The impact of approximate VSCF schemes and curvilinear coordinates on the anharmonic vibrational frequencies of formamide and thioformamide

The accuracy of the vibrational self-consistent field (VSCF) method for the computation of anharmonic vibrational frequencies in the infrared (IR) spectrum of formamide and thioformamide is investigated. The importance of triple potentials in the commonly used hierarchical expansion of the potential energy surface (PES) is studied in detail. The PES is expanded in terms of Cartesian as well as internal coordinate normal mode displacements. It is found that triples play an important role when using rectilinear coordinates. A VSCF computation based on rectilinear displacements exhibits serious shortcomings which are only remedied by a large vibrational configuration interaction (VCI) treatment including triple potentials. These limitations are partially removed when using curvilinear coordinates. The merits and disadvantages of either type of displacements for the generation of the PES are discussed.     

Two-end controllability of elastic vibrations of systems with distributed and lumped parameters

Boundary control problems for the vibrations of a system with distributed and lumped parameters are solved. The vibrations of a distributed-parameter object are described by boundary value problems with boundary conditions of various types. A lumped-parameter object is described by a second-order ordinary differential equation.     

Torsional vibrations and dispersion of torsional waves in orthotropic composite rods

The Barr’s refined theory of torsional vibrations of isotropic rods of noncircular cross section is generalized for an orthotropic material. An analysis of natural frequencies of torsional vibration of free-free orthotropic prismatic rods of rectangular cross section is carried out with the help of an exact solution of the frequency equation. For orthotropic CFRP and GFRP rods, the improved theory, which takes into account the normal stresses and inertia forces in the axial direction, in some cases, predicts a noticeable raise in the natural frequencies compared with those following from the Saint-Venant classical theory. A good agreement is obtained between the experimental and calculated values of natural frequencies of torsional vibrations of rectangular quartz and fiber glass rods. The dispersion of torsional waves in an orthotropic quasi-homogeneous rod is considered. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 165–182, March–April, 2008.     

Dynamics of rotating thermoelastic disks with stationary heat source

Rotating disks are important components of car brakes or sawing units. In both cases, heat effects to be induced via stationary local contacts between pads and disk or workpiece and saw blade, respectively, influence the dynamic behavior and raise interesting problems in theory and practice. Therefore, the discussion of dynamic thermoelasticity in rotating disks with stationary heat sources is of basic interest to understand the interaction of temperature and displacement or stress fields in such structural elements. It will be analyzed here in detail for the case of an elastic disk for which there is a full (but weak) coupling of strain and temperature within the two applications mentioned. As a relatively general case, the combined excitation by a mechanical load and a simultaneously acting heat source will be examined.     

Mathematical Problems of Nuclear Configuration Averaging

The concept of the average of a family of related nuclear configurations, for example, the average of those configurations which are slightly distorted versions of a given stable conformer of a molecule, has a role as both interpretative tool and also as a reference configuration in practical, computational use. However, depending on the actual coordinates used along which the average is defined, the average of nuclear configurations is not necessarily a physically viable arrangement, a fact that has to be taken into account when generating the corresponding electron density averages. Some of the associated mathematical and computational problems are described and the validity of a macroscopically motivated approach to conformation averaging is discussed.     

An experimental investigation of dual-resonant and non-resonant responses for vortex-induced vibration of a long slender cylinder

Experimental results of the dual-resonant and non-resonant responses are presented for vortex-induced vibrations(VIV)of a long slender cylinder.The cylinder has a diameter of 10mm and a length of 3.31 m,giving an aspect ratio of 331.The cylinder was towed by a carriage with the velocity up to 1.5 m/s,with the Reynolds number varying from 2500 to 38000.Three different weights were used to provide the initial tension.Dual resonance means that resonance occurs simultaneously in both the cross-flow(CF)and in-line(IL)directions.The experiments were conducted in two stages.At the first stage,dual-resonant dynamic features of the cylinder subjected to vortex-induced excitation were investigated.The features of CF and IL vibration amplitude,motion orbits,phase angle differences,dominant frequencies and mode order numbers are presented.At the second stage of the experiments,particular emphasis was placed on non-resonant dynamic features.The variation of multi-mode modal displacement amplitudes was investigated in detail.     

Dielectric response of metallic crystal made up of highly polarisable molecules: the semi-classical approach

The dielectric response is considered within models of a one-band metal, a two-band insulator and a two-band metal using the semi-classical approximation. Corresponding dielectric functions are found. The dielectric function of two-band metal is found to be the interpolation between the Sellmeyer and Lorenz-Lorentz expressions, respectively. The frequencies of the collective modes are identified as the zeroes of the dielectric functions. The correspondence between the semi-classical approach used in this paper and the many-body calculation within the random-phase approximation is established.      

Terahertz plasmon and surface-plasmon modes in cylindrical metallic nanowires

We present a theoretical study on collective excitation modes associated with plasmon and surface-plasmon oscilla- tions in cylindrical metallic nanowires. Based on a two-subband model, the dynamical dielectric function matrix is derived under the random-phase approximation. An optic-like branch and an acoustic-like branch, which are free of Landau damp- ing, are observed for both plasmon and surface-plasmon modes. Interestingly, for surface-plasmon modes, we find that two branches of the dispersion relation curves converge at a wavevector qz = qrnax beyond which no surface-plasmon mode exists. Moreover, we examine the dependence of these excitation modes on sample parameters such as the radius of the nanowires. It is found that in metallic nanowires realized by state-of-the-art nanotechnology the intra- and inter-subband plasmon and surface-plasmon frequencies are in the terahertz bandwidth. The frequency of the optic-like modes decreases with increasing radius of the nanowires, whereas that of the acoustic-like modes is not sensitive to the variation of the radius. This study is pertinent to the application of metallic nanowires as frequency-tunable terahertz plasmonic devices.     

Spatiotemporal dynamics of Bose-Einstein condensates in moving optical lattices

Spatiotemporal dynamics of Bose-Einstein condensates in moving optical lattices have been studied. For a weak lattice potential, the perturbed correction to the heteroclinic orbit in a repulsive system is constructed. We find the boundedness conditions of the perturbed correction contain the Melnikov chaotic criterion predicting the onset of Smale-horseshoe chaos. The effect of the chemical potential on the spatiotemporal dynamics is numerically investigated. It is revealed that the variance of the chemical potential can lead the systems into chaos. Regulating the intensity of the lattice potential can efficiently suppress the chaos resulting from the variance of the chemical potential. And then the effect of the phenomenological dissipation is considered. Numerical calculation reveals that the chaos in the dissipative system can be suppressed by adjusting the chemical potential and the intensity of the lattice potential.