Nonlinear modes of parametric vibrations and their applications to beams dynamics

An iterative loop combining nonlinear modes and the Rauscher method is suggested for analyzing finite degree-of-freedom nonlinear mechanical systems with parametric excitation. This method is applied to an analysis of the parametric vibration of beams.     

Structure and electronic properties of hollow‐caged C60 fullerene‐derived (MN4)nC6(10 − n) (M = Zn,Mg, Fe,n = 1−6) complexes

Unique hollow‐caged (MN₄)_nC_{6(10 ? n)} (M = Zn, Mg, Fe, n = 1?6) complexes designed by introduction of n porphyrinoid fragments in C₆₀ fullerene structure were proposed and the atomic and electronic structures were calculated using LC‐DFT MPWB95 and M06 potentials and 6‐311G(d)/6‐31G(d) basis sets. The complexes were optimized using various symmetric configurations from the highest O_h to the lowest C₁ point groups in different spin states from S = 0 (singlet) to S = 7 (quindectet) for M = Fe to define energetically preferable atomic and electronic structures. Several metastable complexes were determined and the key role of the metal ions in stabilization of the atomic structure of the complexes was revealed. For Fe₆N₂₄C₂₄, the minimum energy was reported for C_2h, D_2h, and D_4h symmetry of pentet state S = 2, so the complex can be regarded as unique molecular magnet. It was found that the metal partial density of states determine the nature of HOMO and LUMO levels making the clusters promising catalysts. © 2014 Wiley Periodicals, Inc.     

Nonlinear modes of cylindrical panels with complex boundaries. <Emphasis Type="Italic">R</Emphasis>-function method

Nonlinear vibrations of cylindrical panels with complex base are analyzed. The Donnell-Mushtari-Vlasov equations with respect to displacements are used to study vibrations of shallow shell with geometrical nonlinearity. R-function method is applied to satisfy the panel boundary conditions. The Rayleigh-Ritz method is used to obtain the linear vibrations eigenmodes, which contain R-function. The nonlinear vibrations of panel are expanded by using these eigenmodes. The harmonic balance method and nonlinear normal modes are used to study the free nonlinear vibrations.     

Parametric vibrations of cylindrical shells subject to geometrically nonlinear deformation: multimode models

The nonlinear parametric vibrations of cylindrical shell are described by the Donnell–Mushtari–Vlasov equations. The motions are represented as a mode expansion. Discretization is performed using the Bubnov–Galerkin method. The describing-function method is used to study traveling waves and nonlinear normal modes in systems with and without dissipation     

The electrochemical behavior of commercial clarithromycin and spectroscopic detection of its structural changes

The aim of the present study was to examine the behavior of commercial clarithromycin, Clathrocyn®, comparing to the results previously obtained using pure clarithromycin under the same experimental conditions. The study was performed by cyclic linear sweep voltammetry and the bulk of electrolyte was analyzed by FTIR spectroscopy and HPLC. At gold electrode, in the range of ?1.2 V to 1.0 V vs. SCE in 0.05 M NaHCO₃, the electrochemical determination of pure clarithromycin was previously defined by four anodic and one cathodic reproductive peaks, and commercial clarithromycin is defined by reproductive one anodic peak which appears from 0.60 to 0.80 V vs. SCE. Previously, FTIR analysis of the bulk electrolyte showed the apparent changes in pure clarithromycin molecule structure: in the ester bond of the lactone and in ethers and acetal bonds. FTIR analysis of the bulk electrolyte also showed changes in the molecule structure in commercial-tablets form of clarithromycin: indicating disappearance of lactone structure and changes of carbonyl group at position 9.     

The role of stress on initial stages of crystal growth

Crystallization in undercooled melts is accompanied by development of stress energy, due to the difference in volume of the new system as compared to the ambient phase. Therefore, the growth rate decreases with time. Here, the non-stationary differential equation is solved, accounting for the production of energy of stress deformation as well as for its reduction caused by relaxation. In this way the growth rate and the dependence of crystal size on time are obtained. The change of the growth rate is significant when new formed phase has composition different from the ambient phase, so that particles, creating the new phase can move much faster the main molecules of the matrix. A steady state is determined by the condition that the rate of stress energy production is equal the rate of stress energy consumption. The degree to which the stationary growth rate U_st is reduced as compared to the initial growth rate U_max is controlled mainly by the ratio of the self-diffusion coefficient of the building units to the diffusion coefficient of the building units creating the new phase. A clear break in the size versus time dependence of the growing crystal is seen.     

