Соотношения взаимности для открытых нелинейных систем в переменных полях

А proof of reciprocity relations for nonlinear systems in inhomogeneous variable electric and magnetic fields in the presence of unsteady spin currents, thermodynamic flows and mechanical disturbances is obtained by the Kubo method in the approximation of Markov relaxation and locally quasi-equilibrium distribution.

The Effects of Copolymer Compatibilizers on the Phase Structure Evolution in Polymer Blends—A Review

This paper summarizes the results of studies describing the effect of block and graft copolymers on the phase structure formation and evolution in immiscible polymer blends. The main phenomenological rules for prediction of the copolymer compatibilization efficiency are briefly described and compared with selected experimental data. The results of the theories of equilibrium distribution of a copolymer between the blend interface and the bulk phases and its effect on the blend interfacial tension are summarized. The theories of the compatibilizer effect on the droplet breakup in flow are analyzed. The mechanisms of the copolymer effect on the coalescence of droplets in flow are compared and their effect on the droplet size is shown. The problems of reliable description of the effect of a copolymer on the coalescence in quiescent state are presented. Obstacles to derivation of a realistic theory of the copolymer effect on the competition between the droplet breakup and coalescence are discussed. Selected experimental data are compared with the theoretical results.

Molecular dynamics lattice gas equilibrium distribution function for Lennard–Jones particles

The molecular dynamics lattice gas (MDLG) method maps a molecular dynamics (MD) simulation onto a lattice gas using a coarse-graining procedure. This is a novel fundamental approach to derive the lattice Boltzmann method (LBM) by taking a Boltzmann average over the MDLG. A key property of the LBM is the equilibrium distribution function, which was originally derived by assuming that the particle displacements in the MD simulation are Boltzmann distributed. However, we recently discovered that a single Gaussian distribution function is not sufficient to describe the particle displacements in a broad transition regime between free particles and particles undergoing many collisions in one time step. In a recent publication, we proposed a Poisson weighted sum of Gaussians which shows better agreement with the MD data. We derive a lattice Boltzmann equilibrium distribution function from the Poisson weighted sum of Gaussians model and compare it to a measured equilibrium distribution function from MD data and to an analytical approximation of the equilibrium distribution function from a single Gaussian probability distribution function. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

Model Kinetic Equations for Multiply Ionized Gas Mixtures

Model kinetic equations are proposed for the description of ionized monoatomic gas mixture flows. The mixtures are assumed enough rarefied to be treated as ideal gases after multiple ionization steps. The model equations contain the equilibrium distribution functions for the components of the gas mixtures under consideration like it was done in BGK equations and their well-known generalizations. However, in this paper the new forms of the equilibrium distribution functions are used which correspond to the entropy maximum under the constraints of momentum, total energy, nuclei and electrons (both bound and free) conservation. It is shown that the derived model equations allow us to study the local equilibrium flows of the ionized gases and the transport processes of energy, nuclei and electrons in the non-equilibrium conditions.

Olefin oligomerization by main group Ga3+ and Zn2+ single site catalysts on SiO2

In heterogeneous catalysis, olefin oligomerization is typically performed on immobilized transition metal ions, such as Ni2+ and Cr3+. Here we report that silica-supported, single site catalysts containing immobilized, main group Zn2+ and Ga3+ ion sites catalyze ethylene and propylene oligomerization to an equilibrium distribution of linear olefins with rates similar to that of Ni2+. The molecular weight distribution of products formed on Zn2+ is similar to Ni2+, while Ga3+ forms higher molecular weight olefins. In situ spectroscopic and computational studies suggest that oligomerization unexpectedly occurs by the Cossee-Arlman mechanism via metal hydride and metal alkyl intermediates formed during olefin insertion and β-hydride elimination elementary steps. Initiation of the catalytic cycle is proposed to occur by heterolytic C-H dissociation of ethylene, which occurs at about 250 °C where oligomerization is catalytically relevant. This work illuminates new chemistry for main group metal catalysts with potential for development of new oligomerization processes.