as one ligand is lost from the electrogenerated manganese(II) porphyrin, thus maintaining one pyridine ligand within the cavity. A different change in the coordination number is observed in the case of (PCB)FeClCoCl. Here the initial Fe(III) complex can be assigned as (PCB)Fe(III)ClCo(III)(py), which has no pyridine molecule within the cavity and the singly reduced form is characterized as (PCB)Fe(II)(py)2Co(III)(py)2, which contains two pyridine ligands inside the cavity. A following one-electron reduction of the Fe(II)/Co(III) complex then gives [(PCB)Fe(II)(py)2Co(II)]-.