External electric field effect on electronic properties and charge transfer in CoI2/NiI2 spinterface

Electronic structure and spin-related properties of CoI₂/NiI₂ heterostructure were studied by means of density functional theory. It was shown that the electronic structure at the Fermi level can be characterized by a band gap. The effect of the external electric field on charge transfer and electronic properties of the CoI₂/NiI₂ interface was investigated, and it was found that band gap width depends on the strength of the applied electric field, switching its nature from semiconducting to a half-metallic one. An easy control of the electronic properties and promising spin-polarized nature of the CoI₂/NiI₂ spinterface allows the heterostructure to be used in spin-related applications.     

Interaction of low-energy ions and atoms of light elements with a fluorinated carbon molecular lattice

The mechanism of interaction of low-energy atoms and ions of light elements (H, H+, He, Li, the kinetic energy of the particles 2-40 eV) with C6H6, C6F12, C60, and C60F48 molecules was studied by ab initio MD simulations and quantum-chemical calculations. It was shown that starting from 6 A from the carbon skeleton for the "C6H6 + proton" and "C60 + proton" systems, the electronic charge transfer from the aromatic molecule to H+ occurs with a probability close to 1. The process transforms the H+ to a hydrogen atom and the neutral C6H6 and C60 molecules to cation radicals. The mechanism of interaction of low-energy protons with C6F12 and C60F48 molecules has a substantially different character and can be considered qualitatively as the interaction between a neutral molecule and a point charge. The Coulomb perturbation of the system arising from the interaction of the uncompensated proton charge with the Mulliken charges of fluorine atoms results in an inversion of the energies of the electronic states localized on the proton and on the C6F12 and C60F48 molecules and makes the electronic charge transfer energetically unfavorable. On the different levels of theory, the barriers of the proton penetration for the C6F12 and C60F48 molecules are from two to four times lower than those for the corresponding parent systems (C6H6 and C60). The penetration barriers of the He atom and Li+ ion depend mainly on the effective radii of the bombarding particles. The theoretical penetration and escaped barriers for the "Li+ + C60" process qualitatively explain the experimental conditions of synthesis of the Li@C60 complex.     

Separation of strontium from calcium by the use of sodium hydroxide and its application for the determination of long-term background activity concentrations of <Superscript>90</Superscript>Sr in 100 km area around Kozloduy Nuclear Power Plant (Bulgaria)

The method for the determination of ⁹⁰Sr which employs sodium hydroxide for the separation of strontium from calcium was further improved introducing the use of elevated temperatures. The results from 11-year study of background activity concentrations of ⁹⁰Sr in different environmental objects in 100 km zone around Kozloduy Nuclear Power Plant (Bulgaria) are presented as an application of the analytical method. The measured mean values are as follows: air precipitation − 0.0015±0.0009 Bq(m^2.d), tap water − 0.0017±0.0012 Bq/L, soil − 1.90±1.26 Bq/kg, grass − 1.54±0.80 Bq/kg, milk − 0.023±0.012 Bq/L and for the Danube river: water − 0.0046±0.0026 Bq/L, bottom sediments − 0.64±0.60 Bq/kg, algae − 1.99±1.56 Bq/kg. The calculated transfer coefficients (soil-grass) are in the range of 0.33–0.84. Between 2 and 5 times reduction in actual background activities of ⁹⁰Sr is observed compared to 1972–1974.     

Redox freezing temperature and Bartenev equation in a 25Na2O-15B2O3-60SiO2 glass doped with chromium and manganese

In a melt with the base mol% composition 25Na₂O-15B₂O₃-60SiO₂, doped with chromium and manganese, a redox reaction takes place during cooling the melt. This reaction was studied using high temperature UV-vis spectroscopy. Above 600 °C, the reaction is in equilibrium and shifted during cooling to the Cr³⁺ and Mn³⁺ species. At temperatures between 500 and 600 °C, the kinetics of the redox reaction is decisive and the cooling rate plays an important part. At temperatures < 500 °C, the reaction is frozen in. The smaller the cooling rate, the smaller is the Cr⁶⁺ concentration and the lower is the fictive redox temperature.The kinetics of the reaction was described by a differential equation assuming Arrhenian behaviour. The equation was numerically solved and fictive temperatures were calculated. These temperatures depended on cooling rate similar to Bartenev equation. Activation energies calculated hereof were around 38 kJ?mol⁻¹ larger than those inserted into the kinetic equation. The experimentally determined activation energy is 565 kJ?mol⁻¹, a value much larger than the activation energies of diffusion of the polyvalent elements. The rate determining step in the case of the Cr³⁺/Cr⁶⁺/Mn²⁺/Mn³⁺ system is the electron transfer reaction, because a notable structural rearrangement is necessary during the course of the electron transfer reaction (Cr³⁺ and Cr⁶⁺ occur in octahedral and tetrahedral coordination, respectively). The latter leads to a large inner reorganisation energy and to an activation energy similar to that of the viscous flow. In the case of the redox reaction between copper and arsenic, the activation energy is much smaller (210 kJ?mol⁻¹), because here the coordination numbers do not change during the course of the redox reaction.