Self-consistent Boundary Conditions Research Articles

Ten-moment fluid model with heat flux closure for gasdynamic flows

The gasdynamic 10-moment equations are revisited, applying a Chapman-Enskog type expansion to achieve the closure for heat flux. The resulting gradient-based closure performs favorably against previously employed closures in regions of shocks when compared to the kinetic results obtained from Direct Simulation Monte Carlo simulations. The 10-moment model can capture finite kinetic effects due to non-Maxwellian velocity distribution functions, as compared to the 5-moment Navier-Stokes equations, and remains hyperbolic-parabolic with real wave speeds under all initial conditions. Self-consistent kinetic boundary conditions are derived without consideration of a distinct Knudsen layer. The model is applied to a number of canonical gasdynamics problems in one and two dimensions such as steady normal and oblique shocks, as well as the Sod shock tube problem.

Effect of ion stress on properties of magnetized plasma sheath

In the plasma sheath, there is a significant gradient in ion velocity, resulting in strong stress on ions treated as a fluid. This aspect has often been neglected in previous sheath studies. This study is based on the Braginskii plasma transport theory and establishes a 1D3V sheath fluid model that takes into account the ion stress effect. Under the assumption that ions undergo both electric and diamagnetic drift in the presheath region, self-consistent boundary conditions, including the ion Bohm velocity, are derived based on the property of the Sagdeev pseudopotential. Furthermore, assuming that the electron velocity at the wall follows a truncated Maxwell distribution, the wall floating potential is calculated, leading to a more accurate sheath thickness estimation. The results show that ion stress significantly reduces the sheath thickness, enhances ion Bohm velocity, wall floating potential, and ion flux at the wall. It hinders the acceleration of ions within the sheath, leading to notable alterations in the particle density profiles within the sheath. Further research indicates that in ion stress, bulk viscous stress has the greatest impact on sheath properties.

太阳极轨天文台

<p indent="0mm">Solar magnetic fields and related solar magnetic activities dominate the heliospheric environments from the near-Earth space, to the interplanetary space, and up to the interstellar boundary. The polar magnetic fields of the Sun and its dynamic processes are especially vital in the aspects of manifesting the internal dynamo of the Sun, and shaping magnetic fields in the heliosphere. But so far, almost all the solar satellites have been limited in the vicinity of the ecliptic plane. Due to the serious projection effect, the polar regions remain as the least-known mysterious territory of the Sun. The spacecraft of “Solar Polar-orbit Observatory (SPO)” has been designed to directly image the solar polar regions in an unprecedented way by traveling in a large solar inclination angle (≥ 80°) and a small ellipticity. Based on multi-band remote-sensing and <italic>in-situ</italic> measurements, the SPO will make breakthrough on the following top-level scientific objectives: (1) Provide decisive observations for solving the problem of the century—How the solar magnetic activity cycle originates that shapes the living environment of human beings; (2) provide direct observational supports for unveiling the origin, mechanism, and effect of the “primitive” high-speed solar wind that connects the Sun and celestial bodies in the solar system; (3) provide the necessary, complete, and self-consistent initial and boundary conditions for creating a data-driven global heliospheric numerical model that serves as the foundation for space weather prediction. To achieve these scientific objectives, the SPO will be equipped with six remote-sensing instruments and one <italic>in-situ</italic> instrument package. The remote-sensing instruments are Magnetic and Helioseismic Imager (MHI; FOV: 34′ (full disk)/17′ (high resolution); pixel resolution: 1″/0.5″; sensitivity: 10 G (longitudinal), 200 G (transverse); cadence: <sc>15 min;</sc> sensitivity of Doppler velocity: <sc>30 m/s;</sc> Cadence: <sc>1 min),</sc> Extreme Ultraviolet Solar Telescope (EUST; FOV: 51′; spatial resolution: 3.5″; imaging band: 19.3, 17.1, 13.1 and <sc>30.4 nm;</sc> cadence: <sc>1 min),</sc> Visible-light Coronagraph (VISCO; FOV: 0.69°–2.67° annular; pixel resolution: 4.8″; wave band: <sc>700±40 nm;</sc> cadence: <sc>2 min),</sc> Very Large Angle Coronagraph (VLACOR; FOV: 2.67°–24° annular; pixel resolution: 45″; wave band: <sc>600–750 nm;</sc> cadence: <sc>10 min</sc> (white light), <sc>60 min</sc> (polarization)), X-ray Imaging Telescope (XIT; FOV: 48′; angular resolution: 10″; energy range: Energy spectrum <sc>0.5–10 keV;</sc> spectral resolution: <sc>1 keV@6 keV;</sc> time resolution: <sc>5 s</sc> (common), <sc>1 s</sc> (burst)), and Low Frequency Radio Spectrometer (LFRS; frequency range: <sc>10 kHz–2.0 MHz</sc> and <sc>1.0–50 MHz;</sc> spectral resolution: <sc>≤5 kHz@2.0 MHz</sc> and <sc>≤0.1 MHz@50 MHz;</sc> time resolution: <sc>1 s;</sc> dynamic range: <sc>&gt;72 dB)</sc>. The <italic>in-situ</italic> instrument package includes Solar Wind Ion Analyzer (SWIA), Solar Energetic Particles Analyzer (SEPA), and Magnetometer (MAG).

