Partition of Euclidean space into polyhedra induced by a small deformation of the densest lattice sphere packing

The number of combinatorially nonequivalent Dirichlet-Voronoi diagrams constructed for the centers of balls in the packing obtained from the densest lattice packing of equal spheres by a small displacement of the spheres is estimated. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 79–84, 2005.     

Convergence of optimal controls in some optimization problems

We consider the behavior of bundles of optimal controls when the initial state of the system goes to some given vector. We investigate three types of optimization problems: problems with fixed process length and a free right endpoint; problems with fixed process length and a fixed right endpoint; time-optimal problems. The article is a review of recent results obtained by the author. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 301–314, 2004.     

Colorings of spaces,and random graphs

This work deals with some problems on the embeddings of finite geometric graphs into the random ones. In particular, we study here applications of the random graph theory to the Nelson-Erdös-Hadwiger problem on coloring spaces.     

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007     

Gas solubility of carbon dioxide in poly(lactic acid) at high pressures: Thermal treatment effect

The sorption of carbon dioxide in glassy Poly(lactic acid) (PLA) films was studied by quartz crystal microbalance (QCM) at high pressures. Two thermal treatments, melted and quenched, were performed in PLA with two different L:D contents, 80:20 and 98:2, films and compared with a third thermal protocol, annealed, and used in a previous work. The results obtained show that for pressures higher than 2 MPa, the carbon dioxide solubility is larger in PLA 80:20 than in PLA 98:2, indicating that the L:D plays a dominant role on this property. The thermal treatments only affect the gas solubility in PLA 98:2. Sorption isotherms at temperatures 303, 313, and 323 K, below the glass transition temperature of the polymer, and pressures up to 5 MPa were measured and analyzed with three different models, the dual‐mode sorption model, the Flory–Huggins equation, and a modified dual‐mode sorption model where the Henry's law term was substituted by the Flory–Huggins equation. This last model performs especially well for CO₂ in PLA 80:20, due to the convex upward curvature of the solubility isotherms for that system. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 616–625, 2007     

On the law of corresponding states for thermodynamic properties of a crystal

To study thermodynamic similarity of the properties of crystalline substances, we propose an approach connected with engaging of the metastable state region. Internal pressure and specific volume on the crystal’s stability boundary at T = 0 K are used as characteristic scales of thermodynamic variables. A semiempirical method of calculation of the stability boundary by the thermodynamic data related to the stable states region of a solid body is described. In the cases of argon and natrium, the stability boundary is calculated for a wide range of temperatures and pressures. Analysis of the properties of neon, argon, krypton, and xenon crystals in these variables indicates that the law of corresponding states holds for these substances.     

Behavior of the intensity of galactic and anomalous cosmic rays in the outer heliosphere and large-scale electric fields

The behavior of the intensity of anomalous and galactic cosmic rays in the outer heliosphere is compared. The previous hypothesis, according to which the lowest energy galactic cosmic rays affected by large-scale electric fields far beyond the termination shock wave of the solar wind may contribute to the behavior of the anomalous component intensity, is analyzed.