On the dynamics of a particle on a cone

A detailed study of the classical and quantum mechanics of a free particle on a double cone and a particle bound to its tip by a harmonic oscillator potential is presented.     

On the dynamics of a particle on a hyperboloid

A free particle moving on a one-sheeted hyperboloid is discussed both at the classical and quantum levels.     

Appearance of a knee on the Fowler-Nordheim plot of carbon nanotubes on a substrate

Existing theories for electron-field emission of carbon nanotubes (CNTs) cannot interpret why there appears in certain cases a knee on some Fowler-Nordheim (F-N) plots while not on others. We consider the interaction between substrate and CNTs and introduce a double-barrier model to explain the knee on the F-N plot. The knee on the F-N plot is a consequence of the transition from direct tunneling to F-N tunneling. The absence of the knee for the CNT films on titanium is attributed to the removal of the interface barrier by the formation of a conductive titanium carbide interlayer. The double-barrier model is helpful in understanding the field emission mechanism of CNTs and can explain the experimental results regardless whether or not there is a knee on F-N plot.     

Effect of a Magnetic Field on the Phase Transitions in the Heisenberg Model on a Triangular Lattice

Physics of the Solid State - The phase transitions, magnetic and thermodynamic properties of a three-dimensional antiferromagnetic Heisenberg model on a layered triangular lattice in a magnetic...     

Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis

A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted L _p space is obtained, i.e., the existence of an index n for which the Kolmogorov n-diameter is finite. For the case in which a continuous embedding exists, the reduced Sobolev class is constructed together with a continuous operator of a natural embedding of the class in a weighted L _p -space.     

Influence of the Porosity of the Surface of a Graphite Furnace on the Atomization of a Sample

The influence of the wear of a tube graphite furnace and the morphological features of its surface on the formation of an atomic-absorption signal has been investigated. Electron-microscopic and mass-spectrometric investigations have shown that, prior to atomization, copper in the form of elementary metal microparticles is found not only on the surface of the furnace but also in the bulk of its pores. Free atoms are formed as a result of the concurrent processes of atomization of a sample on the surface of the furnace and in the bulk of its pores. The change in the apparent energy of formation of free atoms of metals interacting actively with graphite in the process of atomization and the inflection on their Arrhenius plot have been explained qualitatively.     

Analysis of the force action of a gas jet on the surface of a liquid

The results of theoretical and experimental investigations of the interaction of a gas jet with the surface of a viscous liquid are reported. Relations are derived for calculating the force exerted by the gas jet on the liquid surface. A dependence of the gas jet compression ratio in the nozzle outlet on the pressure in front of the nozzle is revealed. The values of the shape factor for the indentation formed by the gas jet on the surface of the liquid are determined for various diameters of the indentation and the distances between the outlet hole of the nozzle and the liquid surface. The theoretical conclusions formulated here are confirmed by the results of experiments.     

Fluctuations of the charge on a dust grain in a plasma

A dust grain in a plasma acquires an electric charge by collecting electron and ion currents. These currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value 〈Q〉. Electrons and ions are collected at random intervals and in a random sequence, with probabilities that depend on the grain's potential. We developed a model for these probabilities and implemented it in a numerical simulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain's charge. Electron emission from the grain is not included, although it could be added easily to our method. We obtained the power spectrum and the RMS fluctuation level, as well as the distribution function of the charge. Most of the power in the spectrum lies at frequencies much lower than 1/τ, the inverse charging time. The RMS fractional fluctuation level varies as 0.5 |〈N〉|^-1/2, where 〈N〉=〈Q〉/e is the average number of electron charges on the grain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can experience fluctuations to neutral and positive polarities, even in the absence of electron emission     

Influence of a hydrophilic spacer on the structure of a phospholipid monolayer

Summary We present the results of thermodynamical and X-ray grazing incidence diffraction experiments performed on Langmuir monolayers of ether lipids with hydrophilic spacers between the glycerol backbone and the phosphatidylcholine head group: DHPC, DH-E01-PC, and DH-E02-PC. As a spacer the oxy-ethylene group is used, which is a typical hydrophilic unit of non-ionic tensides. It turns out that the introduction of the hydrophilic spacers leads to a fluidization of the monolayer and reduces the tilt angle of the chains. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Effect of the field of a nonlinear electromagnetic wave on the shape of a soliton in a semiconductor superlattice

The effect of the electric component of the field of a high-frequency (HF) nonlinear electromagnetic (EM) wave on the propagation of a solitary EM wave (soliton) in a quantum semiconductor superlattice is studied. It is noted that in the collisionless approximation, the solution of the modified sine-Gordon equation corresponding to the amplification of an EM pulse that, with allowance made for interminiband electron transitions, transforms into a dissipative soliton is possible. The effect of electron collisions with irregularities of the crystal lattice on the soliton dynamics under the action of the field of a HF nonlinear wave is considered. The condition for an increase in the traveling time of the solitary wave is found.     

Formation of a Wave Structure on the Surface of a Graphene Film

A wavy structure of the surface of graphene nanoparticles on a hydrocarbon substrate has been obtained. It has been shown that the wavy surface is the manifestation of the Kelvin-Helmholtz instability at the interface between liquid paraffin and graphene suspension with the inhomogeneity length λ = 250 nm. The manifestation of such wavy structures is due primarily to van der Waals forces.