A Novel Solution for Resonant Scattering Using Self-consistent Boundary Conditions

We present two novel additions to the semianalytic solution of Lyα radiative transfer in spherical geometry: (1) implementation of the correct boundary condition for a steady source, and (2) solution of the time-dependent problem for an impulsive source. For the steady-state problem, the solution can be represented as a sum of two terms: a previously known analytic solution of the equation with mean intensity J = 0 at the surface, and a novel, semianalytic solution which enforces the correct boundary condition of zero-ingoing intensity at the surface. This solution is compared to that of the Monte Carlo method, which is valid at arbitrary optical depth. It is shown that the size of the correction is of order unity when the spectral peaks approach the Doppler core and decreases slowly with line center optical depth, specifically as , which may explain discrepancies seen in previous studies. For the impulsive problem, the time, spatial, and frequency dependence of the solution are expressed using an eigenfunction expansion in order to characterize the escape time distribution and emergent spectra of photons. It is shown that the lowest-order eigenfrequency agrees well with the decay rate found in the Monte Carlo escape time distribution at sufficiently large line center optical depths. The characterization of the escape time distribution highlights the potential for a Monte Carlo acceleration method, which would sample photon escape properties from distributions rather than calculating every photon scattering, thereby reducing computational demand.

Interface dynamics with heat and mass fluxes

Unstable interfaces ubiquitously occur in fluids, plasmas and materials, from the celestial event of supernova to the atomic level of plasma fusion. Knowledge of their fundamentals is in demand in science, mathematics, and engineering. Our work considers the classical problem of stability of a phase boundary having heat and mass fluxes across it and yields a rigorous theory resolving challenges not addressed before. By employing self-consistent boundary conditions for thermal heat flux, by identifying the perturbation waves' structure, and by thoroughly investigating the dependence of waves' coupling on system parameters, we discover new fluid instabilities in the advection, diffusion and low Mach regimes. We find that the interface stability is set primarily by the interplay of macroscopic inertial stabilization with destabilizing acceleration, and the microscopic thermodynamics and thermal heat flux creates vortical fields in the bulk.

