Vacuum Region Research Articles

Global Existence of Finite Energy Weak Solutions of Quantum Navier–Stokes Equations

In this paper we consider the Quantum Navier-Stokes system both in two and in three space dimensions and prove global existence of finite energy weak solutions for large initial data. In particular, the notion of weak solutions is the standard one. This means that the vacuum region are included in the weak formulations. In particular, no extra term like damping or cold pressure are added to the system in order to define the velocity field in the vacuum region. The main contribution of this paper is the construction of a regular approximating system consistent with the effective velocity transformation needed to get necessary a priori estimates.

Depth-Dependent Three-Layer Model for the Surface Second-Harmonic Generation Yield

We present a generalization of the three-layer model to calculate the surface second harmonic generation (SSGH) yield, that includes the depth dependence of the surface nonlinear second order susceptibility tensor $\boldsymbol{\chi}(-2\omega;\omega,\omega)$. This model considers that the surface is represented by three regions or layers. The first layer is a semi-infinite vacuum region with a dielectric function $\epsilon_{v}(\omega)=1$, from where the fundamental electric field impinges on the material. The second layer is a thin layer ($\ell$) of thickness $d$ characterized by a dielectric function $\epsilon_{\ell}(\omega)$, and it is in this layer where the SSHG takes place. We consider the position of $\boldsymbol{\chi}(-2\omega;\omega,\omega)$ within this surface layer. The third layer is the bulk region denoted by $b$ and characterized by $\epsilon_{b}(\omega)$. We include the effects caused by the multiple reflections of both the fundamental and the second-harmonic (SH) fields that take place within the thin layer $\ell$. {\color{red} As a test case, we calculate $\boldsymbol{\chi}(-2\omega;\omega,\omega)$ for the Si(111)(1$\times$1):H surface, and present a layer-by-layer study of the susceptibility to elucidate the depth dependence of the SHG spectrum. We then use the depth dependent three-layer model to calculate the SSHG yield, and contrast the calculated spectra with experimental data. We produce improved results over previous published work, as this treatment can reproduce key spectral features, is computationally viable for many systems, and most importantly remains completely \emph{ab initio}.

Electrostatic potential barrier for electron emission at graphene edges induced by the nearly free electron states

Using the density functional theory, we studied the electronic structures of zigzag graphene nanoribbons with hydroxyl, H, ketone, aldehyde, or carboxyl terminations under a lateral electric field. The critical electric field for electron emission is proportional to the work function of the functionalized edges except the hydroxylated edge, which leads to the anomalous electric field outside the edge, owing to the electrons in the nearly free electron (NFE) state in the vacuum region. The strong electric field also causes a potential barrier for the electron emission from the H-terminated edge owing to the downward shift of the NFE state.

Coherent radiation at the fundamental frequency by a Smith-Purcell free-electron laser with dielectric substrate

This letter reports an approach to realize coherent radiation at the fundamental frequency of the wave that is resonant with the electron beam in a Smith-Purcell (SP) free-electron laser (FEL). We found that a two-dimensional grating structure equipped with a dielectric substrate could provide an electromagnetic mode which shows the property of a surface wave in the vacuum region where the beam-wave interaction occurs, and operates as a radiative wave in the dielectric region. Thus, an electron beam holding medium energy resonant with the mode could radiate at the fundamental frequency, which is different from the typical Smith-Purcell free-electron laser that radiates only at harmonics of the resonant frequency.

Influence of Ionization Source Conditions on the Gas-Phase Protomer Distribution of Anilinium and Related Cations.

