Local instability and localization of attractors. From stochastic generator to Chua's systems

This paper discusses the connection between various instability definitions (namely, Lyapunov instability, Poincaré or orbital instability, Zhukovskij instability) and chaotic movements. It is demonstrated that the notion of Zhukovskij instability is the most adequate for describing chaotic movements. In order to investigate this instability, a new type of linearization is offered and the connection between that and the theorems of Borg, Hartman-Olech, and Leonov is established. By means of new linearization, analytical conditions of the existence of strange attractors for impulse stochastic generators are obtained. The assumption is expressed that an analogous analytical tool may be elaborated for continuous dynamical systems describing Chua's circuits. The paper makes a first step in this direction and establishes a frequency criterion of the existence of positive invariant sets with positive Lebesgue measure for piecewise linear systems, which are unstable in every region of phase space where they are linear.     

Pyroelectric effect in lead-magnoniobate-based solid solutions

A coordinated study of the dielectric, electrostriction, and pyroelectric properties of the lead-magnoniobate-based ceramic solid solutions 0.9PbMg_1/3Nb_2/3O₃-0.1PbTiO₃ and 0.55PbMg_1/3Nb_2/3O₃-0.45PbSc_1/2Nb_1/2O₃ conducted at the relaxor transition temperatures is reported. Electromechanical coupling stimulated by the giant electrostriction effect is shown to play an essential part in the pyroelectric effect.     

Molecule without electrons: binding bare nuclei with strong laser fields

We show how a carefully chosen combination of strong linearly and circularly polarized laser fields can bind two same-sign charges, not only suppressing their Coulomb repulsion in all three spatial dimensions, but also creating an effective attraction. As an example, we show how a molecule HD2+ stripped of both electrons can be kept bound by the laser fields.     

Use of electron correlation to make attosecond measurements without attosecond pulses

We describe how correlations between electrons can be used to trace the dynamics of correlated two-electron ionization with attosecond precision, without using attosecond pulses. The approach is illustrated using the example of Auger or Coster-Kronig decay triggered by photoionization with an extreme ultraviolet pulse. It requires correlated measurements of angle-resolved energy spectra of both the photo- and Auger electrons in the presence of a laser pulse. To reconstruct the dynamics, we use not only classical time and energy correlation, but also entanglement between the two electrons.     

Dielectric properties of solid solutions PbMg1/3Nb2/3O3-SrTiO3

Ceramic samples of the solid solutions PbMg_1/3Nb_2/3O₃-SrTiO₃ are synthesized. The dielectric properties are studied and a phase diagram is constructed. The results obtained are discussed in terms of ideas concerning relaxor ferroelectrics for solid solutions on the PMN side and from the standpoint of potential ferroelectrics on the SrTiO₃ side. The introduction of SrTiO₃ into PMN gradually degrades relaxor properties, and the introduction of PMN into SrTiO₃ does not result in initiation of the ferroelectric phase transition, possibly because of the appearance of random fields in the lattice. The possibility of practical applications of the synthesized system is also discussed. Fiz. Tverd. Tela (St. Petersburg) 41, 1091–1095 (June 1999)     

Stability and Oscillations of Solutions of Integro-Differential Equations of Pendulum—like Systems

A system of nonlinear differential equations of the type on a domain of ?ⁿ is studied. Functional relations between the f_j's, j = 1, …, n, and other necessary conditions are deduced when at each point of the domain the system has a manifold of local solutions. A structure theorem, that makes possible to reduce the problems of the system, e.g. the global solvability of it, to the corresponding questions for a connection of the type ?_z?w = g(z, w) in a fibre bundle over a Riemann surface is proved, and through this reduction we obtain theorems of identity, extension, global factorization, and so on, for the solutions of the system. As an example, a system of nonlinear differential equations of the type is studied and its global solutions are constructed.     

Electrochemical Hydrogenation of α-Arylvinylphosphonic Acids on Platinum and Palladium Modified with Adatoms

A general characteristic of cathodic reduction of -phenylvinylphosphonic acid and its methyl- and chloro-parasubstituted derivatives on Pt/Pt, Pd/Pt, and Pd/Pt modified with Cd and Cu adatoms, is given. At effective pressures of about 10³–10⁴ Pa the processes occur at high rates and at some potentials are limited by the reactant diffusion from the bulk solution. In the presence of Cd and Cu adatoms two reduction waves (presumably, single-electron) may be isolated, i.e. the hampering by adatoms is more pronounced for a second successive stage of the process. At low effective hydrogen pressures the hydrogenation rate is higher on Pd electrodes, which possess a larger sorption capacity. Potential intervals where the reduction of substituted reactants may be complicated by destruction, are found. It is shown that -phenylvinylphosphonic acid undergoes a complete reduction with a current efficiency of 100% in both hydrochloric- and sulfuric-acid solutions. Conditions where the reduction of -(4-chlorophenyl)vinylphosphonic acid proceeds largely without destruction are found. Prospects for use of electrochemical reduction as a preparative method of a selective production of -arylethylphosphonic acids are considered.