Three-Dimensional MHD Modeling of Interplanetary Solar Wind Using Self-Consistent Boundary Condition Obtained from Multiple Observations and Machine Learning

Three-dimensional (3-d) magnetohydrodynamics (MHD) modeling is a key method for studying the interplanetary solar wind. In this paper, we introduce a new 3-d MHD solar wind model driven by the self-consistent boundary condition obtained from multiple observations and the Artificial Neural Network (ANN) machine learning technique. At the inner boundary, the magnetic field is derived using the magnetogram and potential field source surface extrapolation; the electron density is derived from the polarized brightness (pB) observations, the velocity can be deduced by an ANN using both the magnetogram and pB observations, and the temperature is derived from the magnetic field and electron density by a self-consistent method. Then, the 3-d interplanetary solar wind from CR2057 to CR2062 is modeled by the new model with the self-consistent boundary conditions. The modeling results present various observational characteristics at different latitudes, and are in better agreement with both the OMNI and Ulysses observations compared to our previous MHD model based only on photospheric magnetic field observations.

A multiscale volume of fluid method with self-consistent boundary conditions derived from molecular dynamics

Molecular dynamics (MD) and volume of fluid (VOF) are powerful methods for the simulation of dynamic wetting at the nanoscale and macroscale, respectively, but the massive computational cost of MD and the sensitivity and uncertainty of boundary conditions in VOF limit their applications to other scales. In this work, we propose a multiscale simulation strategy by enhancing VOF simulations using self-consistent boundary conditions derived from MD. Specifically, the boundary conditions include a particular slip model based on the molecular kinetic theory for the three-phase contact line to account for the interfacial molecular physics, the classical Navier slip model for the remaining part of the liquid–solid interface, and a new source term supplemented to the momentum equation in VOF to replace the convectional dynamic contact angle model. Each slip model has been calibrated by the MD simulations. The simulation results demonstrate that with these new boundary conditions, the enhanced VOF simulations can provide consistent predictions with full MD simulations for the dynamic wetting of nanodroplets on both smooth and pillared surfaces, and its performance is better than those with other VOF models, especially for the pinning–depinning phenomenon. This multiscale simulation strategy is also proved to be capable of simulating dynamic wetting above the nanoscale, where the pure MD simulations are inaccessible due to the computational cost.

Three-dimensional particle-in-cell model of Hall thruster: The discharge channel

There are still many missing elements to complete the physical picture at the basis of the Hall thruster functioning. The origin of the anomalous electron cross-field transport often ascribed to azimuthal electron E × B drift instability remains decoupled from self-consistent ion axial acceleration and radial boundary conditions, at the same time. This study represents the first attempt to correlate the different mechanisms contributing to the electron transport by means of a fully kinetic three-dimensional Particle-in-Cell model. A geometrical scaling scheme has been used to make the simulation possible. This scheme irremediably changes what are some salient characteristics of the discharge, such as the wall interaction and the axial component of the electric field. For this reason, a critical assessment of the effects of reducing dimensions has been addressed. The present paper deals with the physics of discharge channel. Results confirm the occurrence of E × B drift instability along the azimuthal direction. The modulation is almost standing wave: it moves back and forth travelling only a short distance before being axially convected away. In addition, the dielectric floating potential nature of the lateral walls gives to the azimuthal modulation an important radial component creating an oblique pattern in the radial-azimuthal plane. As a consequence, the azimuthal electric field presents a double alternating structure: two phase-opposing waves are present in the first and second half of the radial extension between the two lateral walls. Finally, the effect of secondary electron emission from walls is not sufficient to guarantee the right electron current to neutralize the ion beam, but rather it works as an auxiliary mechanism (together with ion heating and azimuthal rotation) to saturate the electron drift instability leading to smaller amplitude oscillations.

