Table of contents

We investigate the primary resonance of an externally excited nonlinear system under state feedback control with a time delay. Using an appropriate perturbation method, we obtain two slow flow equations on the amplitude and phase. Their fixed points correspond to limit cycles for the nonlinear system and we determine excitation amplitude-response and frequency-response curves. Using energy considerations, we investigate the slow flow equations and demonstrate the existence of limit cycles, which correspond to a two-period quasi-periodic modulated motion for the starting system. Vibration control, high-amplitude response limitation and suppression of the two-period quasi-periodic motion can be performed with appropriate time delay and feedback gains. Analytical results are verified with numerical simulations.

From the equilibrium condition δS = 0 applied to an isolated thermodynamic system of electrically charged particles and the fundamental equation of thermodynamics (dU = TdS - (f · dr)) subject to a new procedure, it is obtained the Lorentz's force together with non-inertial terms of mechanical nature. Other well known ponderomotive forces, like the Stern–Gerlach's force and a force term related to the Einstein–de Haas's effect are also obtained. In addition, a new force term appears, possibly related to a change in weight when a system of charged particles is accelerated.

We study the Heisenberg quantization for systems of identical particles in noncommutative spaces. We get fermions and bosons as special cases of our argument, in the same way as commutative case and therefore we conclude that the Pauli exclusion principle remains valid in noncommutative spaces, which is in agreement with the result presented in Chaichian et al, Phys. Lett. B 568 146 (2003).

A D-dimensional Schrödinger equation with a Coulomb plus inverse-square potential is carried out. The relationship between the energy E(n,l,D) and the dimension D is analyzed in great detail. It is shown that the E(n,0,D) first decreases for D ∊ (0,2] and then increases for D ≥ 2. The energy E(n,l,D) is almost independent of the quantum number l for large D, but the quantum number l plays some role in the energy E(n,l,D) when the dimension D is not too large.

The exact general solution of the Schrödinger equation for the time-dependent linear potential (TLP) is obtained in momentum representation. The wave functions in coordinate representation are derived from that in momentum representation by the Fourier transform. Meanwhile, the dynamical and geometrical phases for the unbounded states of TLP are calculated.

Most mechanical systems or structures are subject to parametric or self excitations. In the present work, simultaneous principal parametric resonance of two-degree-of-freedom systems with quadratic and cubic non-linearities subject to multi-frequency parametric excitations in the presence of two-to-one internal resonance is investigated. Two approximate methods are applied to construct a set of first order, non-linear ordinary differential equations governing the modulation of the amplitudes and phases of oscillations. The applied methods are; the method of multiple time scale perturbation and the generalized synchronization methods. Steady state solutions and their stability are studied for selected values of the different parameters. The obtained results from both methods are in excellent agreement.

Two forms of diffusion equation are discussed: (1) the conventional Fick's law with concentration-independent diffusion coefficient and (2) the flux as proportional to the chemical potential gradient with the proportional constant independent of concentration (which is, in most cases, equivalent to the application of Fick's law with a diffusion coefficient inversely proportional to concentration). It is shown that appropriate empirical form of the resistant forces could validate both forms thermodynamically. It is concluded that the ideal form of diffusion equation is absent. It is also shown that the second form of the flux equation might describe the self-diffusion flux better.

Einstein and Smoluchowski's treatment of the Brownian motion has been discussed. It is shown that although the diffusion equations derived from both treatments are mathematically identical, Smoluchowski's equation defines a somewhat concentration-dependent diffusion coefficient, while Einstein's equation defines a constant diffusion coefficient. The reliability of the assumption of a Maxwell–Boltzmann displacement distribution in a steady state diffusion process has been discussed and the appropriateness of both the treatments relating the diffusion coefficient and the Brownian motion have been questioned.

The spectrum of ten times ionized xenon, Xe XI, was observed in the region 105–157 Å with a low-inductance vacuum spark and a 10.7 m grazing-incidence spectrograph. About 200 lines belonging to the 4d⁸–(4d⁷5p + 4d⁷4f + 4p⁵4d⁹) transition array were observed. 140 of these lines are in the region 130–140 Å, which is of importance for extreme ultraviolet (EUV) lithography. The spectrum was interpreted by means of Hartree–Fock calculations and orthogonal parameters using scaling factors for the energy parameters obtained by extrapolation along the Rh II isoelectronic sequence. All 9 levels of the 4d⁸ configuration and 123 levels of the 4d⁷5p + 4d⁷4f + 4p⁵4d⁹ configurations were established. Transition probabilities for all observed lines were calculated with fitted values of the energy parameters. A value of 1847200 ± 1600 cm^-1 (229.02 ±0.20 eV) was obtained for the ionization energy.

