Superposition Of Oscillations Research Articles

The effect of band nonparabolicity on the range function of RKKY interaction

Using an analytical method, we provide the exact derivation of the spatial dependence of the RKKY exchange integral in a system with nonparabolic dispersion. We prove that the RKKY exchange integral shows a sign reversal, being a superposition of oscillations with two different periods. We show that our results describe the magnetic behaviour of semimagnetic semiconductors with planar doping ( δ-doping).

Stability of a model alkali-soluble associative polymer in the presence of a weak and a strong base

Hydrophobically modified alkali-soluble emulsion (HASE) polymer is solubilized by the addition of a base. When the pH is increased to greater than 6.5, methacrylic acids on the polymer backbone are neutralized and the carboxylated latex polymer goes into solution causing a large increase in the viscosity due to inter-molecular associations of the hydrophobes. The stability of the viscosity of the polymer solution at pH in the range 9–10 was studied in the presence of a strong (NaOH) and a weak [1-amino-1-methylpropanol (AMP)] base. No change in the viscosity or the moduli was observed for the polymer in AMP. Reduction in the viscous and elastic properties of the polymer solution in NaOH was observed after 4 weeks. Such small changes are detectable using the superposition of oscillation on the steady shear technique. The decrease in the viscoelastic properties is attributed to the hydrolysis reaction of the urethane groups of the macromonomer, which resulted in a decrease in the number of hydrophobes per polymer chain. It is recommended that a weak base be used to neutralise the HASE polymer in order to avoid the possibility of compositional changes in the polymer after neutralisation for more than 6 weeks.

Superposition of Oscillations on Steady Shear Flow as a Technique for Investigating the Structure of Associative Polymers

The viscoelastic properties over a range of steady shear conditions of an alkali-swellable associative polymer have been determined using the technique of superposition of oscillations upon steady shear flow, thus enabling the structure of the polymer to be investigated. The associative polymer studied consists of a backbone of methacrylic acid and ethyl acrylate to which is attached macromolecules containing C20 hydrophobes via an ethylene oxide−isocyanate linkage. A 1 wt % solution with its pH adjusted to 9.5 was used. At high pHs, the polymer solubilizes to form a network of both intra- and intermolecular associating hydrophobic junctions. The solution shows a non-power-law shear-thinning behavior: the viscosity flow curve, when plotted against shear stress, shows two distinct regions where network rupture is prominent, at stress of 2 Pa and between 40 and 50 Pa. By superimposing small amplitude oscillations on to shear flow at constant stresses, the network structure of the polymer is unperturbed and linear viscoelastic properties of the polymer under the applied stress conditions can be obtained. At an applied stress of 2 Pa and above, both the storage and loss moduli of the polymer are greatly reduced at low frequencies, with the G‘ approaching second-order behavior and η‘ tending toward constant values. By analogy to Maxwell relaxation time, an estimate of the relaxation time of the associative polymer at different stress conditions can be made. The results show that the relaxation time is reduced by up to 4 orders of magnitude as the stress is increased from 1 to 60 Pa, while a much smaller decrease in viscosity is observed. At sufficiently high frequencies, both the storage and loss moduli show an increase above their linear viscoelastic values as the strain amplitude is increased. This behavior is believed to be dependent on the relaxation time of the polymer which is a function of the state of network disruption. Thus the technique may prove to be a powerful tool for probing the structure of network polymer in solution.

Charging effects in quantum dots in a magnetic field

We have studied charging effects in a lateral split-gate quantum dot defined by metal gates in the two dimensional electron gas of a AlGaAs-GaAs heterostructure. Conductance oscillations as a function of magnetic field occur in the integer quantum Hall effect regime. We have observed a superposition of oscillations with two different periods. The larger period is associated with the removal of one electron from the dot. The smaller period is related to the transfer of an electron from the second to the first Landau level (LL). The measurements are interpreted in terms of a simple model which takes into account the charging energy between the LLs in the dot.

Effect of oscillations during extrusion on rheology and mechanical properties of polymers

AbstractAn experimental study associated with the applications of sound and ultrasonic waves to extrusion is conducted. Two laboratory setups are developed for these purposes incorporating orthogonal and parallel superposition of oscillations on pressure flow during extrusion. The orthogonal superposition of sound oscillations is imposed in an annular die. The parallel superposition of ultrasound oscillations is imposed in a circular die. Several materials including unfilled and filled thermoplastics, thermoplastic elastomer, and elastomer are tested. Die characteristics, power consumption, and die swell are determined during extrusion. The rheological properties, molecular weight, tensile properties, and impact strength of materials with and without sound and ultrasound treatment are investigated, indicating permanent changes in these properties. The observed effects are found to depend on melt temperature, flow rate, nature of polymer system, and oscillating parameters such as frequency and deformation amplitude.