Supernova Driving. IV. The Star-formation Rate of Molecular Clouds

Abstract We compute the star-formation rate (SFR) in molecular clouds (MCs) that originate ab initio in a new, higher-resolution simulation of supernova-driven turbulence. Because of the large number of well-resolved clouds with self-consistent boundary and initial conditions, we obtain a large range of cloud physical parameters with realistic statistical distributions, which is an unprecedented sample of star-forming regions to test SFR models and to interpret observational surveys. We confirm the dependence of the SFR per free-fall time, SFRff, on the virial parameter, α vir, found in previous simulations, and compare a revised version of our turbulent fragmentation model with the numerical results. The dependences on Mach number, , gas to magnetic pressure ratio, β, and compressive to solenoidal power ratio, χ at fixed α vir are not well constrained, because of random scatter due to time and cloud-to-cloud variations in SFRff. We find that SFRff in MCs can take any value in the range of 0 ≤ SFRff ≲ 0.2, and its probability distribution peaks at a value of SFRff ≈ 0.025, consistent with observations. The values of SFRff and the scatter in the SFRff–α vir relation are consistent with recent measurements in nearby MCs and in clouds near the Galactic center. Although not explicitly modeled by the theory, the scatter is consistent with the physical assumptions of our revised model and may also result in part from a lack of statistical equilibrium of the turbulence, due to the transient nature of MCs.

The effects of oblique incidences on the XB mode conversion in the electron cyclotron range of frequency

The linear conversion from a fast extraordinary mode to a Bernstein mode (XB) in the electron cyclotron range of frequency is revisited numerically by using a simplified kinetic model. The corresponding wave equations are solved as a standard two-point boundary value problem, where the self-consistent boundary conditions are applied and the scattering coefficients are calculated accordingly. The numerical calculation of the XB conversion efficiency is compared with the analytical formula for the normal incidence (along the direction perpendicular to the equilibrium magnetic field and parallel to the density gradient), where a reasonable agreement is found. The effects of incident angles represented by refractive indexes on the conversion efficiency are analyzed. It is shown that as the incident angle deviates from the normal incidence, the efficiency of XB conversion decreases significantly. The results also indicate that the power loss in the XB process can be ascribed to the reflected fast extraordinary mode and the reflected-converted ordinary mode. The symmetry of the conversion efficiency about the incident angle is discussed, and the rigid restriction on the scale length of the density variation for effective XB conversions can be possibly alleviated through altering the injection direction in realistic experiments.

CONTROL OF CURRENT TRANSPORT IN SCHOTTKY DIODE USING THE QUANTUM DOTS

SummaryPurpose. In the framework of the drift-deformation-diffusion approximation considering the self-consistent boundary conditions, investigate the current-voltage characteristic (CVC) of surface-barrier structure of type Schottky with built layer of quantum dots and establish the criteria for the technological parameters of surface-barrier structure of type Schottky with built layer of quantum dots at which current-voltage characteristic has S-shaped character. Research methods. Method of self-consistent boundary conditions. Research results. As seen from the numerical calculations, the current-voltage characteristic (CVC) of low barrier (åV5.0≤Δ) Schottky diode with built layer of quantum dots in the space charge region is S-shaped nature. With increasing barrier height Δ to 0.9 eV the area of negative differential resistance on CVC is disappears, and in the interval of voltages 0.5V - 1V has exponential character. Variation of thickness i- layer (0d0RLL−=) of  toA150 leads to changing the character of CVC, i.e. the instability current of S-type is disappears. In this work the results of numerical calculations of CVC for the direct direction of displacement at two values of temperature (T = 77 K, 300K) is given. As seen from the graphs CVC in the range of the voltages Â52.0VÂ24.0&lt;&lt; the value of the current density of voltage at T=77 K is smaller than at T=300K.Conclusions1. It is established that current-voltage characteristic (CVC) of low barrier (åÂ5.0≤Δ) Schottky diode with built layer of quantum dots in the space charge region is S-shaped nature, when the layer of quantum dots is located at distances from the boundary of the contact metal-semiconductor of the order of (10-30)0a, where 0a is the period lattice of the semiconductor.2. It is shown that both the increasing barrier height Δof 0.5 eV to 0.9eV, and the distance from the metal to layer of QD (dL) of A50 to A150, the area of negative differential resistance on CVC is disappears.3. At high potential barrier (0.9eV) the contact effects is dominate and the site of the exponential dependence on voltage (0.5V-1V) on CVC is present, and the lower potential barrier the dependence of current on voltage is approximates to a quadratic (V&gt; 0.6B).