The angular anisotropy parameters of the Auger decay α₂ and spin polarization parameters β₂ were calculated for Na, Kr, Xe, Ba, and Hg using the multichannel Dirac–Fock method. These calculations were performed using LSJ and relativistic intermediate coupling. The exchange effect was used in all calculations. We showed numerically that orbital relaxation during the Auger decay had only a small effect on the angular distribution for open-shell atoms. The obtained values for α₂ and β₂ were compared with other theoretical results.

Using the semi-classical perturbation approach by Sahal-Bréchot (1969 Astron. Astrophys.1, 91, 2 322; 1974 Astron. Astrophys.35 321; 1991 Astron. Astrophys.245 322) updated by Dimitrjević and Sahal-Bréchot (1984 J. Quant. Spectrosc. Radiat. Transf.31 301; 1995 Physica Scripta52 41) and by Ben Nessib et al. (1996 Physica Scripta54 608) we have calculated Stark broadening widths of several C II, N II and O II spectral lines and input TOPbase (Opacity Project) sophisticated atomic structure data into the Sahal-Bréchot's computer code. Then we have compared our results with those of available experiments and with Griem's (1974) simplified semi-classical data. We show that our theoretical results, the simplified semi-classical calculations and experimental values are in good agreement. We also give new values of Stark broadening widths for several transitions of singly-ionized nitrogen and oxygen.

We investigate the possibility that the mechanism dynamic trapping can play a role in decoupling dense plasma clouds injected in a thinner ambient plasma, by establishing strong magnetic-field-aligned electric fields in the vicinity or in the edge of the cloud. Dynamic trapping has previously been shown to allow such fields to be established and maintained on the time scale of ion motion, also for arbitrarily low current densities. A model is presented of how such fields could arise and decouple injected plasma clouds, a mechanism which we call dynamic decoupling. A dimensionless parameter, the dynamic decoupling factor FDD, is derived which gives an estimate of the importance of the process. One possible application is the CRRES ionospheric injection experiments where anomalous skidding has recently been reported. However, the dynamic decoupling mechanism might also play a role in naturally occurring situations, e.g. the impulsive penetration of plasmoids from the solar wind into the Earth's magnetosphere.

A theoretical investigation is carried out for understanding the properties of obliquely propagating monotonic double layers in a magneto-plasma. By using Sagdeev's pseudopotential method, we have found an obliquely propagating double layer solution and a relation between the amplitude, the inverse scale length and the obliqueness effects. Furthermore, we show that the monotonic double layers are nonlinear extensions of the solitary holes having negative trapping parameter in magnetized plasma.

Wind tunnel experiments show that plasma generated by on-board discharges can significantly weaken the shock wave generated in front of a 30° half-angle truncated-cone model placed in a Mach 2.5 flow. Experimental results indicate that, in order to give rise significant effect on shock waves, plasma has to be generated in the region upstream of the baseline shock front and has to have a symmetrical spatial distribution with respect to the axis of the model. Experimental results also exclude the thermal effect as a possible cause of the observed shock wave mitigation. A physical mechanism of the observed nonthermal plasma effect on shock waves is presented. Analysis shows that a symmetrically distributed plasma spike in front of the shock can effectively deflect the incoming flow symmetrically. The required electron density of the plasma spike is estimated.

It is shown that the collective nonlinear interactions between intense neutrino or anti-neutrino fluxes and a dense neutrino plasma are governed by a multi-dimensional coupled cubic Schrödinger equation in which the interaction potential is positive or negative depending on the neutrino type. The cubic Schrödinger equation describes the splitting and focusing of intense neutrino beams due to the nonlinear excitations associated with the modifications of the individual neutrino energies in a dense neutrino background.

Nonthermal and anisotropic screening effects on elastic electron-ion collision processes in kappa-Maxwellian distribution plasmas are investigated using the first-order eikonal method. The electron-ion interaction potential in kappa-Maxwellian distribution plasmas has been obtained by the introduction of the longitudinal plasma dielectric function (ε_κM). In the first-order eikonal analysis, it is found that the dynamic screening effect on the eikonal phase becomes the static screening effect. The nonthermal screening effects on the elastic scattering cross sections are found to be more significant for smaller spectral indices.

