Table of contents

The invariance group of a class of reaction-diffusion equations, where the diffusion coefficient varies as some power of the population density, is studied. The Lie algebra of the invariance group and the isovector fields which generate the invariance group are established, and then the isovectors are used to derive a "general" invariant group similarity solution which admits the largest number of group parameters. It is also shown that some exact particular analytical solutions previously reported in the literature for special cases of the equation here considered can be rederived from the present solution.

In this paper we examine the time evolution of a squeezed state of the general driven time-dependent oscillator. Our analysis indicate that the wave function of the time-dependent oscillator starts as a squeezed state at t = 0 and remains as a squeezed state at a later time, and that the time evolution is just a "squeezing" process. So the general driven time-dependent oscillator preserves squeezed states for all time.

The main consequences of "hot" scheme for the cumulative effect are considered: the universality of inclusive spectra slope, the dependences of these spectra on the emission angle and the sort of a hadron. The general model of a "hot" source of cumulative particles is given, which sums the contributions of the nuclear density fluctuations and temporal fluctuations of production process development to the cross section of collective interactions of the nucleons. The information gained from the experimental data on the cumulative effect is discussed.

The emission of neutrons from ¹²⁴Sn(α, xn) reactions at E_α = 50 and 75 MeV has been analyzed in terms of a two-source moving source model. A comparision of the parameter values for two different pre-exponential factors in the formula used in the model has been made. It was found that the data at all angles could be successfully parametrized with a common set of parameters, if the pre-exponential factor was made to depend on both the laboratory angle and source velocity.

In this paper we have discussed certain ambiguities which arise in the description of the mass and charge distributions in heavy ion collisions. We have concentrated on two additional mechanisms, beyond the simple nucleon transfer with average relative momentum, required in the random walk formalism to obtain an agreement with the experimental data. We have shown that these two mechansims, Δ-process involving an additional "Fermi momentum" transfer and γ-process involving new non-transfer process for an energy dissipation, are formally interchangable as regards their effect on the total mass width. We have discussed the possible physical mechanisms responsible for these processes and their relationship to transport theories.

The aim of this paper is to show that the 1/n expansion for n-photon processes can be considered as a quasiclassical one. We discuss qualitatively the domain of validity of the leading term of this expansion and show how corrections to it can be accounted for in a systematic and univocal way. Applications to photoionisation processes in strong laser or microwave fields are also discussed.

We have performed a large-scale configuration interaction calculation of the energies and wavefunctions of many low-lying fine-structure states of neutral atomic chlorine. Accurate oscillator strengths for electric-dipole transitions between these states are reported.

Beam-foil delayed spectra from 89.0 to 101.0 nm are used to identify the intercombination lines connecting the 4s4p²⁴P and 4s²4p²P levels in Kr VI. The existing analysis is extended to include the 4s²5s²S_1/2, 4f²F_5/2, ²F_7/2, 4p³²D_3/2, ²D_5/2, ²P_3/2, ⁴S_3/2 and 4s4p²⁴P_1/2, ⁴P_3/2, ⁴P_5/2 levels. Lifetime measurements for the 4s4p²⁴P_1/2, ⁴P_5/2, 4p³²D_3/2 and ²D_5/2 levels are also discussed in support of these assignments.

Collisions between 1.05 MeV/amu Ar^q+ (q = 14, 10, 8 and 4) ions and CH₄ molecules have been investigated using final charge-selected projectile-recoil ion time-of-flight technique. It is found that, in the overall ionization of target CH₄ molecules, pure ionization processes without any change of the projectile charge is by far dominant over any other processes involving electron capture or loss of projectiles. Electron loss or capture processes of projectiles, though weak relative to pure ionization, are found to result in enhancement of the production of multiply charged atomic carbon ions. Another feature, probably not observed earlier, is the fact that in some electron loss and capture processes multiply charged carbon ions become more dominant than any other molecular ions, suggesting that such violent collisions result in nearly complete dissociation of the molecular ions.