Flow of thermoplastics in an annular die under orthogonal oscillations

Extrusion of several thermoplastics has been carried out through an annular die having the internal surface oscillating in the sound frequency range at different amplitudes. Oscillating shear flow has been imposed orthogonal to the main pressure flow. The die characteristics and average melt temperature at the exit from the die have been measured with and without imposition of oscillations. Modelling of orthogonal superposition of oscillations upon pressure flow has been performed by using the Leonov viscoelastic constitutive equation. Three cases are considered: (i) the process is considered to be isothermal and the change of pressure is only due to a nonlinear interaction of oscillatory and pressure flow; (ii) the process is assumed to be nonisothermal and adiabatic and pressure reduction is due to the nonlinear interaction and the dissipation of oscillatory energy leading to a temperature rise in a polymer melt; (iii) the process is considered to be nonisothermal with heat transfer due to transient heat conduction and the dissipation of oscillatory energy. Pressure reduction occurs due to both nonlinear interaction and temperature rise. It is found that case (i) cannot explain the observed die pressure reduction, while case (ii) does only at high flow rates. The predicted results for case (iii) are found to be in fair agreement with experimental data.

Une analyse numérique des possibilités de résonance d'un bassin portuaire de profondeur variable

Creating, enlarging and excavating a harbour can modify the dynamic response of the basin. A verification of the resonance modes is common practice before undertaking the related work. This can be done numerically if the necessary assumptions are justifiable. It can be done on a small-scale model if the basin has an irregular shape or if the depth varies from one area to the other.A computer-programmed analytical method of resonance modes is presented. It is derived from the direct measure principle of successive oscillation superposition used in the laboratory. Validation is obtained by applying the method to existing theoretical solutions and to the analysis of a small creek of the Gaspe Peninsula where the importance of refraction in the analytical results is demonstrated. Key words: harbour, vibration, agitation, ocean waves, diffraction, refraction, numerical model, application. [Journal translation]

Peculiarities in the plastic deformation of crystals subjected to the acoustoplastic effect

A decrease in the stress of unidirectional plastic deformation during the superposition of oscillations was observed at high ultrasonic frequencies. In a recently published paper, this effect was experimentally studied at low frequencies (about 1 Hz). Such low frequencies allowed the process kinetics to be studied in a sufficiently detailed manner. However, no satisfactory explanation was given for the effects observed. In the present study a model is proposed which describes the process of plastic deformation of a crystal in the field of alternating stresses; this model correlates fairly well with the experimental results obtained both at low frequencies and at higher frequencies.

Time-dependent correlations for a one-component plasma in a uniform magnetic field

Abstract We derive various sum rules for the time-displaced structure function of a classical one-component plasma subjected to an external uniform magnetic field. When the plasma has some translational invariance (i.e., homogeneous or translation-invariant along the field), we find that there are long-wavelength oscillations with well-defined frequencies. The results are obtained from linear response and macroscopic electrodynamics, as well as from the microscopic equations of motion (BBGKY hierarchy). In the presence of the magnetic field, the time-displaced structure function has a polynomial decay at large distances, even in the homogeneous case. When the plasma has no translational invariance, examples show a more complicated temporal behaviour in the long-length-scale limit, involving a superposition of oscillations over a continuous range of frequencies.

SPATIAL LOCKING OF LASER MODES

It is shown that coherent wave fields in the form of a locked superposition of oscillations of degenerate transverse modes can be established in a laser resonator. This approach can be used to reduce the number of frequencies emitted by the laser and to improve the angular divergence of the output radiation.

On surface seismic waves formation

The interpretation of surface seismic waves records is rather complicated as they include a superposition of oscillations of the fundamental mode and higher modes. Besides recorded oscillations depend on spectral characteristics of motions in earthquakes sources. The consideration of these problems is based on results of surface waves two-dimensional modelling [1]3. Some physical ideas about their formation deals with the change of the nature of the oscillation propagating with dispersion. This report represents a condensate of several independent works.

Analysis of the Shubnikov—de Haas Effect in Bismuth

The Shubnikov---de Haas effect has been measured in single crystals of high-purity bismuth. Some of the observed oscillations have periods similar to those found by Lerner and attributed by him to heavy-holes and electrons. Some of these periods are shown to be the result of superposition of oscillations due to different parts of the Fermi surface of the two-carrier model of Smith, Baraff, and Rowell, and the others to be the result of frequency modulation due to oscillations in the Fermi energy.

A quantum theory of refractive index, Čerenkov radiation and the energy loss of a fast charged particle

A quantum theory of the three related subjects of refractive index, Čerenkov radiation, and the excitation and ionization of atoms in a polarisable medium is developed. The classical theory of the electromagnetic field in a medium of extended dipoles is first written in hamiltonian form. This makes obvious a canonical transformation related to refractive index which enables one to express the total field in the medium as a superposition of oscillators. A similar transformation is made on the quantised radiation field variables, which takes account of the modified time dependence of the field due to its interaction with the medium. The processes of Čerenkov radiation and the ionization and excitation of atoms in a polarisable medium are then treated. The partition of the total energy loss between these different primary processes is obtained directly. This is done by making a perturbation expansion on the basis of physical-photon states for processes caused by the passage of a fast charged particle through the medium. For the case in which the reaction of the medium on the particle is neglected we obtain formulae which agree with those obtained previously by other authors i.e., in the first approximation the quantum theory frequently gives the same result as the classical theory for these processes.