Table of contents

The diffusion of particles and conservative, passive tracer density fields in random hydrodynamic flows is considered. The crucial feature of this diffusion in a divergent hydrodynamic flow is the clustering of the conservative, passive tracer density field (in the Euler description) and occasionally of the particles themselves (in the Lagrange description) — a coherent phenomenon which occurs with probability unity and should arise in almost all dynamic scenarios of the process. In the present paper, statistical clustering parameters are described in statistical topography terms. Because of their inertial properties, particles and their concentration field can also cluster in random divergence-free velocity fields, the divergence of the particle velocity field itself being a crucial aspect of such a diffusion. The delta-correlated in time velocity field for fluctuating flow (as, e.g., in the Fokker–Planck diffusion equation for low-inertia particles) is in principle an invalid approximation for the statistical description of particle dynamics, and the diffusion approximation accounting for the finite time correlation radius should instead be used for this purpose.

The large number of available stable isotopes and well developed isotope separation technology have enabled growing crystals of C, LiH, ZnO, CuCl, CuBr, Cu₂O, CdS, α-Sn, Ge, Si, etc. with a controlled isotope composition. Experimental and theoretical studies provide evidence that the isotope effect has an influence on the thermal, elastic, and vibrational properties of crystals. In this paper it is shown that in Ge and C crystals isotope effect causes only weak phonon scattering whereas in LiH the scattering potential changes are so strong that they lead to experimentally observable phonon localization. It is emphasized that a systematic description of isotope effects requires that anharmonicity be taken into account.

Of all the radioactive wastes known in nuclear power industry and engineering, long-lived actinides and fission products from spent nuclear fuel are the most hazardous. One way to reduce their radiation hazard is to resort to nuclear transmutation, which can be performed either in reactors of various types or in accelerator-driven subcritical systems, whose nuclear safety is superior to that of conventional reactors. Fundamentally resolving the problem of the destruction of long-lived radioactive wastes is likely to stimulate progress in the development of the nuclear power industry.

Progress in particle accelerator technology makes it possible to use a proton accelerator to produce energy and to destroy nuclear waste efficiently. The energy amplifier (EA) proposed by Carlo Rubbia and his group is a subcritical fast neutron system driven by a proton accelerator. It is particularly attractive for destroying, through fission, transuranic elements produced by presently operating nuclear reactors. The EA could also efficiently and at minimal cost transform long-lived fission fragments using the concept of adiabatic resonance crossing (ARC), recently tested at CERN with the TARC experiment. The ARC concept can be extended to several other domains of application (production of radioactive isotopes for medicine and industry, neutron research applications, etc.).

Ideas on characteristic behavior of correlation functions underlie all models of turbulent diffusion. This paper sets forth a consistent analysis of these correlation ideas, beginning with Taylor's work of 1921, which pioneered the use of the autocorrelation function, and ending with works on the percolation theory of turbulent diffusion. Despite the fact that specific physical problems are significantly different, the commonality of the theoretical notions involved is emphasized. It is shown how the ideas of 'long-range' correlations and fractality enter into the percolation method. The 'universality' of the percolation approach to the description of turbulent diffusion is discussed at some length.