Estimating the Distance between Two Bodies inside an n-Ball of Unit Volume

Mathematical Notes - The problem of estimating the distance between two bodies of volume e inside an n-dimensional ball U of unit volume as n → ∞ is considered.     

The Crystal Structures of α- and β-F2 Revisited

The crystal structures of α-F₂ and β-F₂ have been reinvestigated using neutron powder diffraction. For the low-temperature phase α-F₂, which is stable below circa 45.6 K, the monoclinic space group C2/c with lattice parameters a=5.4780(12), b=3.2701(7), c=7.2651(17) Å, β=102.088(18)°, V=127.26(5) ų, mS8, Z=4 at 10 K can now be confirmed. The structure model was significantly improved, allowed for the anisotropic refinement of the F atom, and an F−F bond length of 1.404(12) Å was obtained, which is in excellent agreement with spectroscopic data and high-level quantum chemical predictions. The high-temperature phase β-F₂, stable between circa 45.6 K and the melting point of 53.53 K, crystallizes in the cubic primitive space group Pm n with the lattice parameter a=6.5314(15) Å, V=278.62(11) ų, cP16, Z=8, at 48 K. β-F₂ is isotypic to γ-O₂ and δ-N₂. The centres of gravity of the F₂ molecules are arranged like the atoms in the Cr₃Si structure type.     

Critical point in complex plasmas

The occurrence of liquid-vapor phase transition and the possible existence of a critical point in complex plasmas--systems that consist of charged micrograins in a neutralizing plasma background--is investigated theoretically. An analysis based on the consideration of the intergrain interaction potential suggests that under certain conditions systems near and at the critical point should be observable. Measurements under microgravity conditions would appear to be required. The analysis aims at determining the plasma parameter regime most suitable for planned experimental investigations.     

Shear instability in fluids with a density-dependent viscosity

We present a shear instability, which can be triggered in compressible fluids with density-dependent viscosity at shear rates above critical. The instability mechanism is generic: It is based on density-dependent viscosity, compressibility, as well as flow two-(three-)dimensionality that provides coupling between streamwise and transversal velocity components and density variations. The only factor stabilizing the instability is fluid elasticity. The corresponding eigenvalue problem for a plane Couette flow is solved analytically in the limiting cases of large and small wave numbers.     

Heat transport in a two-dimensional complex (dusty) plasma at melting conditions

The heat transport in a two-dimensional complex (dusty) plasma undergoing a phase transition was studied experimentally. A single layer of highly charged polymer microspheres was suspended in a plasma sheath. A part of this lattice was heated by two counterpropagating focused laser beams that moved rapidly around in the lattice and provided short intense random kicks to the particles. Above a threshold, the lattice locally melted. The spatial profiles of the particle kinetic temperature were analyzed to find a thermal conductivity, which did not depend on temperature.     

Vertical pairing of identical particles suspended in the plasma sheath

It is shown experimentally that vertical pairing of two identical microspheres suspended in the sheath of a radio-frequency (rf) discharge at low gas pressures (a few Pa) appears at a well-defined instability threshold of the rf power. The transition is reversible, but with significant hysteresis on the second stage. A simple model which uses measured microsphere resonance frequencies and takes into account, in addition to the Coulomb interaction between negatively charged microspheres, their interaction with positive-ion-wake charges, seems to explain the instability threshold quite well.     

Paramagnetic shifts in complexes of N-vinylimidazole with manganese,iron, cobalt,nickel, and copper chlorides

The observed paramagnetic shifts and broadenings of the resonance lines in the PMR spectrum of N-vinylimidazole upon the addition of its complexes with manganese, iron, cobalt, nickel, and copper chlorides are compared.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 994–995, July, 1972.We thank Doctor of Chemical Sciences Yu. N. Molin for his assistance in carrying out this investigation.     

Optical constants of substances of atmospheric aerosol

The optical constants of the chemical compounds constituting the atmospheric aerosol were investigated in a wide spectral range. This investigation indicates that higher values of the refractive index than that of water must be used in calculations of the optical characteristics of the aerosol in the IR region. The main absorption bands of the aerosol in the atmospheric windows are determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 91–97, May, 1972.