The thermal diffusivity of a low conducting solid is measured by means of a capacitive method, providing the thermal expansion of the specimen as a function of time. The simultaneous knowledge of the temperature profile vs. time at the thermal source, in contact with the sample base, allows a rapid, accurate and reliable determination (within ∼ 2%) of thermal diffusivity. No sensor is inserted into the specimen, thus avoiding any perturbation of the temperature field.

A model of nonequilibrium freely localized (not bounded by the walls of the chamber) discharge in the field of a converging axisymmetric wave is investigated. Evolution of the system in time is studied under conditions where the built-up discharge plasma exerts strong influence on the wave field.

It is shown that simple and complex (with several maxima) effectively localized dissipative structures in the distribution of electron concentration can emerge in the system at the developed stage.

An investigation is made of the nonlinear interaction of electrostatic waves at a narrow inhomogeneous layer of a warm magnetoactive plasma. The amplitudes of the radiated second-harmonic waves are calculated. The effect of the external magnetic field is to increase the amplitudes of the generated waves.

The electromagnetic wave dispersion of a waveguide, partially filled with semiconductor plasma is investigated in the case of a finite magnetic field. It is shown, that an optimal filling exists, for which there is a maximum resolution of the low-frequency plasma modes. Some coupling effects are studied. New anisotropic EH-modes are investigated.

The dispersion characteristics of a waveguide filled with magnetoactive semiconductor plasma in the region of complex transverse wave numbers are investigated. A new family of modes with a pseudo-surface space structure is found. Their characteristics are described and their genesis from the slow space-plasma modes in such waveguides is established. The critical parameters of the system are determined which divide the parameter space into regions where the new modes are possible and such where they are forbidden.

Using a two-fluid description of a large, magnetized, self-gravitating plasma cloud, we derive a fully nonlinear system of equations for electrostatic and gravitational potentials. In the regime when nonlinear effects, arising from the particle drift, are dominating over the gravitational condensation, we obtain a stationary solution in the form of travelling double vortex, with the charge separation being localized to the vortex core, and its immediate surroundings. Density perturbation has a long range spatial extend, in the form of alternating condensations and rarefactions with the typical scale length of the order of Jeans' critical length. Influence of higher order effects, and their role in the gravitational contraction of the vortex, is discussed.

We consider the problem of the metastable atomic state life-time in a nonisothermal plasma. A comparison is made of the effectiveness of the binary-collision and collective mechanisms for metastability breakdown. For the latter mechanism, we examine the interaction of an atomic system with the field of ionic waves in the plasma. For hydrogen-like ions, we have determined the range of parameters in which the interaction with the ionic wave field is the most effective. The obtained numerical estimates provide evidence for the possible experimental confirmation of the importance of this mechanism for metastability breakdown.

A class of isodynamic equilibria for an arbitrary toroidal configuration with anisotropic pressure could exist if the divergence of the parallel component of the modified current density vanishes. The solution of the problem of this class of equilibria is reduced to that for a "force-free" problem.

The theoretical analysis of ion Langmuir plasma oscillations in a plasma filled in a cylindrical waveguide has been done using fluid equations. Neglecting electron perturbation, which is permissible for k_⊥²λ_De² ≫ 1, the analysis shows that the propagation of such modes is possible because of the finite radius of the cylindrical waveguide. Further, it is found that in the nonlinear regime, small as well as large amplitude compressive solutions are formed.

We present a theoretical investigation of the lattice dynamics of α-aluminium phosphate (berlinite) which takes only into account short-range interactions and axially symmetric tensor forces between (i) the first nearest-neighbours metal-oxygen or oxygen-oxygen pairs and (ii) the second nearest-neighbours metal-metal pairs. Our calculation accounts satisfactorily for the experimental phonon frequencies deduced from infrared and Raman data and for the corresponding absorption strength of Raman scattering intensities.

