Phasing of three vircators simulated in terms of coupled van der Pol oscillators

Phase synchronization in a system of three virtual-cathode microwave oscillators (vircators) simulated by coupled van der Pol oscillators is studied. The phasing dynamics of the vircators is visualized with the phase portraits of the system in the triangular coordinates. Different phasing conditions are found.     

Fundamental aspects of initiated oxidation of tridecane and polyethylene in solutions

Specific features of the initiated oxidation of polyethylene and its low-molecular-weight analogue tridecane, associated with the occurrence of the process in the short-chain mode, were studied.     

Thermodynamic properties of ternary systems: Calculation of standard enthalpies of solvation of triols, diols, and a series of their ethers in water-methanol mixed solvent

An equation for the standard enthalpy of solvation of a compound in a binary solvent is derived. The enthalpies of solvation in water-methanol mixtures are estimated for 1,3-propane-and 1,6-hexanediols, 1,2,4-butane-and 1,3,5-pentanetriols, 2-methoxy-and 2-propoxyethanols, and diethylene glycol. The enthalpy of solvation of 1,2-dimethoxyethane in the water-methanol mixed solvent is determined experimentally.     

Optimality problem for infinite dimensional bilinear systems

For any finite dimensional control system with arbitrary cost, Pontryagin's Maximum Principle (PMP) [N. Bensalem, Localisation des courbes anormales et problème d'accessibilité sur un groupe de Lie hilbertien nilpotent de degré 2, Thèse de doctorat, Université de Savoie, 1998. [6]] gives necessary conditions for optimality of trajectories. In the infinite dimensional case, it is well known that these conditions are no more true in general. The purpose of this paper is to establish an “approached” version of PMP for infinite dimensional bilinear systems, with fixed final time and without constraints on the final state. Moreover, if the set of control is contained in a closed bounded convex subset with operators defining its dynamics are compact, or if it is contained in a finite dimensional space, we get an “exact” version of PMP. We also give two applications of these results. The first one deals with sub-Riemannian geometry on nilpotent Hilbertian Lie groups for which we can define a sub-Riemannian distance. The second one deals with heat equation for which we analyse the necessary conditions to give the optimal controls.     

Influence of the counterion size on swelling and collapse of polyelectrolyte gel

A theory that predicts the effect of the counterion size on the swelling and collapse of a weakly charged polyelectrolyte gel was developed. In addition to excluded-volume interactions between monomer units of the gel, the theory involves the counterion-monomer unit and counterion-counterion interactions in terms of the virial approximation. The character of interactions between different units in the system varies from repulsion to attraction depending on the type of solvent, counterion, and dielectric permittivity of the solvent. For solvents with a low permittivity, the effect of condensation of counterions resulting in the formation of ion pairs is taken into account.     

The Pontryagin Maximum Principle 50 years later

Proceedings of the Steklov Institute of Mathematics -     

Energy transfer from a flat uranium slab to a fine wire via fission fragments

Energy transfer from a flat fissile uranium slab to a fine wire via fission fragments is calculated. The rate of energy transfer versus the thicknesses of the slab and protecting aluminum film, as well as the wire-slab gap, is found. An expression for the absorption coefficient of the wire is derived, and the effect the thickness of the wire has on the energy transfer process is studied. The amount of the edge effect for a finite-size fissioner slab is demonstrated with calculations for vacuum conditions and for argon under a pressure of 0.25 atm.