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[en] Ion profiling of analyzer materials to determine the distribution of elements in the depth of the specimen is used widely in various experimental methods, for example Auger electron spectroscopy, mass spectrometry of secondary ions, X-ray electronic spectrometry, etc. Since the ion effect may cause real changes in the distribution of the components as a result of selective sputtering or volume mass transport, and also apparent changes as a result of the development of the microrelief of the sputtered and analysed surface, the problem of definition of this apparatus factors remains the subject of attention of experts using these analytical methods
[en] In most cases the hexagonal packing of fibrous structures or rods extremizes the energy of interaction between strands. If the strands are not straight, then it is still possible to form a perfect hexatic bundle. Conditions under which the perfect hexagonal packing of curved tubular structures may exist are formulated. Particular attention is given to closed or cycled arrangements of the rods like in the DNA toroids and spools. The closure or return constraints of the bundle result in an allowable group of automorphisms of the cross-sectional hexagonal lattice. The structure of this group is explored. Examples of open helical-like and closed toroidal-like bundles are presented. An expression for the elastic energy of a perfectly packed bundle of thin elastic rods is derived. The energy accounts for both the bending and torsional stiffnesses of the rods. It is shown that equilibria of the bundle correspond to solutions of a variational problem formulated for the curve representing the axis of the bundle. The functional involves a function of the squared curvature under the constraints on the total torsion and the length. The Euler-Lagrange equations are obtained in terms of curvature and torsion and due to the existence of the first integrals the problem is reduced to the quadrature. The three-dimensional shape of the bundle may be readily reconstructed by integration of the Ilyukhin-type equations in special cylindrical coordinates. The results are of universal nature and are applicable to various fibrous structures, in particular, to intramolecular liquid crystals formed by DNA condensed in toroids or packed inside the viral capsids
[en] A statistical approach based on Markov chains is proposed for the description of powder-coating wear in slipping friction. A matrix of transition probabilities for Markov-chains corresponding to steady wear is obtained.
[en] We present a theory for equilibria of elastic torus knots made of a single thin, uniform, homogeneous, isotropic, inextensible, unshearable rod of circular cross-section. The theory is formulated as a special case of an elastic theory of geometrically exact braids consisting of two rods winding around each other while remaining at constant distance. We introduce braid strains in terms of which we formulate a second-order variational problem for an action functional that is the sum of the rod elastic energies and constraint terms related to the inextensibility of the rods. The Euler-Lagrange equations for this problem, partly in Euler-Poincare form, yield a compact system of ODEs suitable for numerical solution. By solving an appropriate boundary- value problem for these equations we study knot equilibria as the dimensionless ropelength parameter is varied. We are particularly interested in the approach of the purely geometrical ideal (tightest) limit. For the trefoil knot the tightest shape we could get has a ropelength of 32.85560666, which is remarkably close to the best current estimate. For the pentafoil we find a symmetry-breaking bifurcation