The 2D boundary layer code TECXY has been used to study the evolution of the so-called Marfes, thermal instabilities which arise locally in a zone near the high-field side of the TEXTOR tokamak boundary layer, as a result of strong plasma cooling by the interaction with the deuterons recycled at the bumper limiter, and by the subsequent highly increased radiation which is limited by the heat transport along the magnetic field and radially from the core. The bumper limiter is introduced into the scrape-off layer in a region between -45° and +45° below and above the high-field side, leaving a width of about 2 cm between the bumper surface and the last closed flux surface. We model the bumper region by assuming high additional recombination losses inside this region and a suitably chosen profile for the recycled neutrals penetrating from the bumper surface into the adjacent plasma. A parameter study has been carried out which shows that for sufficiently high particle influx into the plasma edge layer and/or sufficiently low energy influx a stability boundary is crossed and the Marfe develops during about 1 msec. The stability boundary between the Marfe and the no-Marfe region is not sharp because bifurcated solutions are possible which depend on the history (initial conditions) of the plasma. Critical values (taken at the separatrix and the low-field side) which always produce Marfes are densities n_e ≳ 8 × 10¹⁸/m³ or temperatures (T_e+T_i)/2 ≲ 50 eV. Within the Marfe n_e increases up to about 10²⁰/m³ and T_e, T_i decrease down to about 4 eV. The effect of drifts as found by TECXY is a shift of the Marfe position towards the upper bumper edge and a weakening of the Marfe strength, but the stability boundary is not affected. The influence of additional radiation losses by carbon impurities is also investigated.

Tellurite glasses containing CuO with the nominal composition (CuO)_x(TeO₂)_1−x, where x = 0.1, 0.2, 0.3, 0.4 and 0.5, have been prepared and investigated by x-ray photoelectron spectroscopy (XPS). The core level binding energies of Cu 2p, Te 3d, and O 1s in these glasses have been measured. The appearance of a satellite peak in the Cu 2p spectra provides definitive evidence for the presence of Cu²⁺ ions in these glass samples where the asymmetry and broadening of the peaks are indicative of the presence of both Cu²⁺ and Cu⁺ ions. The broadened Cu 2p_3/2 peaks were decomposed into two distinct peaks separated by approximately 2.0 eV, with the lower energy peak being associated with Cu⁺ and the higher energy peak with Cu²⁺. The relative Cu²⁺ content determined from the relative areas under these peaks and the satellite peak is found to be 44% for x = 0.5 glass sample while it is more than 70% for the remaining samples.

The O 1s spectra for all glasses show slight asymmetry and were, therefore, fitted with two contributions, one from bridging oxygen (BO) and the other from non-bridging oxygen (NBO). The BO signal is due to the presence of oxygen atoms in the environment Te–O–Te while the NBO is due to oxygen atom in the environment Te–O–Cu. The ratio BO/Total oxygen was evaluated for each glass sample and was found to be in good agreement with the theoretical values. The Te 3d core level spectra show symmetry for all glass samples indicating that the chemical environment of Te atoms does not vary much with the concentration of copper.

The lowest values of effective segregation coefficients K_eff of impurities in tellurium are the main parameters required to obtain an optimal purification ( ≥ 6N). A series of (13 × 4) values of K_eff were determined at the same starting concentration C₀ and velocity of interface v. Four different temperatures of the molten zone were used. The effect of some of these values was investigated for the first time. The influence of temperature in zone refining was analyzed through the relation of ln K_eff versus 1/T. Experimental study showed two kinds of impurities. The first one was easily removed despite the variation of T while the other was strongly affected by T and trapped in the molten zone. The activation energies of 13 impurities in tellurium were also determined. The values of K_eff seems to be acceptable about 773°K. For the molten zone, we proposed an adequate temperature range which was about 50°K higher than the melting temperature of tellurium. This was necessary to achieve an electronic grade purification of tellurium with a good efficiency by zone melting process.

Undoped InSe and Gd doped InSe (InSe:Gd) single crystals were grown by using the stockbarger method. Ingots had no cracks and voids on the surface. There was no process to polish and clean treatments at cleavage faces of these samples because of the natural mirror-like cleavage faces. Absorption measurements were carried out in InSe and InSe:Gd samples in the temperature range 10–320 K with a step of 10 K. The first exciton energies for n = 1 were calculated as 1.323, 1.239 eV in InSe and were 1.317, 1.235 eV in InSe:Gd at 10 K and 300 K, and the second exciton energies for n = 2 in InSe were calculated as 1.338, 1.328 eV and in InSe:Gd were 1.331, 1.321 eV at 10 K and 80 K, respectively. Binding energies of InSe and InSe:Gd were calculated as 20.0 and 18.0 meV, respectively. The direct band gaps are estimated as 1.343, 1.259 eV in InSe and 1.335, 1.253 eV in InSe:Gd at 10 and 300 K, respectively. The steepness parameters and Urbach energy for InSe and InSe:Gd samples increased with increasing sample temperature in the range 10–320 K.

The electromagnetic wave theory is employed to study a magnetic impurity layer in a ferromagnetic/non-magnetic superlattice. Using "transfer matrix" formalism we find that, in addition to bulk magnetic polaritons modes, there may be localized modes associated with the impurity layer. The dispersion relation for localized magnetic polaritons is derived theoretically in long-wavelength limit. The considerations are restricted to the case of in-plain magnetization and to wave propagation in the Voigt geometry. The dispersion curves for different magnetic impurities are calculated numerically and then discussed.