A linear problem in diffusion in a region with a mobile boundary

The speed V(t) of the boundary is an arbitrary, continuous, and bounded function of time t. A mathematical model is derived, and a general method of solution based on thermal potentials is given. The particular case of V constant is considered. The solution is obtained as a sum of thermal potentials with unknown densities, which is reduced to a system of integral equations, which are solved by operational methods. The expression for the density of the potentials is obtained in a form suitable for further use.I am indebted to Professor G. M. Bartenev for direction and to Professor V. I. Levin and Dr. I. V. Razumovskaya for discussions of the results.     

A diffusion problem in a two-medium system

A solution is obtained to the boundary-value diffusion-equation problem in a system of two anisotropic semiinfinite media, separated by a movable boundary region. The solution is obtained for arbitrary initial values and concentration on the boundary region. Thus, this class of boundary-value problems is completely solved in the given range.     

Self-trapping and splitting of bright vector solitons under inhomogeneous defocusing nonlinearities

We show that bimodal systems with a spatially nonuniform defocusing cubic nonlinearity, whose strength grows toward the periphery, can support stable two-component solitons. For a sufficiently strong cross-phase-modulation interaction, vector solitons with overlapping components become unstable, while stable families of solitons with spatially separated components emerge. Stable complexes with separated components may be built not only of fundamental solitons, but of multipoles, too.     

Disorder-induced soliton transmission in nonlinear photonic lattices

We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range in which the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.     

Stereochemistry of addition of mercury salts to alkynes

Reactions of Hg(OOCR)₂ (R=Et, Prⁿ, Prⁱ, and Buⁿ) with methylphenylacetylene (with the corresponding acids as solvents) give mixtures ofcis- andtrans-adducts. The quantity of thecis-adduct increases with increase in the length of the acyl substituent.syn-Addition also occurs in the acetoxymercuration ofm-chlorophenyl(methyl)acetylene and 1-methoxybut-2-yne; in the latter case, this route predominates. The stereochemistry of the reaction can also depend on the ratio of the reactants. It is proposed that the reaction occurs by several schemes in which these factors manifest themselves in different degrees. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No.8, pp. 1617–1624, August, 1998.     

Surface waves in defocusing thermal media

We predict that the interface of materials with defocusing thermal nonlinearities supports stable fundamental and higher-order surface waves when the opposite edges of the medium are maintained at different temperatures. Such surface waves exist due to the interplay between repulsion from the interface and the defocusing thermal nonlinearity that deflects light beams from the bulk of the medium toward its edges.     

Surface solitons in chirped photonic lattices

We study surface modes at the edge of a semi-infinite chirped photonic lattice in the framework of an effective discrete nonlinear model. We demonstrate that the lattice chirp can change dramatically the conditions for the mode localization near the surface, and we find numerically the families of discrete surface solitons in this case. Such solitons do not require any minimum power to exist provided the chirp parameter exceeds some critical value. We also analyze how the chirp modifies the interaction of a soliton with the lattice edge.     

Ordering of cations in the voids of the anionic framework of the crystal structure of catapleiite

The pseudohexagonal crystal structure of the mineral catapleiite Na_1.5Ca_0.2[ZrSi₃(O,OH)₉] · 2(H₂O,F) from the Zhil’naya Valley in the central part of the Khibiny alkaline massif (Kola Peninsula, Russia) is studied by X-ray diffraction (XCalibur-S diffractometer, R = 0.0346): a = 20.100(4), b = 25.673(5), and c = 14.822(3) Å; space group Fdd2, Z = 32, and ρ_calcd = 2.76 g/cm³. Fluorine atoms substituting part of H₂O molecules in open channels of the crystal structure have been found for the first time in the catapleiite composition by microprobe analysis. The pattern of distribution of Na and Ca atoms over the voids of the mixed anionic framework consisting of Zr-octahedra and three-membered rings of Si-tetrahedra accounts for the pronounced pseudoperiodicity along the a and c axes of the pseudohexagonal unit cell and for the lowering of crystal symmetry to the orthorhombic one. It is shown that part of the hydrogen atoms of water molecules is statistically disordered; their distribution correlates with the pattern of the population of large eight-vertex polyhedra by Na and Ca atoms.     

Stationary one-dimensional dispersive shock waves

We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defects in defocusing media with linear gain and two-photon absorption. We found that, in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from a defect or generating beam, the competition between gain and two-photon absorption in a dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed a certain critical value.