Electron-TO-phonon interaction in polar crystals

In the present work, the interaction between electrons and long-wavelength transverse optical (TO) vibrations in a polar insulator is considered. The crystal model employed for the theoretical analysis includes classical potentials and electronic polarizabilities. A significant enhancement of the strength of the electron-TO-phonon interaction in ferroelectrics has been found. A microscopic justification of this effect is given. A bridge that relates the interaction of electrons with the polar long-wavelength TO modes of lattice vibrations to the long-range dipole-dipole interaction is established. As an application of our analysis, a novel method for quantitative predictions of the electron-TO-phonon interaction constants in polar crystals via the data of experimental studies is suggested.     

Harmonic Force Field and Mean Amplitudes for Gallium Tribromide and Triiodide Dimers

Harmonic force fields are developed for the Ga₂Br₆ and Ga₂I₆ molecules. The analysis confirms previous assignments of experimental frequencies. Mean amplitudes of vibration are calculated.     

A refined integro-surface energy-based model for vibration of magnetically actuated double-nanowire-systems carrying electric current

A novel surface energy-based model is developed to examine more precisely vibrations of current-carrying double-nanowire-systems immersed in a longitudinal magnetic field. Using Biot-Savart and Lorentz laws, a more refined version of interwire interactional magnetic forces is presented. By employing Rayleigh beam theory, the equations of motion are derived. In fact, these are coupled integro-differential equations which are more accurate with respect to those of the previously developed models. For simply supported and clamped nanosystems, governing equations are analyzed via assumed mode method. The effects of interwire distance, slenderness ratio, electric current, magnetic field strength, and surface effect on the fundamental frequency are addressed carefully. The obtained results display the importance of exploiting the refined model for vibration analysis of nanosystems with low interwire distance, high electric current, and high magnetic field strength.     

Effects of several lanthanide trichloride hydrates on the melting behavior and spherulitic superstructure of poly(ethylene oxide)

Binary mixtures of poly(ethylene oxide) (PEO) with the trichloride hydrates of lanthanum, cerium, europium, terbium, and ytterbium have been studied with calorimetry, polarized optical microscopy, and infrared spectroscopy. Melting‐point depression of the PEO‐rich phase occurs in all cases. At sufficiently high concentrations of the low molecular weight lanthanide complex, crystallization of the polymer is absent. The lighter lanthanides with larger ionic radii, such as lanthanum and cerium, are more effective in suppressing PEO crystallization from solution or the molten state because they are more oxophilic. The spherulitic superstructure of PEO disappears at rather low concentrations of the lanthanide salts, between 2 and 8 mol % Ln³⁺. Lanthanum and terbium are most efficient at disrupting the formation of PEO spherulites, and europium is least efficient. Infrared spectroscopy identifies twisting and wagging vibrational absorptions of CH₂ groups in the polymer that are sensitive to the morphologies of these mixtures. Modifications of the PEO infrared absorbances in the presence of these five lanthanide salts correlate more closely with the presence or absence of major PEO melting, not the formation of a spherulitic superstructure. The phase behavior is rather simple, with no evidence of eutectic solidification upon cooling from the molten state. Multiple melting endotherms are observed in the differential scanning calorimetry heating traces of binary mixtures containing 8 mol % Yb³⁺ and between 10 and 20 mol % Eu³⁺, but the concentration dependence of these first‐order endothermic transitions is not characteristic of eutectic phase behavior. The presence of trivalent cations, such as Eu³⁺ or Yb³⁺, in these complexes perturbs the crystallization kinetics of PEO upon cooling from the molten state, as well as the melting behavior upon heating. Ion–dipole or electrostatic interactions between the lanthanide cation and the ether oxygen of PEO might alter the surface free energy at the periphery of the crystalline lamellae and perturb the chain‐folding characteristics of PEO. Consequently, coupling between the amorphous matrix and the PEO crystallites is strengthened, and this provides stability for the existence of multiple‐chain‐folded crystals composed of rather thin lamellae that could be responsible for multiple melting behavior. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2200–2213, 2003     

Response probability density functions of strongly non-linear systems by the path integration method

The paper discusses challenges in numerical analysis and numerical/analytical results for strongly non-linear systems—systems with “signum”-type non-linearities. Such non-linearities are implemented for instantaneous variations of the systems’ parameters, to reduce their mean energy response when subjected to random excitations. Numerical results for displacement and velocity response probability density functions (PDFs), energy response PDFs and various order moments are obtained by the path integration technique. Attention is also given to evaluation of mean upcrossing rate, related to the system's half period, via Rice's formula informally applied to discontinuous response PDFs.     

Proton induced thermal stress-wave measurements using a Laser Doppler Vibrometer

Thermal stress-waves are generated in the solid target material when the proton beam interacts. These stress waves excite natural oscillations of the target or cause plastic deformations. Hence, an experimental setup with a laser Doppler vibrometer [CITE] was developed to investigate free surface vibrations of cylindrical targets. The target configurations for RIB and conventional neutrino beams (CNGS project) were investigated to analyze proton induced thermal stress-wave generation and propagation.     

Forced flexural-and-torsional vibrations of a cantilever beam of constant cross section

The paper addresses the forced flexural-and-torsional vibrations of a cantilever beam of constant cross section. The relevant boundary-value problem is solved. The system of two partial differential equations of the fourth order that describes these vibrations is analyzed in a vector-function space and is subjected to an equivalent transformation to obtain one vector equation of the fourth order with two matrices as coefficients. One is an idempotent matrix; the other is a diagonal matrix. This makes it much easier to construct a Cauchy vector function as an analytic function of these matrices __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 102–114, August 2007.     

Vibrations of a piezoceramic cylinder subject to nonstationary electric excitation

The paper proposes a method to solve the problem of vibrations of a radially polarized piezoelectric cylinder subject to nonstationary electric excitation. The dynamic electromechanical state of the cylinder is analyzed. The time-dependences of electric and mechanical characteristics are plotted. The distribution of these characteristics over the cross section of a short cylinder is examined. The region of end disturbances in a long cylinder is identified __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 73–79, March 2007.     

On the accumulation of eigenvalues of operator pencils connected with the problem of vibrations in a viscoelastic rod

In this paper, we study the problem of the boundary accumulation of a discrete spectrum, which is essential for a boundary-value problem of fourth order arising in the theory of small transverse vibrations in an inhomogeneous viscoelastic rod (a Kelvin—Voigt body). We establish conditions for such an accumulation and its asymptotics, which are expressed in terms of the coefficients defining the problem posed by the differential expression. The results obtained are illustrated by numerical computation data.