Spatially self-similar locally rotationally symmetric perfect fluid models

Einstein's field equations for spatially self-similar locally rotationally symmetric perfect fluid models are investigated. The field equations are rewritten as a first order system of autonomous ordinary differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system of differential equations is reduced as far as possible. The system is subsequently analyzed qualitatively for some of the models. The nature of the singularities occurring in the models is discussed.Comment: 27 pages, pictures available at ftp://vanosf.physto.se/pub/figures/ssslrs.tar.g

Charged-Surface Instability Development in Liquid Helium; Exact Solutions

The nonlinear dynamics of charged-surface instability development was investigated for liquid helium far above the critical point. It is found that, if the surface charge completely screens the field above the surface, the equations of three-dimensional (3D) potential motion of a fluid are reduced to the well-known equations describing the 3D Laplacian growth process. The integrability of these equations in 2D geometry allows the analytic description of the free-surface evolution up to the formation of cuspidal singularities at the surface.Comment: latex, 5 pages, no figure

Classical artificial two-dimensional atoms: the Thomson model

The ring configurations for classical two-dimensional atoms are calculated within the Thomson model and compared with the results from `exact' numerical simulations. The influence of the functional form of the confinement potential and the repulsive interaction potential between the particles on the configurations is investigated. We also give exact results on those eigenmodes of the system whose frequency does not depend on the number of particles in the system.Comment: 9 pages, RevTeX, 4 figure

Stability of multi-electron bubbles in liquid helium

The stability of multi-electron bubbles in liquid helium is investigated theoretically. We find that multi-electron bubbles are unstable against fission whenever the pressure is positive. It is shown that for moving bubbles the Bernoulli effect can result in a range of pressures over which the bubbles are stable.Comment: 7 pages, 5 figure

Low-Temperature Mobility of Surface Electrons and Ripplon-Phonon Interaction in Liquid Helium

The low-temperature dc mobility of the two-dimensional electron system localized above the surface of superfluid helium is determined by the slowest stage of the longitudinal momentum transfer to the bulk liquid, namely, by the interaction of surface and volume excitations of liquid helium, which rapidly decreases with temperature. Thus, the temperature dependence of the low-frequency mobility is \mu_{dc} = 8.4x10^{-11}n_e T^{-20/3} cm^4 K^{20/3}/(V s), where n_e is the surface electron density. The relation T^{20/3}E_\perp^{-3} << 2x10^{-7} between the pressing electric field (in kV/cm) and temperature (in K) and the value \omega < 10^8 T^5 K^{-5}s^{-1} of the driving-field frequency have been obtained, at which the above effect can be observed. In particular, E_\perp = 1 kV/cm corresponds to T < 70 mK and \omega/2\pi < 30 Hz.Comment: 4 pages, 1 figur

Electron Clusters in Inert Gases

The paper addresses counterintuitive behavior of electrons injected into dense cryogenic media with negative scattering length $a_0$. Instead of expected polaronic effect (formation of density enhancement clusters) which should substantially reduce the electron mobility, an opposite picture is observed: with increasing $|a_0|$ (the trend taking place for inert gases with the growth of atomic number) and the medium density, the electrons remain practically free. An explanation of this behaviour is provided based on consistent accounting for the non-linearity of electron interaction with the gaseous medium in the gas atom number density

Giant Magnetoresistance Oscillations Induced by Microwave Radiation and a Zero-Resistance State in a 2D Electron System with a Moderate Mobility

The effect of a microwave field in the frequency range from 54 to 140 $\mathrm{GHz}$ on the magnetotransport in a GaAs quantum well with AlAs/GaAs superlattice barriers and with an electron mobility no higher than $10^6$ $\mathrm{cm^2/Vs}$ is investigated. In the given two-dimensional system under the effect of microwave radiation, giant resistance oscillations are observed with their positions in magnetic field being determined by the ratio of the radiation frequency to the cyclotron frequency. Earlier, such oscillations had only been observed in GaAs/AlGaAs heterostructures with much higher mobilities. When the samples under study are irradiated with a 140-$\mathrm{GHz}$ microwave field, the resistance corresponding to the main oscillation minimum, which occurs near the cyclotron resonance, appears to be close to zero. The results of the study suggest that a mobility value lower than $10^6$ $\mathrm{cm^2/Vs}$ does not prevent the formation of zero-resistance states in magnetic field in a two-dimensional system under the effect of microwave radiation.Comment: 4 pages, 2 figur