The emission properties, structure and stability of ionic liquid menisci undergoing electrically assisted ion evaporation

The properties and structure of electrically stressed ionic liquid menisci experiencing ion evaporation are simulated using an electrohydrodynamic model with field-enhanced thermionic emission in steady state for an axially symmetric geometry. Solutions are explored as a function of the external background field, meniscus dimension, hydraulic impedance and liquid temperature. Statically stable solutions for emitting menisci are found to be constrained to a set of conditions: a minimum hydraulic impedance, a maximum current output and a narrow range of background fields that maximizes at menisci sizes of 0.5–3 ${\rm \mu}{\rm m}$ in radius. Static stability is lost when the electric field adjacent to the electrode that holds the meniscus corresponds to an electric pressure that exceeds twice the surface tension stress of a sphere of the same size as the meniscus. Preliminary investigations suggest this limit to be universal, therefore, independent of most ionic liquid properties, reservoir pressure, hydraulic impedance or temperature and could explain the experimentally observed bifurcation of a steady ion source into two or more emission sites. Ohmic heating near the emission region increases the liquid temperature, which is found to be important to accurately describe stability boundaries. Temperature increase does not affect the current output when the hydraulic impedance is constant. This phenomenon is thought to be due to an improved interface charge relaxation enhanced by the higher electrical conductivity. Dissipated ohmic energy is mostly conducted to the electrode wall. The higher thermal diffusivity of the wall versus the liquid, allows the ion source to run in steady state without heating.

Solvability of a moving contact-line problem with interface formation for an incompressible viscous fluid

We investigate the free-boundary problem of a steadily advancing meniscus in a circular capillary tube. The problem is described using the “interface formation model,” which was originally introduced with the aim of avoiding the singularities that arise when classical hydrodynamics is applied to problems with a moving contact line. We prove the existence of an axially symmetric solution in weighted Hölder spaces for low meniscus speeds.

Energy levels of an electron in a circular quantum dot in the presence of spin-orbit interactions

The two-dimensional circular quantum dot in a double semiconductor heterostructure is simulated by a new axially symmetric smooth potential of finite depth and width. The presence of additional potential parameters in this model allows us to describe the individual properties of different kinds of quantum dots. The influence of the Rashba and Dresselhaus spin-orbit interactions on electron states in quantum dot is investigated. The total Hamiltonian of the problem is written as a sum of unperturbed part and perturbation. First, the exact solution of the unperturbed Schrödinger equation was constructed. Each energy level of the unperturbed Hamiltonian was doubly degenerated. Further, the analytical approximate expression for energy splitting was obtained within the framework of perturbation theory, when the strengths of two spin-orbit interactions are close. The numerical results show the dependence of energy levels on potential parameters.

Effects of gravitational lensing on neutrino oscillation in $$ \gamma $$-spacetime

We study the effects of gravitational lensing on neutrino oscillations in the $$\gamma $$ γ -spacetime which describes a static, axially-symmetric and asymptotically flat solution of the Einstein’s field equations in vacuum. Using the quantum-mechanical treatment for relativistic neutrinos, we calculate the phase of neutrino oscillations in this spacetime by considering both radial and non-radial propagation. We show the dependence of the oscillation probability on the absolute neutrino masses, which in the two-flavour case also depends upon the sign of mass squared difference, in sharp contrast with the well-known results of vacuum oscillation in flat spacetime. We also show the effects of the deformation parameter $$\gamma $$ γ on neutrino oscillations and reproduce previously known results for the Schwarzschild metric. We then extend these to a more realistic three flavours neutrino scenario and study the effects of the parameter $$\gamma $$ γ and the lightest neutrino mass while using best fit values of neutrino oscillation parameters.

Static solutions in the Freund – Nambu scalar-tensor theory of gravitation

Herein, the system of Einstein equations and the equation of the Freund – Nambu massless scalar field for static spherically symmetric and axially symmetric fields are considered. It is shown that this system of field equations decouples into gravitational and scalar subsystems. In the second post-Newtonian approximation, the solutions for spherically symmetric and slowly rotating sources are obtained. The application of the obtained solutions to astrophysical problems is discussed.