[en] This paper proposes escape exponent to characterize localization or escape of moving particles, which will determine the diffusion process. So the diffusion process can also be described by the evolution of the distribution density of escape exponent with time. We studied some typical distribution density of escape exponent and discussed their properties, and an interesting phenomenon is that the escape exponent distribution of Brownian particles is δ function in the long time limit. Furthermore, we generate new diffusion process by linear transformation of the escape exponent, and many types of diffusion processes can be obtained by selecting appropriate control parameters. Among the various transformations, only the new diffusion process under the translation transformation correspond to the solution of the distorted diffusion equation. (paper)

[en] The role of prominent Soviet physicist B I Davydov in the development of our understanding of diffusion is briefly reviewed, with emphasis on the ideas he put forward in the 1930s: introducing additional partial derivatives into diffusion equations and extending diffusion concepts to phase space. (from the history of physics)

No abstract available

[en] The equations describing diffusion on a heterogeneous lattice for low concentrations are considered taking into account lattice site blocking. It is shown that lattice site blocking cannot be disregarded in the case of a strongly heterogeneous lattice even for low concentrations. It is established that the equation with a fractional time derivative holds only in a bounded time interval. Anomalous diffusion, which is described by the equation with a fractional time derivative at the initial stage, must be described over long time periods by an ordinary diffusion equation with a concentration-dependent diffusion coefficient

[en] An increasing number of natural phenomena do not fit into the relatively simple description of diffusion developed by Einstein a century ago. As all of us are no doubt aware, this year has been declared 'world year of physics' to celebrate the three remarkable breakthroughs made by Albert Einstein in 1905. However, it is not so well known that Einstein's work on Brownian motion - the random motion of tiny particles first observed and investigated by the botanist Robert Brown in 1827 - has been cited more times in the scientific literature than his more famous papers on special relativity and the quantum nature of light. In a series of publications that included his doctoral thesis, Einstein derived an equation for Brownian motion from microscopic principles - a feat that ultimately enabled Jean Perrin and others to prove the existence of atoms (see 'Einstein's random walk' Physics World January pp19-22). Einstein was not the only person thinking about this type of problem. The 27 July 1905 issue of Nature contained a letter with the title 'The problem of the random walk' by the British statistician Karl Pearson, who was interested in the way that mosquitoes spread malaria, which he showed was described by the well-known diffusion equation. As such, the displacement of a mosquito from its initial position is proportional to the square root of time, and the distribution of the positions of many such 'random walkers' starting from the same origin is Gaussian in form. The random walk has since turned out to be intimately linked to Einstein's work on Brownian motion, and has become a major tool for understanding diffusive processes in nature. (U.K.)

[en] Here we consider an unsteady detonation with diffusion included. This introduces an interaction between the reaction length scales and diffusion length scales. Detailed kinetics introduce multiple length scales as shown though the spatial eigenvalue analysis of hydrogen-oxygen system; the smallest length scale is ∼ 10⁷ m and the largest ∼ 10^-2 m; away from equilibrium, the breadth can be larger. In this paper, we consider a simpler set of model equations, similar to the inviscid reactive compressible fluid equations, but include diffusion (in the form of thermal/energy, momentum, and mass diffusion). We will seek to reveal how the complex dynamics already discovered in one-step systems in the inviscid limit changes with the addition of diffusion.

[en] Highlights: • Localised patterns, isolated spots and sharp fronts emerge in biological models. • These naturally occurring patterns can be linked to subcritical Turing instabilities. • Combining theoretical approaches helps elucidating the different mechanisms involved. • It sheds light on disjointed developmental and ecological phenomena in nature. • Biology favours multistability and hysteresis above supercritical instability. A synthesis is presented of recent work by the authors and others on the formation of localised patterns, isolated spots, or sharp fronts in models of natural processes governed by reaction–diffusion equations. Contrasting with the well-known Turing mechanism of periodic pattern formation, a general picture is presented in one spatial dimension for models on long domains that exhibit sub-critical Turing instabilities. Localised patterns naturally emerge in generalised Schnakenberg models within the pinning region formed by bistability between the patterned state and the background. A further long-wavelength transition creates parameter regimes of isolated spots which can be described by semi-strong asymptotic analysis. In the species-conservation limit, another form of wave pinning leads to sharp fronts. Such fronts can also arise given only one active species and a weak spatial parameter gradient. Several important applications of this theory within natural systems are presented, at different lengthscales: cellular polarity formation in developmental biology, including root-hair formation, leaf pavement cells, keratocyte locomotion; and the transitions between vegetation states on continental scales. Philosophical remarks are offered on the connections between different pattern formation mechanisms and on the benefit of subcritical instabilities in the natural world.

[en] This work is devoted to investigate explicit solutions of the time-fractional diffusion equations with external forces by considering various diffusion coefficients and an absorbent rate. Besides, the 2nth moment related to such an equation is also discussed. Consequently, the diffusion type can be determined from the mean-square displacement. In addition, a rich class of diffusive processes, including normal and anomalous ones, can be obtained

[en] Modern notions in the field of theory and practice of the obtaining of complex diffusion coatings are presented. Rational procedures carbo-chromizing, chromo-nitridation, chromo-boriding and titaniding to obtain the surfaces with special physicochemical properties for the use under complex conditions of exploitaion are presented. The results of metallographical, physical, chemical, mechanical and other methods of investigation of complex coatings are given. Examples of the application of such coatings and modern equipment for their obtaining are described

[en] Description is given of a treatment for porous metallic filters used in isotope separation of UF₆ with a view to improve their mechanical and corrosion resistance. The filters are introducted in presence of a Al base cement into a heat and oxidation resisting receptacle. The closed receptacle is filled up with an inert gas and heated in a furnace between 800 and 1000⁰C during one hour