The relation between the velocity and mass distributions. The role of collisionless relaxation processes

We consider steady-state mass distributions (mass functions) attained at the nonlinear stage of fragmentation as a result of fragment coalescence. The influence of the fragment velocity distribution on the mass function is discussed. The kinetic equations governing the fragments quasiparticles are solved using the group symmetry properties of the collision integral. We have calculated power indices and locations of the breaking points for the mss spectrum (luminosity function) associated with the transition from the collisionless Lynden-Bell type to the Maxwellian distribution, as well as with the predominance of either purely geometric or Newtonian collision cross sections. The power indices found are in a reasonable agreement with the values observed for star or galaxy clusters.     

The synthesis and magnetic properties of nanosized hematite (alpha-Fe2O3) particles

The synthesis of nanosized superparamagnetic hematite particles by dissolving ferric salts in hydrochloric acid and heating at 100 degrees C is described. A hydrolysis reaction causes the formation of hematite particles. The influence of the sequence of additions on the resulting precipitates was studied using TEM and XRD. The magnetic behavior was characterized by magnetization measurements. It was found that small changes in the reaction conditions led to remarkable changes in final size and shape of the hematite crystallites. A well-defined subrounded morphology and an average diameter of 41 nm were obtained for superparamagnetic hematite particles. This is the largest size reported thus far for superpara-magnetic hematite particles.     

An extension of the Rabinowitz bifurcation theorem to Lipschitz potential operators in Hilbert spaces

The main result of the paper is an extension of the bifurcation theorem of Rabinowitz to equations with continuous jointly in and of class . We also prove a bifurcation theorem for critical points of the function which is just continuous and changes at an isolated minimum (in ) to isolated maximum when passes, say, zero. The proofs of the theorems, as well as the the theorems themselves, are new, in certain important aspects, even when applied to smooth functions.

     

Synthesis of new polymeric rhodium carborane complexes serving as homogeneous catalysts for the hydrosilylation of 1-hexene

The coordination of Rh(PPh₃)₃Cl on a dicarbaundecaborate polyamide gives a new polymeric rhodium hydride complex with catalytic activity in the hydrosilylation of 1-hexene by triethylsilane. The rhodium derivative of 7,9-dicarbanido-undecaborate(11)-7,9-dicarboxyanilide was synthesized as a model of the monomeric unit. Co^III and Ni^IV bis(dicarbollyl) complexes also display catalytic activity in hydrosilylation reactions.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 960–962, April, 1991.     

Synthesis of monodisperse high-aspect-ratio colloidal silicon and silica rods

We describe the synthesis and the physical properties of suspensions of colloidal silicon and silica rodlike particles. In addition to pure silicon and pure silica rods, we have also synthesized silicon rods with a silica shell and silica rods with a fluorescent silica layer. Pre-patterned p-type (100) silicon wafers were electrochemically etched in electrolyte solutions containing hydrogen fluoride. By the current density being varied while etching, macropores were etched with controllable modulated pore diameters. These silicon structures were transformed into rods with indentations 5.5 mum apart and with lengths up to 100 mum using iterative oxidation in air and dissolution of the silica by HF. Complete oxidation of these rods was also achieved. Sonication of the modulated rods resulted in monodisperse particles of 5.5 mum length and 300 nm width. A high yield of 10(12) particles, or more, is possible with this method. At high concentrations, these particles show nematic ordering in charge-stabilized suspensions. The oxidized silica outer layer of the silicon rods makes the further growth of silica in solution or on a wafer possible. This allows for control of the particles' interaction potential. Labeling with a fluorescent dye and index matching of the complete silica rods enable the study of concentrated dispersions quantitatively, on a single particle level, with confocal microscopy. Because of their high refractive index in the near-IR, the nematic phases of rods with a silica core are also interesting for photonic applications.