A. V. Kalinin

Stationary and nonstationary models of the global electric circuit: Well-posedness, analytical relations, and numerical implementation

We analyze the formulation of the problem of global atmospheric electric circuit modeling. It was shown that under some relatively simple and widely used simplifying assumptions this problem can be reduced to finding the temporal and spatial dependencies of the electric potential on the specified generators, which are determined by the external electric current density. They correspond to thunderclouds in the real atmosphere. The ionospheric potential (the potential difference between the upper and lower atmospheric boundaries) is not specified explicitly but can be uniquely determined from the solution. The formulations of the stationary and nonstationary problems are given in terms of the potential and their well-posedness is discussed. We obtained a number of analytical relations under some restrictions on the distribution of conductivity. They include the formulas which explicitly express the ionospheric potential in terms of the problem parameters. The examples of numerical calculations using the software developed on the basis of general formulations of the stationary and nonstationary problems are demonstrated.

Influence of Large-Scale Conductivity Inhomogeneities in the Atmosphere on the Global Electric Circuit

AbstractTheoretical estimation of the influence of large-scale conductivity inhomogeneities on the global electric circuit and, in particular, on the ionospheric potential is considered. A well-posed formulation of this problem is presented, on the basis of which an approximate method is developed so as to take account of large-scale conductivity inhomogeneities. Under certain restrictions imposed on the distributions of the conductivity and the external current density, explicit approximate formulas for the ionospheric potential are derived. The approximation developed is shown to be equivalent to that of classical models of atmospheric electricity in which the atmosphere is divided into two or more columns and is replaced by a simple equivalent electric circuit. The effect of conductivity inhomogeneities located inside and outside thunderclouds is discussed and, in particular, it is demonstrated that taking account of the conductivity reduction inside thunderclouds leads to a substantial increase in the...

Enantiomer differentiation in intramolecular carbon—hydrogen insertion reactions of racemic secondary alkyl diazoacetates catalyzed by chiral dirhodium(ii) carboxamidates

Highly efficient kinetic resolution of racemic secondary alkyl diazoacetates in intramolecular carbon-hydrogen insertion reactions has been achieved using chiral dirhodium(ii) carboxamidates. Products formed from catalytic diazo decomposition of racemic 2-octyl diazoacetate and, separately, its (2R)- and (2S)-enantiomeric forms, as well as bothcis- andtrans-2-methylcyclohexyl diazoacetates, have been systematically evaluated. Enantioselectivities up to 99 %ee have been obtained for γ-lactone formation. β-Lactone production has been observed and, although minor with cyclohexyl diazoacetates, is the major insertion pathway for diazo decomposition of 2-octyl diazoacetate.

Reaction of silylated aminonitrofurazane with N-magnesium amine derivatives

A study was carried out on the reaction of N-trimethylsilylaminonitrofurazane with magnesyl amines, leading to the corresponding asymmetric diazene oxides.

Peculiarities of the interaction of dinitrobenzenes witht-BuNHMgBr andt-BuNHLi

Reactions ofm- andp-dinitrobenzenes witht-BuNHMgBr andt-BuNHLi were studied. The reactions afford azo- and azoxy-derivatives and products of nucleophilic substitution.

Synthesis of 1-tert-butyl-2-aryldiazene-2-oxides by reactions of t-BuNHMgBr with nitrobenzenes

A new method has been developed for the synthesis of alkylaryldiazene oxides by the reactions of t-BuNHMgBr with nitrobenzenes. The cis-azoxy compound 1-tert-butyl-2-(2-chlorophenyl)diazene-2-oxide, which irreversibly isomerizes to the trans isomer upon heating, was obtained for the first time under chemical reaction conditions.

Preparation of trimethylsilyl derivatives of substituted hydrazones containing functional groups

ConclusionsGeneral methods were developed for the silylation of functionally substituted hydrazines and a number of trimethylsilyl derivatives of these compounds were obtained.

REGIOSELECTIVE RH2(OAC)4-PROMOTED REACTIONS OF METHYL DIAZOACETATE WITH TERMINAL TRIPLE BOND ENYNES

The selective Rh2(OAc)4-promoted methoxycarbonylmethylenation of a triple bond in enynes, with a terminal triple bond, by methyl diazoacetate is established, and the main factors, affecting the regioselectivity of the process, are elucidated. The easy in situ[2 + 2]-dimerization of methyl 1-alkenylcyclopropene-3-carboxylates in dimethyl trans-1,2-dialkenyltricyclo[3.1.0.02,4]hexane-3,6-dicarboxylates 2 is found, and their thermal rearrangement into dimethyl trans-1,2-dialkenylcyclohexa-1,4-diene-3,6-dicarboxylates 7 is also described.

Formation of nitrohydrazones by acidic nitration of organic hydrazine derivatives

It was found by means of NMR spectroscopy that the nitration of trinitroethyl hydrazine derivatives affords nitrohydrazones rather than nitrohydrazines as supposed previously.

Catalytic reaction of methyl diazoacetate with silylated enynes

Factors affecting the regioselectivity of the catalytic reaction of methyl diatoacetate with 1-trimethylsilylalkene-1-ynes have been revealed. Conditions for selective cyclopropanation of the double bond in 1-trimethylsilylbut-3-ene-1-yne and 1-trimethylsilyl-3-methylbut-3-ene-1-yne in the presence of Rh2(OAc)4 have been found.