Table of contents

We discuss in this paper equations describing processes involving non-linear and higher-order diffusion. We focus on a particular case (u_t = 2λ₂(uu_x)_x + λ₂u_xxxx), which is put into analogy with the KdV equation. A balance of nonlinearity and higher-order diffusion enables the existence of self-similar solutions, describing diffusive shocks. These shocks are continuous solutions with a discontinuous higher-order derivative at the shock front. We argue that they play a role analogous to the soliton solutions in the dispersive case. We also discuss several physical instances where such equations are relevant.

Orientation-free discrete velocity model and diffuse-reflection boundary conditions are adopted together to solve the stationary noble-gas transport problem within a bubble in microdomains. Once the gas inside the bubble is dilute enough, we observe unusual very-high velocity (or pressure) and temperature fields for noble gases (corresponding to rather small Knudsen number: Kn ≤ 0.01, which is defined as the ratio of the mean free path of the noble gas to the bubble diameter) inside the bubble. The transport coefficients, or gas-velocity and gas-temperature fields (depending on Kn) are not uniform inside the bubble and there are sudden drops near the bubble wall. The latter, perhaps, is due to the heat-conducting bubble-wall. These results might give us some insights related to the initial state of the noble gases within the bubble before the on-set of sonoluminescence.

The spectra of gold till bismuth were studied in the 90–135 Å region. Nine most intense lines belonging to the 5s²5p⁶5d–5s²5p⁵5d6s array were identified in Au XI to Bi XV ions. The 5s²5p⁶7p ²P_3/2,1/2 levels in Au XI and the 5s²5p⁶7p ²P_3/2 level in Hg XII were also identified. The observed wavelengths and intensities agree quite well with the Hartree–Fock calculations.

A first small set of W III oscillator strengths has been obtained from combined lifetime and branching fraction measurements. The branching fractions in the wavelength region of 154–334 nm were measured with a Penning discharge and a Fourier transform spectrometer. Three levels have been calibrated on absolute scales with lifetimes measured with the time-resolved laser-induced fluorescence technique. The f-values derived have uncertainties of about 8% at best. A comparison with Cowan-code calculations is given since no other data are available in the literature.

The s-parameterized characteristic function (CF) is given for the output field from a linear amplifier with the superposition of CS's as input field. The s-parameterized quasi-probability distribution function (QDF) for the output field with superposition of CS's as input state is investigated. Various moments are calculated by using the s-parameterized CF for that field. The auto-correlation second-order coherence function is calculated and numerically investigated. The quadratures squeezing for the output field are discussed. Some QDF's of the output fields are plotted as functions of the interaction time. The phase properties of the superposition of CS's are studied and numerically investigated. The s-parameterized phase distribution obtained by integrating the s-parameterized QDF over the radial variable is illustrated.

The exact shape and position of the free surface of a liquid, being at rest in a moving container, is investigated and all possibilities of formation of such a surface are examined in detail. Also the changes of the form of the free surface in terms of the variation of some basic parameters of the problem are studied. The obtained results determine immediately the mass distribution of the liquid in the container.

We consider solitons in a nonlinear optical fiber with a single polarization in a region of parameters where it carries exactly two distinct modes, viz., the fundamental one and the first-order helical mode. From the viewpoint of applications to dense-WDM communication systems, this opens a way to double the number of channels carried by the fiber. Aside from that, experimental observation of helical (spinning) solitons (that can be launched and detected, using helicity-generating phase masks) and collisions between them and with fundamental solitons in (ordinary or hollow) optical fibers is an issue of fundamental interest, especially because it has been very recently found that spatiotemporal spinning solitons in bulk optical media with various nonlinearities are unstable. We introduce a system of coupled nonlinear Schrödinger equations for fundamental and helical modes, computing nonstandard values of the cross-phase-modulation coupling constants in it, and investigate, analytically and numerically, results of "complete" and "incomplete" collisions between solitons carried by the two modes. We conclude that the collision-induced crosstalk is partly attenuated in comparison with the usual WDM system, which sometimes may be crucially important, preventing merger of the colliding solitons into a breather. The interaction between the two modes is found to be additionally strongly suppressed in comparison with that in the WDM system in the case when a dispersion-shifted or dispersion-compensated fiber is used.

