Influence of Initial Conditions on the Postcritical Behavior of a Nonlinear Aeroelastic System

The behavior of a nonlinear, non-Hamiltonian system in the postcritical (flutter) domain is studied with special attention to the influence of initial conditions on the properties of attractors situated at a certain point of the control parameter space. As a prototype system, an elastic panel is considered that is subjected to a combination of supersonic gas flow and quasistatic loading in the middle surface. A two natural modes approximation, resulting in a four-dimensional phase space and several control parameters is considered in detail. For two fixed points in the control parameter space, several plane sections of the four-dimensional space of initial conditions are presented and the asymptotic behavior of the final stationary responses are identified. Amongst the latter there are stable periodic orbits, both symmetric and asymmetric with respect to the origin, as well as chaotic attractors. The mosaic structure of the attraction basins is observed. In particular, it is shown that even for neighboring initial conditions can result in distinctly different nonstationary responses asymptotically approach quite different types of attractors. A number of closely neighboring periodic attractors are observed, separated by Hopf bifurcations. Periodic attractors also are observed under special initial conditions in the domains where chaotic behavior is usually expected.     

Effect of damping on the postcritical behaviour of autonomous non-conservative systems

Postcritical behavior of non-linear autonomous non-conservative systems is studied with special attention to the effects produced by the damping forces non-uniformly distributed among the natural modes (or the degrees of freedom). The objective is to find out, to what degree the well-known destabilization effect of damping primarily observed in linear systems affects the postcritical behaviour of a system if non-linearities are taken into account. As a bench model, an initially planar elastic panel is considered subjected to the supersonic gas flow. However, the qualitative conclusions may be extrapolated upon a wide class of phenomena in non-linear autonomous non-conservative systems such as airfoils and panel flutter, instabilities induced by the jet thrust or jet pressure, etc. The main conclusion confirms the already formulated statement that, from the rigorous viewpoint, all these phenomena are to be treated taking into account the initial complete positive damping, however small. There are no “paradoxes” neither in the linear nor the non-linear statement of a problem under the condition that the concept of stability is used in the proper sense. On the other hand, a strong effect is demonstrated by the ratio of partial damping factors on the postcritical behaviour. In general, the ratio of these factors influences the postcritical behaviour to a higher degree that their absolute magnitudes, at least if the latter are small or moderate.     

Sputtering yields of PMMA films bombarded by keV C60 ions

A quartz crystal microbalance (QCM) has been used to determine total-mass sputtering yields of PMMA films by 1-16 keV C₆₀^+,2+ ion beams. Quantitative sputtering yields for PMMA are presented as mass loss per incident ion Y_m. Mass-lost rate QCM data show that a 13 keV C₆₀ cluster leads to emission equivalent to 800 PMMA molecules per ion. The power law obtained for the increase in sputtering yield with primary ion energy is in good agreement those predicted by “thermal spike” regime and MD models, when crater sizes are used to estimate sputtering.     

Minimal heteroclinic geodesics for the n-torus

This paper gives an extension of earlier work of Morse and of Hedlund on minimal heteroclinic geodesics for to the case of provided that an additional geometrical condition is satisfied. It also gives lower bounds on the number of such geodesics.     

Stability of a thin panel with added elements in a supersonic gas flow

Thin elastic panels subjected to compression in the median plane and to supersonic gas flow are considered. An element is attached to the panel by an elastic spring and linear dashpot. The stability of the initial planar state of the panel is studied as a function of the main control parameters—such as the gas velocity and membrane force—and the parameters of the attached element. The evolution of the stability regions in the control-parameter plane is considered. Special attention is paid to compound bifurcation points and stabilization islets. Institute of Machine Science, Russian Academy of Sciences, Moscow, Russia. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 3–10, December, 1999.     

Complex Formation by Galacturonic Acid with Copper(II) and Neodymium(III) Ions in Water Solution

Complex formation by galacturonic acid with copper(II) ion in water solution is studied by themethods of EPR spectroscopy. At the pH > 3 the EPR signal (g 2.174) confirms the complex formation at theligand carboxylic group. The following complex formation parameters are measured: equilibrium constant'g factor, hyperfine coupling constant, average complex lifetime. From the data of electron spectra invisible region the complex composition and stability constant is defined for copper(II) and neodymium(III).     

Electrochemical Synthesis of Complex Compounds of Transition Elements with Carboxyl- and Carbonyl-containing Ligands

Complex compounds of d- and f-elements with carboxyl- and carbonyl-containing ligands were synthesized by the electrochemical method. The influence exerted by a number of factors on the process course was studied. The dependence of the electrosynthesis parameters on the composition of the forming compounds was established. The composition of these compounds was determined. A new method for anodic synthesis of these compounds was developed.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 6, 2005, pp. 918–923.Original Russian Text Copyright © 2005 by Frolov, Bolotin, Panyshkin.     

Structural studies and T c dependence in La2−x Dy x Ca y Ba2Cu4+y O z type mixed oxide superconductors

A new series of mixed oxide superconductors with the stoichiometric composition La_2−x Dy _x Ca _y Ba₂Cu_4+y O _z (x=0.0 − 0.5, y=2x) has been studied for structural and superconductiong properties. Our earlier studies on La_2−x (Y/Er) _x Ca _y Ba₂Cu_4+y O _z series, show a strong dependence of T _c on hole concentration (p _sh). In the present work, the results of the analysis of the neutron diffraction measurements at room temprerature on x=0.3 and 0.5 samples are reported. It is interesting to know that Ca substitutes for both La and Ba site with concomitant displacement of La onto Ba site. Superconductivity studies show that maximum T _c is obtained for x=0.5, y=1.0 sample (T _c ∼ 75 K), for La_1.5Dy_0.5Ca₁Ba₂Cu₅O _z (La-2125).