Self-consistent time-dependent boundary conditions for static and dynamic simulations of small electron devices

A quasi-analytical self-consistent and time-dependent boundary conditions algorithm for micro- and nanoscale electron transport simulators is presented and discussed. The algorithm is the result of imposing overall charge neutrality and current conservation along the reservoirs, the leads and the active region. Only an explicit numerical simulation of the active region is required. By means of analytical solutions of the spatial distribution for the charge density, electric field and potential energy along the leads, the algorithm is able to self-consistently translate standard "metallic" boundary conditions in the reservoirs into intricate constraints at the borders of the active region. The algorithm is robust, requires small computational effort and it is suitable for any (classical or quantum) electronic device simulator for stationary (DC) and dynamic (transients, noise and AC) regimes up to several THz. The algorithm is specially welcomed for dynamical regime simulations, where the predictions of the time-evolution of the electrostatic potential, electric field and charge density at the borders of the active region are rather complicated.

Negative ion extraction by particle model

More self-consistent injection boundary conditions from the source region have been used in the extraction region model to examine the negative ion formation and transport. Bulk kinetic, plasma-surface, and gas-surface processes have been all included. This work represents a first example of coupling between different models, and it shows the important role of positive ion conversion on plasma grid for the extracted negative ion current.

Topological superconductivity and Majorana fermions in hybrid structures involving cuprate high-Tcsuperconductors

The possibility of inducing topological superconductivity with cuprate high-temperature superconductors (HTSC) is studied for various heterostructures. We first consider a ballistic planar junction between a HTSC and a metallic ferromagnet. We assume that inversion symmetry breaking at the tunnel barrier gives rise to Rashba spin-orbit coupling in the barrier and allows equal-spin triplet superconductivity to exist in the ferromagnet. Bogoliubov-de Gennes equations are obtained by explicitly modeling the barrier, and taking account of the transport anisotropy in the HTSC. By making use of the self-consistent boundary conditions and solutions for the barrier and HTSC regions, an effective equation of motion for the ferromagnet is obtained where Andreev scattering at the barrier is incorporated as a boundary condition for the ferromagnetic region. For a ferromagnet layer deposited on a (100) facet of the HTSC, triplet p-wave superconductivity is induced. For the layer deposited on a (110) facet, the induced gap does not have the p-wave orbital character, but has an even orbital symmetry and an odd dependence on energy. For the layer on the (001) facet, an exotic f-wave superconductivity is induced. We also consider the induced triplet gap in a one-dimensional half-metallic nanowire deposited on a (001) facet of a HTSC. We find that for a wire axis along the a-axis, a robust triplet p-wave gap is induced. For a wire oriented 45 degrees away from the a-axis the induced triplet p-wave gap vanishes. For the appropriately oriented wire, the induced p-wave gap should give rise to Majorana fermions at the ends of the half-metallic wire. Based on our result, topological superconductivity in a semi-conductor nanowire may also be possible given that it is oriented along the a-axis of the HTSC.

Microscopic theory for a ferromagnetic nanowire/superconductor heterostructure: Transport, fluctuations, and topological superconductivity

Motivated by the recent experiment of Wang et al. [Nature Physics 6, 389 (2010)], who observed a highly unusual transport behavior of ferromagnetic Cobalt nanowires proximity-coupled to superconducting electrodes, we study proximity effect and temperature-dependent transport in such a mesoscopic hybrid structure. It is assumed that the asymmetry in the tunneling barrier gives rise to the Rashba spin-orbit-coupling in the barrier that enables induced p-wave superconductivity in the ferromagnet to exist. We first develop a microscopic theory of Andreev scattering at the spin-orbit-coupled interface, derive a set of self-consistent boundary conditions, and find an expression for the p-wave minigap in terms of the microscopic parameters of the contact. Second, we study temperature-dependence of the resistance near the superconducting transition and find that it should generally feature a fluctuation-induced peak. The upturn in resistance is related to the suppression of the single-particle density of states due to the formation of fluctuating pairs, whose tunneling is suppressed. In conclusion, we discuss this and related setups involving ferromagnetic nanowires in the context of one-dimensional topological superconductors. It is argued that to realize unpaired end Majorana modes, one does not necessarily need a half-metallic state, but a partial spin polarization may suffice. Finally, we propose yet another related class of material systems -- ferromagnetic semiconductor wires coupled to ferromagnetic superconductors -- where direct realization of Kitaev-Majorana model should be especially straightforward.