Effects of dust on the amplitude modulation of two possible types of kinetic Alfvén waves, modified and dust kinetic Alfvén waves, in a magnetized dusty plasma have been investigated. The appropriate nonlinear dispersion relations of the amplitude modulation predict that the carrier kinetic Alfvén waves are modulationally unstable for long wave-length perturbations. It has been found that the parameter σ plays a significant role on the amplitude modulation of the waves, where σ is the ratio of the equilibrium number densities of the ions and the electrons and is a measure of the charge carried by the dust component. The maximum growth rate of the modulational instability increases with the parameter σ, whereas, the range of the perpendicular component of the modulation wavenumber K_⊥ of the unstable wave remains almost constant for the case of dust kinetic Alfvén waves. On the other hand, the maximum growth rate is almost constant with σ, while the range of K_⊥ of the unstable wave drastically decreases for the case of modified kinetic Alfvén waves.

A theoretical investigation of one dimensional dynamics of nonlinear electrostatic dust ion acoustic waves in a magnetized dusty plasma has been made by reductive perturbation technique. The effects of both the adiabatic and the nonadiabatic dust charge variation are incorporated. The most interesting feature is that the nonlinear evolution equation of the dust ion acoustic wave for nonadiabatic dust charge variation is the Korteweg-de Vries (KdV) Burger equation, whereas for adiabatic dust charge variation, the equation is the KdV equation. A nonadiabaticity generated anomalous dissipative effect causes generation of dust ion acoustic shock waves, a new mechanism for the generation of shock waves. Numerical integration of the KdV Burger equation shows that dust ion acoustic waves admit oscillatory (dispersion dominant) or monotone (dissipation dominant) shock solutions. It is also seen that the magnetic field and the dust charge variations significantly modify the wave amplitude.

A theoretical investigation has been made of low-frequency waves and their instability or damping associated with dust oscillations in a nonuniform strongly coupled dust-electron plasma, by taking into account of the dc electric field, the dust grain charge fluctuation, the equilibrium dust grain charge inhomogeneity, and the strong correlation between the dust particles. It is found here that under certain conditions, the combined effects of the dc electric field and the equilibrium dust grain charge inhomogeneity can drive the dust-acoustic waves unstable. It is also observed that the effect of the strong correlation between the dust particles, which with the combined effects of the dc electric field and the equilibrium dust grain charge inhomogeneity introduces a new low-frequency damped mode, quenches the instability of the dust-acoustic mode.

In the present work, a kinetic analysis on glass-crystal transformation from differential scanning calorimetry (DSC) data under non-isothermal condition is described. A method has been developed for analyzing the evolution with time of the volume fraction crystallized and for calculating the kinetic parameters at non-isothermal reactions in materials involving formation and growth of nuclei. Considering the assumptions of extended volume and random nucleation, a general expression of the fraction crystallized has been obtained, as a function of the temperature in bulk crystallization. The kinetic parameters have been deduced, assuming that the crystal growth rate has an Arrhenius-type temperature dependence, and the nucleation frequency is either constant or negligible. The theoretical procedure described has been applied to the crystallization kinetics of glassy alloy Sb_0.16As_0.29Se_0.55 with and without previous reheating. According to the study carried out, the n-values have been found: 3.1 for the as-quenched glass and 2.1 for the reheated glass. As n decreases with reheating, it is possible to state that the annealing causes the appearance of new nuclei. The phases at which the alloy crystallizes after the thermal process have been identified by x-ray diffraction. The diffractogram of the transformed material suggests the presence of microcrystallites of Sb₂Se₃ and AsSe remaining in a residual amorphous matrix.

The critical behavior of a ferromagnetic spin-1 Ising superlattice is studied using the effective field theory with a probability distribution technique that accounts for the self-spin correlation functions. The critical temperature of the system is calculated as a function of the exchange interactions in each material and the thickness of the constituents in a unit cell. A critical value of the interface exchange interaction above which the interface magnetism appears is found.

Al/p-AgGa_0.25In_0.75Se₂ polycrystalline thin film Schottky barrier diodes have been prepared. The current-voltage, capacitance-voltage and photoresponse have been investigated. Various important physical parameters of these diodes were derived from these measurements.

A thorough search for blueshifts in Quasi Stellar Objects (QSOs) has not yet been made, although possibilities have been suggested. The main reason appears to be the usual practice of identifying observed lines always with search lines in the UV/blue region, and ignoring the red/IR region. We demonstrate that sufficient search lines are available for blueshift measurements in QSOs, and show that within observational errors observed emission lines can be identified with alternative lines at higher wavelengths, that are blueshifted to the observing window. Blueshifts are calculated with the same or higher levels of accuracy as redshifts. Consideration of equivalent widths demonstrates further that blueshift identifications of observed lines are more convincing than redshift identifications.