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 -lactone formation. -Lactone production has been observed and, although minor with cyclohexyl diazoacetates, is the major insertion pathway for diazo decomposition of 2-octyl diazoacetate.Dedicated to Academician of the RAS N. S. Zefirov (on his 60th birthday).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1798–1803, September, 1995.Financial support for this research from the National Institutes of Health (GM 46503) and the National Science Foundation of the United States is gratefully acknowledged. We thank D. A. Pierson for her preparation of 2-methylcyclohexyl diazoacetates and preliminary studies of their diazo decomposition and A. Melekhov from the Higher College of Chemistry for his preparation and catalytic studies of rac-2-octyl diazoacetate.     

Lattice-BGK approach to simulating granular flows

Many continuum theories for granular flow produce an equation of motion for the fluctuating kinetic energy density (granular temperature) that accounts for the energy lost in inelastic collisions. Apart from the presence of an extra dissipative term, this equation is very similar in form to the usual temperature equation in hydrodynamics. It is shown how a lattice-kinetic model based on the Bhatnagar-Gross-Krook (BGK) equation that was previously derived for a miscible two-component fluid may be modified to model the continuum equations for granular flow. This is done by noting that the variable corresponding to the concentration of one species follows an equation that is essentially analogous to the granular temperature equation. A simulation of an unforced granular fluid using the modified model reproduces the phenomenon of clustering instability, namely the spontaneous agglomeration of particles into dense clusters, which occurs generically in all granular flows. The success of the continuum theory in capturing the gross features of this basic phenomenon is discussed. Some shear flow simulations are also presented.     

Self-avoiding walks and trees in spread-out lattices

LetG _R be the graph obtained by joining all sites ofZ ^d which are separated by a distance of at mostR. Let (G _R ) denote the connective constant for counting the self-avoiding walks in this graph. Let (G _R ) denote the coprresponding constant for counting the trees embedded inG _R . Then asR, (G _R ) is asymptotic to the coordination numberk _R ofG _R , while (G _R ) is asymptotic toek _R. However, ifd is 1 or 2, then (G _R )-k _R diverges to –.Dedicated to Oliver Penrose on this occasion of his 65th birthday.     

Retrieval and chaos in extremely dilutedQ-Ising neural networks

Using a probabilistic approach, the deterministic and the stochastic parallel dynamics of aQ-Ising neural network are studied at finiteQ and in the limitQ. Exact evolution equations are presented for the first time-step. These formulas constitute recursion relations for the parallel dynamics of the extremely diluted asymmetric versions of these networks. An explicit analysis of the retrieval properties is carried out in terms of the gain parameter, the loading capacity, and the temperature. The results for theQ network are compared with those for theQ=3 andQ=4 models. Possible chaotic microscopic behavior is studied using the time evolution of the distance between two network configurations. For arbitrary finiteQ the retrieval regime is always chaotic. In the limitQ the network exhibits a dynamical transition toward chaos.     

Trend to equilibrium of weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions

Recently R. Illner and the author proved that, under a physically realistic truncation on the collision kernel, the Boltzmann equation in the one-dimensional slab [0, 1] with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense. Here it is proved that when the Maxwellians associated with the boundary conditions atx=0 andx=1 are the same MaxwellianM _w , then the solution is uniformly bounded and tends toM _w fort.     

An energy-transport model for semiconductors derived from the Boltzmann equation

An energy-transport model is rigorously derived from the Boltzmann transport equation of semiconductors under the hypothesis that the energy gain or loss of the electrons by the phonon collisions is weak. Retaining at leading order electron-electron collisions and elastic collisions (i.e., impurity scattering and the elastic part of phonon collisions), a rigorous diffusion limit of the Boltzmann equation can be carried over, which leads to a set of diffusion equations for the electron density and temperature. The derivation is given in both the degenerate and nondegenerate cases.     

Subtleties in data analysis related to the size of critical region

We comment on the analysis of the critical behavior of a layered driven diffusive system recently done by Achahbar and Marro. We discuss why we believe their method of taking the thermodynamic limit and determining the order-parameter exponent leads to unreliable estimates.     

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast.This research was supported in part by the National Science Foundation under Grant DMS 91-11794 and in part by the Italian M.U.R.S.T. project Problemi non lineari...Part of this author's work was done while visiting Ohio University.     

Effects of steric and hydrophobic forces on the rheological properties of ZrO2 suspensions

 The effect of pH on the flow behavior of ZrO₂ suspensions containing polyacrylic and octanoic acids was evaluated. In the flocculated pH regime, the flow behavior is highly shearthinning and can be described by a power-law model. The shear-thinning behavior increases with increasing degree of flocculation. Maximum shearthinning was observed at the zero zeta potential condition. Hydrophobic interaction arising from adsorbed octanoic acid was found to enhance the shear-thinning behavior. No such enhancement was observed for adsorbed polyacrylic acid. It was also illustrated that the viscosity–pH behavior is a mirror image of the yield stress–pH behavior. A quantitative particle-pair interactions model incorporating steric and hydrophobic interactions was proposed to explain the effects of polyacrylic and octanoic acids on the maximum yield stress. Received: 23 May 1997 Accepted: 4 June 1997     

A zero differential overlap study of chemical binding in ammonia-borane and carbony l-borane

A cndo/2D study of the charge distribution obtained through Mulliken population analysis in the ground state of the title compounds shows that the features of charge distribution found by severalab initio calculations are fairly well reproduced by this method. The one-particle density, the interference density at the mid-point of the bond axis and the kinetic part of the interference energy calculated through the deorthogonalized density matrices over a wide range of intermolecular separation between the donor and the acceptor show that the one-particle density and the interference density steadily grow with decreasing internuclear separation, while the kinetic interference energy starts with negative value at large distance, then decreases and passes through a minima near but above the equilibrium distance and then increases rapidly below it conforming to the characteristic general behaviour of the kinetic component of Morse curve. The orbital pairwise interference density and the corresponding kinetic energy components reveal that the orbitals involved in the covalent binding are σ_2p AO of B and 2S and σ_2p AO of N and C atoms in H₃B-NH₃ and H₃B-CO respectively.