A macrokinetic model of redox sorption on metal–ion exchanger nanocomposites at electrochemical polarization

A conceptual macrokinetic model of redox sorption on metal–ion exchanger nanocomposites upon electrochemical polarization is formulated and a corresponding mathematical model is constructed. The solution to a multi-point boundary value problem for the concentration of a sorbed substance (oxygen) is given. The concentration front of the sorbed substance is characterized by a concentration gradient in the near-surface layer of the solution, by layers of the products of metal oxidation in the composite forming due to both external and internal diffusion transfer, and by chemical and electrochemical reactions at the interphase boundaries. A considerable reduction in the concentration gradient of the sorbate in layers of the products of oxidation of metal and the growth of the diffusion layer of the solution with polarizing currents weaker than the limiting diffusion current are noted.     

Almost cover-free codes and designs

An s-subset of codewords of a binary code X is said to be \((s,\,\ell )\) -bad in X if the code X contains a subset of \(\ell \) other codewords such that the conjunction of the \(\ell \) codewords is covered by the disjunctive sum of the s codewords. Otherwise, the s-subset of codewords of X is called \((s,\,\ell )\) -good in X. A binary code X is said to be a cover-free (CF) \((s,\,\ell )\)-code if the code X does not contain \((s,\,\ell )\)-bad subsets. In this paper, we introduce a natural probabilistic generalization of CF \((s,\,\ell )\)-codes, namely: a binary code X is said to be an almost CF \((s,\,\ell )\)-code if the relative number of its \((s,\,\ell )\)-good s-subsets is close to 1. We develop a random coding method based on the ensemble of binary constant weight codes to obtain lower bounds on the capacity of such codes. Our main result shows that the capacity for almost CF \((s,\,\ell )\)-codes is essentially greater than the rate for ordinary CF \((s,\,\ell )\)-codes.     

Surface topography formation in a region of plate collision: Mathematical modeling

The collision of earth’s crustal plates is modeled mathematically based on a numerical solution of the equations of deformable solid mechanics using a finite element method with the MSC software. The interaction of the plates with each other and with the mantle is described by the solution of the contact problem with an unknown contact boundary between the solids considered. The mantle material is assumed to be ideal elastic-plastic with the Huber-Mises yield surface, and the properties of the plate material are described using an elastic-plastic model with the Drucker-Prager parabolic yield function which takes into account fracture in the tensile stress region. The results of the mathematical modeling show that the surface profiles of the plates in the region of their collision are consistent, both qualitatively and quantitatively, to the surface topography observed in nature under similar conditions.     

Direct one-index transformations in multiconfiguration response calculations

The evaluation of gradient vectors of a general operator with one-index, double-one-index, or higher-order one-index transformed integrals is a key operation in multiconfiguration response theory calculations. We describe an integral-driven direct algorithm that carries out this operation efficiently without pretransforming the integrals. The use of this algorithm leads to a considerable reduction in disk space and timing. © 1994 by John Wiley & Sons, Inc.     

Kinetics of the reduction of molecular oxygen from water by ultrafine copper in an ion-exchange matrix

The rate of the reduction of molecular oxygen from water with a low-capacity copper-containing electron-ion exchanger at various initial ionic forms, grain radii, and sizes of metal particles dispersed into pores. The applicability of the mixed-diffusion and diffusional-kinetic models incorporating a first-order irreversible reaction to describing the system under study was examined. The kinetic parameters of the system were determined within the framework of these models. It was found that the limiting stage of the process in the stationary mode is the internal diffusion of oxygen molecules to the redox sorbent particle. The increase in the rate of the absorption of oxygen by samples containing copper of higher dispersity was observed at the initial stage of the process and was likely associated with an increase in the surface area of the reactive interface.