Steady-state Ion Transport through a Three-Layered Membrane System: A Mathematical Model Allowing for Violation of the Electroneutrality Condition

A relatively simple mathematical model based on the Poisson equation is considered. The model is intended for modeling transport through multilayered ion-exchange membranes operating at overlimiting currents. The boundary-value problem is solved by a numerical method of parallel shooting and by an approximate method based on the assumption that the charge density is distributed quasi-uniformly. Concentration profiles in diffusion layers and membranes, current–voltage curves, and dependences of effective transport numbers on the current density are examined.     

Joint Effect of the Dipole–Dipole Interaction and Constant Dipole Moment on the Shape of the Field Pulse without an Envelope

Journal of Experimental and Theoretical Physics - An integrable model is proposed for a two-level medium with a constant dipole moment, which describes the evolution of electromagnetic field pulses...     

Integrable equations of a few cycle optical pulse propagation

Evolution of the integrable Reduced Maxwell-Bloch equations describing interaction of light pulses with the two-level system in dipole approximation beyond the slow envelopes application is reviewered.     

Asymptotic formulas for subharmonic functions in Rm of order zero

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 47, pp. 125–128, 1987.     

Sodium chloride concentration by electrodialysis with hybrid organic-inorganic ion-exchange membranes: An investigation of the process

This study examines how conditions for modifying homogeneous MF-4SK and heterogeneous MK-40 membranes with tetraethoxysilane affect membrane properties. The microstructure of the bulk membrane and its surface, both before and after exposure to the modifying agent, is examined by scanning electron microscopy, spark spectrophotometry, and standard contact porosimetry. The process of sodium chloride concentration by electrodialysis with hybrid organic-inorganic membranes in cells with noncirculating concentration compartments is investigated, and a mathematical model of the concentration process by electrodialysis is used to determine transport properties: current efficiency, diffusion and osmotic permeabilities, and the salt hydration number. For highly hydrophilic membranes, it is shown that water transport occurs both in ion hydration shells and also as free water. It is established that after modified membranes undergo additional heat treatment, the transport of free water ceases, and the water transport number decreases. This is in accord with an increase in the salt content of the concentrate during concentration by electrodialysis.     

Effect of an aprotic solvent on the properties and structure of ion-exchange membranes

The effect of the aprotic solvent dimethylacetamide on the equilibrium and transport properties of heterogeneous (MK-40, MA-40, and MA-41) and homogeneous (MF-4SK) ion-exchange membranes is investigated. On the basis of concentration dependences of the conductivity and diffusion permeability of membranes, model calculations of transport-structural parameters that reflect the structural and kinetic characteristics of conducting phases of the swollen polymer are performed. The effect of the aprotic solvent on the flow of current through the structural fragments of the ion-exchange material is estimated. The causes of changes that are induced in the properties of the membranes by the aprotic solvent are ascertained.     

Formation of an encapsulated Fe2O3 nanostructure during mechanochemical interaction of iron oxide and excess alumina

The reasons for an abrupt deceleration of the mechanical synthesis of the composite (Al₂O₃ nanoceramics with inclusions of iron intermetallides) from the (Fe₂O₃ + Al) source mixture at Al excess are explained using Mossbauer spectroscopy and electron microscopy. Dependence of the morphology of the obtained composites on the initial concentrations of the mixture components is considered.     

Dynamics of a light field in a composite integrable model

The inverse scattering transform method is used to solve the model that describes the evolution of light pulses in an optical system that includes a set of media with different nonlinear optical properties. As a physical example, we analyze a model composed of the systems of equations that describe the resonant interaction of a very short light pulse with an energy transition of the medium and the ensuing propagation of the light field in an optical fiber. The constant boundary value of one of the fields is shown to result in an asymptotic quasi-radiative solution of the model.     

Generation of soliton packets in a two-level laser

A variant of perturbation theory is constructed for a system of nearly integrable equations. Perturbations of a special type are considered, which makes it possible to represent the system in the form of compatibility condition for “deformed” linear systems. The corresponding deformation of the Whitham equations is found. The mathematical apparatus is used to theoretically examine the generation of a sequence of solitons in a two-level laser. The generation process is described by a system of Maxwell-Bloch equations with pumping of the upper level and with allowance for some relaxation effects. The dynamics of the transformation of the initial perturbation into a sequence of solitons under pumping is studied. Finally, the various generation regimes are analyzed and compared with the experimental data. Zh. éksp. Teor. Fiz. 112, 2237–2251 (December 1997)