Statistics of reduced words in locally free and braid groups: Abstract studies and application to ballistic growth model

We study numerically and analytically the average length of reduced (primitive) words in so-called locally free and braid groups. We consider the situations when the letters in the initial words are drawn either without or with correlations. In the latter case we show that the average length of the reduced word can be increased or lowered depending on the type of correlation. The ideas developed are used for analytical computation of the average number of peaks of the surface appearing in some specific ballistic growth modelComment: 29 pages, LaTeX, 7 separated Postscript figures (available on request), submitted to J. Phys. (A): Math. Ge

First principles quasiparticle damping rates in bulk lead

First principles calculations of the damping rates (inverse inelastic lifetimes) of low energy quasiparticles in bulk Pb are presented. Damping rates are obtained both for excited electrons and holes with energies up to 8 eV on a set of k vectors throughout the Brillouin zone (BZ). Strong localization effects in the calculated lifetimes are found. Averaged over the BZ inelastic lifetimes versus quasiparticle energy are reported as well. In addition, the effect of the spin-orbit induced splitting in the band structure on the calculated lifetimes in Pb is investigated.Comment: 10 pages, 8 figures, 5 table

The effect of fluorine-containing inhibitors of corrosion of copper in atmospheric conditions

The effect of fluorine-containing inhibitors of corrosion of copper in atmospheric conditions was studied by method of removing anodic polarization curves and corrosion of full-scale tests. The introduction of the inhibiting compositions as corrosion inhibitor of copper polyfluorinated amines leads to a decrease of the peak current of active dissolution of copper, which increases the corrosion resistance of copper wire rod during transportation in various climate conditions

Random Hierarchical Matrices: Spectral Properties and Relation to Polymers on Disordered Trees

We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization. Using the explicit expression for eigenvalues of such matrices, we compute the spectral density for the Gaussian distribution of matrix elements. We also compute the averaged "survival probability" (SP) having sense of the probability to find a system in the initial state by time $t$. Using the similarity between the averaged SP for locally constant randomized Parisi matrices and the partition function of directed polymers on disordered trees, we show that for times $t>t_{\rm cr}$ (where $t_{\rm cr}$ is some critical time) a "lacunary" structure of the ultrametric space occurs with the probability $1-{\rm const}/t$. This means that the escape from some bounded areas of the ultrametric space of states is locked and the kinetics is confined in these areas for infinitely long time.Comment: 7 pages, 2 figures (the paper is essentially reworked

Multiple electron-hole scattering effect on quasiparticle properties in a homogeneous electron gas

We present a detailed study of a contribution of the T matrix accounting for multiple scattering between an electron and a hole to the quasiparticle self-energy. This contribution is considered as an additional term to the GW self-energy. The study is based on a variational solution of the T-matrix integral equation within a local approximation. A key quantity of such a solution, the local electron-hole interaction, is obtained at the small four-momentum transfer limit. Performed by making use of this limit form, extensive calculations of quasiparticle properties in the homogeneous electron gas over a broad range of electron densities are reported. We carry out an analysis of how the T-matrix contribution affects the quasiparticle damping rate, the quasiparticle energy, the renormalization constant, and the effective mass enhancement. We find that in comparison with the GW approximation the inclusion of the T matrix leads to an essential increase of the damping rate, a slight reduction of the GW band narrowing, a decrease of the renormalization constant at the Fermi wave vector, and some "weighting" of quasiparticles at the Fermi surface.Comment: 12 pages, 11 figures, 1 tabl

Field-driven tracer diffusion through curved bottlenecks: Fine structure of first passage events

Using scaling arguments and extensive numerical simulations, we study dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall boundary. A tracer particle is affected by an external force pointing along the channel, and performs an unbiased diffusion in the perpendicular direction. We present a detailed analysis a) of the distribution function of the height above the funnel's boundary at which the first crossing of a given bottleneck takes place, and b) of the distribution function of the first passage time to such an event. Our analysis reveals several new features of the dynamical behaviour which are overlooked in the studies based on the Fick-Jacobs approach. In particular, trajectories passing through a funnel concentrate predominantly on its boundary, which makes first-crossing events very sensitive to the presence of binding sites and a microscopic roughness.Comment: 9 pages, 8 figure

Formation of a single innovation space in the agrarian sector of the EAEU Member States

The relevance of the study is determined by the need to form a single innovative space in the agricultural sector of the EAEU Member States in order to make rational use of the aggregate scientific potential of the countries of the Union. Models of interstate cooperation in the scientific and technical sphere were developed and a “panel of indicators” for the development of the market for scientific and technical products was proposed. Practical recommendations on the transfer of innovations in the agricultural sector of the economy of the EAEU member states are given.peer-reviewe