Melting of ultrathin lubricant film due to dissipative heating of friction surfaces

Melting of an ultrathin lubricant film during friction between atomically smooth surfaces is studied. Additive noise of shear stress and strain as well as of film temperature is introduced and the phase diagram is constructed. On the diagram, the noise intensity for this temperature and the temperature of friction surfaces determine the regions of sliding, dry, and stick-slip friction. As a result of numerical analysis of the Langevin equation for various regions of the diagram, time series of stresses are constructed, which make it possible to explain the experiment on friction, in which intermittent motion is observed. Lubricant melting due to dissipative heating of friction surface is considered and the experimental time dependences of friction force are interpreted.     

Isomorphous substitutions of rare earth elements for calcium in synthetic hydroxyapatites

Polycrystalline hydroxyapatites Ca(10-x)REE(x)(PO(4))(6)(OH)(2-x)O(x) were synthesized and studied by X-ray powder diffraction, infrared absorption, diffuse-reflectance spectroscopy, and thermogravimetry. The solubility limits x(max) of rare earth elements (REE) in Ca hydroxyapatites decreases with an increasing REE atomic number from x(max) = 2.00 for La, Pr, and Nd to x(max) = 0.20 for Yb at 1100 °C. Refinements of X-ray diffraction patterns by the Rietveld method show that REE atoms substitute for Ca preferentially at the Ca(2) sites of the apatite structure. The substitution decreases the Ca(2)-O(4) atomic distances in the calcium coordination polyhedra and increases the Ca(2)-O(1,2,3) distances. This observation shows that interatomic distances depend not only on radii of the ions involved in the substitution but also on their charges.     

Tribological system in the boundary friction mode under a periodic external action

A mechanical analog of a tribological system in the boundary friction mode is studied. A thermodynamic model is used to analyze the first-order phase transition between liquidlike and solidlike structures of a lubricant. The time dependences of the friction force, the relative velocity of the interacting surfaces, and the elastic component of the shear stresses appearing in the lubricant are obtained. It is shown that, in the liquidlike state, the shear modulus of the lubricant and the elastic stresses become zero. The intermittent (stick-slip) friction mode detected experimentally is described. It is shown that, as the lubricant temperature increases, the frequency of phase transitions between the lubricant structural states decreases and the total friction force and elastic stress amplitudes lower. When the temperature or the elastic strain exceeds the corresponding critical value, the lubricant melts and a kinetic slip mode in which the elastic component of the friction force is zero takes place.     

Photodynamic laser therapy and diagnostics of tumor localization on the basis of new types of photosensitizers

Characteristics of photophysical and photochemical processes in molecules of new symmetric indotricarbocyanine dyes in solutions and biostructures are studied. Correlations between the efficiency of these processes and the specific features of the dye molecule structure, as well as the influence of the physical and chemical parameters of the medium and exciting radiation on these processes are established.     

On the stability of the spectral Galerkin approximation

We study stability properties of the spectral Galerkin approximation of the solutions of semilinear problems. Assuming that the data of the problem are known within a certain error, we investigate when the solution of the Galerkin approximate equation provides a desired accuracy uniformly with respect to small perturbations of the data. We show that for certain classes of semilinear problems an additional compactness assumption is sufficient to assure that the spectral Galerkin method provides an accurate approximation to the exact solution uniformly with respect to small perturbations of the data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Spectroscopic and electronic structure studies of a dimethyl sulfoxide reductase catalytic intermediate: implications for electron- and atom-transfer reactivity

The electronic structure of a genuine paramagnetic des-oxo Mo(V) catalytic intermediate in the reaction of dimethyl sulfoxide reductase (DMSOR) with (CH(3))(3)NO has been probed by electron paramagnetic resonance (EPR), electronic absorption, and magnetic circular dichroism (MCD) spectroscopies. EPR spectroscopy reveals rhombic g- and A-tensors that indicate a low-symmetry geometry for this intermediate and a singly occupied molecular orbital that is dominantly metal centered. The excited-state spectroscopic data were interpreted in the context of electronic structure calculations, and this has resulted in a full assignment of the observed MCD and electronic absorption bands, a detailed understanding of the metal-ligand bonding scheme, and an evaluation of the Mo(V) coordination geometry and Mo(V)-S(dithiolene) covalency as it pertains to the stability of the intermediate and electron-transfer regeneration. Finally, the relationship between des-oxo Mo(V) and des-oxo Mo(IV) geometric and electronic structures is discussed relative to the reaction coordinate in members of the DMSOR enzyme family.     

Three-dimensional structure of laccase from Coriolus zonatus at 2.6 Å resolution

Laccase (oxygen oxidoreductase, EC 1.14.18.1) belongs to the copper-containing oxidases. This enzyme catalyzes reduction of molecular oxygen by different organic and inorganic compounds to water without the formation of hydrogen peroxide. The three-dimensional structure of native laccase from Coriolus zonatus was solved and refined at 2.6 Å resolution (R _factor = 21.23%, R _free = 23.82%, rms deviations for the bond lengths and bond angles are 0.008 Å and 1.19°, respectively). The primary structure of the polypeptide chain and the architecture of the active site were refined. The carbohydrate component of the enzyme was identified. The access and exit water channels providing the access of molecular oxygen to the active site and release of water, which is the reduction product of molecular oxygen, from the protein molecule were found in the structure.     

Models for optimal harvest with convex function of growth rate of a population

Two models for growth of a population, which are described by a Cauchy problem for an ordinary differential equation with right-hand side depending on the population size and time, are investigated. The first model is time-discrete, i.e., the moments of harvest are fixed and discrete. The second model is time-continuous, i.e., a crop is harvested continuously in time. For autonomous systems, the second model is a particular case of the variational model for optimal control with constraints investigated in [1]. However, the prerequisites and the method of investigation are somewhat different, for they are based on Lemma1 presented below. In this paper, the existence and uniqueness theorem for the solution of the discrete and continuous problems of optimal harvest is proved, and the corresponding algorithms are presented. The results obtained are illustrated by a model for growth of the light-requiring green alge Chlorella. Bibliography: 6 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 75–86.