Erratum to: Transport across nanogaps using self-consistent boundary conditions

Erratum to: Transport across nanogaps using self-consistent boundary conditions

Transport across nanogaps using self-consistent boundary conditions

Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework. The determination of self-consistent boundary conditions across the gap forms the central theme in order to allow for realistic interface potentials (such as metal-vacuum) which are smooth at the boundary and do not abruptly assume a constant value at the interface. It is shown that a semiclassical expansion of the transmitted wavefunction leads to approximate but self consistent boundary conditions without assuming any specific form of the potential beyond the gap. Neglecting the exchange and correlation potentials, the quantum Child-Langmuir law is investigated. It is shown that at zero injection energy, the quantum limiting current density (J c ) is found to obey the local scaling law J c ∼ V g α/D 5-2α with the gap separation D and voltage V g . The exponent α > 1.1 with α → 3/2 in the classical regime of small de Broglie wavelengths.

Competition between the barrier and injection mechanisms of nonlinearity of the current-voltage characteristic in Mott-barrier detector diodes

We obtain an analytical solution to the problem of transverse injection current in an undoped semiconductor i layer of arbitrary thickness with account of self-consistent boundary conditions. Charge transfer in the semiconductor bulk is described in the drift-diffusion approximation. Current transfer through the boundaries of an undoped layer is described in terms of the thermoelectron emission theory. Thus, the generalized thermoemission-diffusion approach applies for semiconductors with both low and high mobilities of charge carriers. On the basis of the obtained solution, we analyze the characteristics of the current nonlinearity of the Mott-barrier diodes. The generalized approach is used for describing current transfer in low-barrier diodes based on Mott contacts with near-surface δ-doping. Characteristics of detection of low-barrier diodes are analyzed. Limiting values of the volt-watt and threshold sensitivities of the detectors based on these diodes in the subterahertz frequency range (up to 1 THz) are determined.

Analytical solution for charge-carrier injection into an insulating layer in the drift diffusion approximation

Using a drift-diffusion approximation, we obtain an analytical solution to the problem of charge-carrier injection into an insulating i layer of finite thickness with account of self-consistent boundary conditions. The main assumption is that the self-doping of the i layer is neglected. The solution makes it possible to calculate the potential, electric field, and current-voltage characteristics of a variety of structures such as metal-i layer-n+ (or p+) semiconductor, metal-i layer-metal, and n+(p+)-i-n+(p+) structures. The solution admits a generalization for structures having heterobarriers at the interface of the semiconductor layers. The proposed approach allows for the contact phenomena and bulk effects related to that the current is space charge-limited in the i layer. The solution is valid for both the limiting cases and the transient regimes.

Solution of the problem of charge-carrier injection into an insulating layer under self-consistent boundary conditions at contacts

The problem of charge carrier injection into a finite-length insulating layer is analytically solved in the drift-diffusion approximation, taking into account self-consistent boundary conditions. The main assumption is the neglect of intrinsic doping of the i-type layer. The solution allows calculation of the potential, electric field, and current-voltage characteristics of various structures, i.e., metal-i-n + (or p +)-semiconductor, metal-i-layer-metal, and n +(p +)-i-n +(p +) structures. The solution allows generalization for structures having heterobarriers at semiconductor layer interfaces. The proposed approach considers contact phenomena and volume effects associated with the space-charge-limited current in the i-type layer. The solution is valid in both extreme cases and intermediate conditions.