Elastic backscattering of electrons from surfaces

A Monte Carlo algorithm is proposed for calculating the elastic reflection coefficient, η_E, for elements. The algorithm accounts for the multiple elastic scattering of electrons in solids. The calculated values of η_E compare well with the literature data for elements with atomic number up to 47 and at primary energies above 2 keV. The proposed Monte Carlo method makes it possible to determine the functional relation between η_E and the inelastic mean free path, λ. This relation turned out to be non-linear, arid it deviates from a similar relation based on published earlier single elastic scattering model. The deviation is especially pronounced for elements with medium atomic numbers. The calculated function $\text{η}{}_{\mathrm{<mtext>E</mtext>}}\text{=}\text{f}\text{(λ)}$ offers a convenient method for determining the inelastic mean free path. The values of λ derived in the present work from published experimental values of η_E compare very well with the literature data.     

On the existence of general solutions of the initial-value problem for the nonlinear Boltzmann equation with a cut-off

We consider a Boltzmann gas which fills all of space and is under the influence of a field of conservative external force whose potential is bounded from below.Assuming the intermolecular force has a cut-off, we prove existence and uniqueness for the general solution of the nonlinear Maxwell-Boltzmann equation at least in a finite interval of time. The solution can be constructed by the method of successive approximations in corresponding complete spaces. Definitions of these spaces are connected with an exponential function of the total energy of the molecule.Some indications of future generalizations and investigations are given.     

A Monte Carlo algorithm for solving systems of non-linear equations

A Monte Carlo method for solving systems of non-linear equations is presented and discussed. The method does not require the differentiation of left side functions of the system and provides the solution with arbitrary accuracy, although it may be applied only to systems with not too large a number of equations. Illustrative examples are given.     

Experimental observations of tyre deformation characteristics on heavy mining vehicles under static and quasi-static loading

Due to large sidewall and bead thicknesses, multi-piece rims are necessary for use with large off-the-road (OTR) tyres. This paper presents the testing protocol and observed load/deflection and vertical/sidewall deflection characteristics of three Goodyear OTR tyre assemblies, namely, (1) a radial 29.5R29 (2) a bias-ply 29.5-29, and (3) a bias-ply 26.5-26. Localized tyre deformations and rim displacements were measured using optical displacement transducers and post-processing high-speed camera images using digital image analysis software. A validation analysis illustrated a maximum difference of 4.05% of vertical wheel displacements between the aforementioned methods. Quasi-static tests show the maximum values of vertical rim displacement and lateral tyre deflection are in the range of 72.2–78.9 mm and 23.3–27.1 mm, respectively, for a severe excitation condition. Differences ranging from 0.2% to 21.5% for maximum vertical and lateral tyre deflections were found between static load tests and engineering data provided by the tyre manufacturer. Linear relationships were observed for both vertical wheel displacement and lateral tyre deflection versus load for all tests. This study demonstrates a thorough methodology to study deflection characteristics of heavy duty OTR tyres and the collected data could be very useful in the development of numerical models of wheel and tyre assemblies for mining vehicles.     

Pd electrodeposited from membrane-separated thin layer cell

Polycarbonate (PC) membranes of different porosity (from 50 nm to 400 nm pore size) were used as separators in a thin layer cell for palladium electrodeposition. Atomic force microscopy (AFM) confirmed the formation of Pd layer between the cathode and porous membrane, with subsequent growth inside the pores induced by space limitations of further growth of initial layer. Our estimates confirm that at this stage Pd deposit feels the pronounced mechanical pressure and consider it as a possible reason of specific hydrogen sorption behaviour in the region of β-phase hydride formation. Up to c.a. 1.0 H/Pd atomic ratio is observed for some samples. We consider possible (nano)structural peculiarities responsible for this behaviour.     

Synthesis and structure of novel copper(II) complexes with pyrazole derived ligands and metal–ligand interaction in solution

Two new ligands of the coumarin type have been synthesized and characterized by ¹H, ¹³C NMR, IR and MS. The crystal and molecular structures of ligand 2, determined by the X-ray diffraction method, are presented. With copper(II) these ligands create solid complexes of the type CuLCl₂, where L is 5-(2-hydroxybenzoyl)-3-methyl-1-(2-pyridinyl)pyrazol-4-carboxylic acid methyl ester (2) or 3-methyl-1-(2-pyridinyl)-1H-chromene[4,3-c]pyrazol-4-on (3). The new copper(II) complexes have been characterized by elemental analysis and solid state FT-IR. The protonation constants of ligands 2 and 3 have been determined in 5% v/v 1,4-dioxane–water solution (25 °C). The coordination modes in the complexes with copper(II) are discussed for 2 on the basis of potentiometric and UV–Vis data.     

Polymer composites of nano-sized particles isolated in matrix

The kinetic and mechanism of thermal decay of transition metal acrylates or its cocrystallites are studied. At 200–300°C the rate of thermal decay can be described by first-order rate equations. The thermal transformations of the metal-containing monomers under study involve dehydration, solid-phase polymerization and thermolysis processes. The composition of products of the thermal transformations are studied. The products of the decay are analyzed by optical and electron microscopy as well as by magnetic measurements, IR and mass spectroscopy. The main solid-state products of decomposition are nanometer-sized particles of metal or its oxide and ferrites with a narrow size distribution stabilized by the polymeric matrix. The average particle sizes, L_av, are 6.0–13.0 nm in the case of FeAcr₃ and 6.0 nm for cocrystallites FeCoAcr and Fe₂CoAcr. © 1998 John Wiley & Sons, Ltd.     

Averaging principle and hyperbolic evolution equations

An averaging principle is derived for the abstract nonlinear evolution equation where the almost periodic right hand-side is a continuous perturbation of the time-dependent family of linear operators determining a linear evolution system. It generalizes classical Henry’s results for perturbations of sectorial operators on fractional spaces. It is also proved that the main hypothesis of the nonlinear averaging principle is satisfied for general hyperbolic evolution equations introduced by Kato.