A Bose gas of quasiparticles in crystals is described in terms of a two-fluid hydrodynamics based of both the momentum and quasimomentum conservative laws. The full set of hydrodynamic equations is deduced. Under certain conditions the quasiparticle gas possesses superfluid properties. They appear only in the case of a non-quadratic quasiparticle dispersion law. The possibility of a second-sound-type wave propagation is considered, and corresponding dispersion laws are obtained for all interesting limits. The results are expressed by means of the thermodynamic functions of the quasiparticle gas under consideration.

The melting and solidification of copper atom systems of different size was studied using the Monte Carlo simulation method at various temperatures between 25 and 1700°C. Because of the lack of nucleation centres, the system does not melt until at about 1600°C, which is well above the experimental melting point 1083°C. After a sudden drop of temperature down to 25°C, the system of 108 atoms relaxes into a glassy state. When the simulation run is continued, there is a well defined transition into a partially ordered state. In the liquid state, the calculated pair correlation functions are almost identical for systems of 108 and 1372 atoms, including the behaviour of their tails. The relaxation kinetics was studied by preparing a highly inhomogenous system with a crystal-liquid interface. It is the characteristic of the MC simulation that relaxation in such a system is to a great degree biased in favour of the disordered part.

On the basis of a new method of treatment of angular correlation of annihilation radiation data there have been calculated the numbers N_NF of nearly free- and N – N_NF of d-localized-electrons as well as the positive ion core radii r_c and interstitial electron densities n_int for Pd_1−xAg_x, Pd_1−xCu_x and Ni_1−xCu_x alloys. The linear character of changes of N – N_NF and n_int with x reject the applicability of the rigid band model while the n_int linearity confirms the electron redistribution model expectations. The values of the differences in r_c and n_int for pure metals are suggested to be the main reason for the different type of electronic structure of these alloys.

The problem addressed concerns surface Green function matching for continuous media, i.e., in terms of differential calculus. This involves simultaneous differential equations. When the coefficients are position-dependent, as in a pseudopotential model, a transfer matrix algorithm proves very useful to evaluate numerically the intervening Green functions and derivatives thereof. The flexibility of the method is demonstrated by applying it to the study of surface and image states in f.c.c. metals with varying degrees of complexity in the model employed to describe the crystallinity of the surface.

Macroscopic quantum phenomena and superconducting glass state have been observed simultaneously in a random system of linked Josephson junctions in lumps of suitable high temperature superconducting ceramics Y-Ba-Cu-O. This multiply connected Josephson medium was used for radio-frequency SQUID operation at temperatures up to 90 K. The effect of nonergodic glass state on SQUID behaviour readily was observed. The presence of a wide range of relaxation times in glass state leads to an appreciable noise of 1/f type in the SQUID output signal at f ≲ 10³ Hz.

A 2D square lattice with nearest neighbor interactions (V₀) and periodic boundary conditions is used to analyze the quantum localization of eigenstates of a binary mixed crystal in the split-band limit. The lattice sites are randomly occupied either by A molecules with energy E_A = Δ at concentration x or by B molecules with energy E_B = −Δ at concentration 1 − x. Because of the random distribution of the molecules the general Hamiltonian implicitly accounts for both diagonal and off-diagonal disorders. The full diagonalization of the Hamiltonian provides all eigenstates in the energy domains of A and B from which the inverse participation ratios (IPR) and their band averages ⟨L⟩_E are evaluated and configurationally averaged. The two limiting cases Δ ⩾ V₀ and Δ ≅ V₀ are investigated and compared. In the latter case it is shown that the statistical fluctuations are smoothed out relative to that of the infinite split-band. Furthermore, our results show a gradual decrease of the band averages when increasing x and a strong dependence on Δ.

The tunneling-time behaviour for a rectangular barrier, as described by a semiclassical analysis which at the top of the barrier predicts an unphysical divergence, can be sensibly improved taking into account energy losses by a simple phenomenological model. The results are comparable with the experimental data obtained by a microwave simulation.