The gas-phase-ion generation technique and specific ion-source settings of a mass spectrometer influence heavily the protonation processes of molecules and the abundance ratio of the generated protomers. Hitherto that has been attributed primarily to the nature of the solvent and the pH. By utilizing electrospray ionization and ion-mobility mass spectrometry (IM-MS), we demonstrate, even in the seemingly trivial case of protonated aniline, that the protomer ratio strongly depends on the source conditions. Under low in-source ion activation, nearly 100% of the N-protomer of aniline is produced, and it can be subsequently converted to the C-protomer by collisional activation effected by increasing the electrical potential difference between the entrance and exit orifices of the first vacuum region. This activation and transformation process takes place even before the ion is mass-selected and subjected to IM separation. Despite the apparent simplicity of the problem, the preferred protonation site of aniline in the gas phase-the amino group or the aromatic ring-has been a topic of controversy. Our results not only provide unambiguous evidence that ring- and nitrogen-protonated aniline can coexist and be interconverted in the gas phase, but also that the ratio of the protomers depends on the internal energy of the original ion. There are many dynamic ion-transformation and fragmentation processes that take place in the different physical compartments of a Synapt G2 HDMS instrument. Such processes can dramatically change the very identity even of small ions, and therefore should be taken into account when interpreting product-ion mass spectra. Graphical Abstract ᅟ.

Electronic band structure of TiN/MgO nanostructures

Various nanostructured TiN(001)/MgO(001) superlattices based on a repeated slab model with a vacuum region have been investigated by the total energy pseudopotential method. They are rectangular and rectangular parallelepiped TiN(001) dot structures on MgO(001)-2×2 and 3×3 substrates. A rectangular TiN(001) structure on a MgO(001)-2×1 substrate has also been calculated. Their detailed electronic and internal lattice properties were investigated systematically. The internal atomic coordinates in a unit cell were fully relaxed. The rectangular TiN(001) structure on the MgO(001)-2×1 superlattice, which is not a dot owing to its periodicity, corresponds to metallicity. The electronic states of relaxed rectangular TiN(001) dot/MgO(001)-2×2 and MgO(001)-3×3 superlattices are semiconducting. All relaxed rectangular parallelepiped TiN(001) dot/MgO(001)-2×2 and MgO(001)-3×3 superlattices correspond to metallicity. The electronic properties depend on the shape of the TiN dot and the size of the MgO substrate.

Atomically modified thin interface in metal-dielectric hetero-integrated systems: control of electronic properties

We have performed first-principles studies of the electronic properties of Cu-diamond hetero-integrated systems, particularly placing emphasis on elucidating the effects of surface modification of diamond with H or O. It is found that the electronic properties crucially depend on the chemical compositions of the modified atomically thin interface region. The local density of states (LDOS) of the H-terminated diamond moiety near the Cu surface exhibits a clearly different distribution from that near the vacuum region, whereas the LDOS of the O-terminated diamond is almost independent of the Cu deposition. In other words, the effects of the electronic interactions between Cu and diamond on the electronic properties in the interface region are readily controlled by surface modification with only one atomic (i.e. H or O) layer. Electric field (EF) effects on the Cu-diamond systems also strongly depend on the electronic details, i.e. atomistic modification in the interface regions. In particular, at the interface between the H-terminated diamond moiety and the vacuum region, its conduction band energy is strongly affected by an applied EF much more than the valence band energy; that is, the band gap can be varied with an applied EF. The band gap variation is found to be attributed to an atomistic level difference in the spatial extension of the valence and conduction bands and thus is not explained with a macroscopic band diagram model. It has been demonstrated that the electronic properties of hetero-integrated systems are described and controlled well by carefully designing atomically thin interface regions.

On the Motion of Free Interface in Ideal Incompressible MHD

For the free boundary problem of the plasma-vacuum interface to three-dimensional ideal incompressible magnetohydrodynamics (MHD), the a priori estimates of smooth solutions are proved in Sobolev norms by adopting a geometrical point of view and some quantities such as the second fundamental form and the velocity of the free interface are estimated. In the vacuum region, the magnetic fields are described by the div-curl system of pre-Maxwell dynamics, while at the interface the total pressure is continuous and the magnetic fields are tangent to the interface, but we do not need any restrictions on the size of the magnetic fields on the free interface. We introduce the "virtual particle" endowed with a virtual velocity field in vacuum to reformulate the problem to a fixed boundary problem under the Lagrangian coordinates. The $L^2$-norms of any order covariant derivatives of the magnetic fields both in vacuum and on the boundaries are bounded in terms of initial data and the second fundamental forms of the free interface and the rigid wall. The estimates of the curl of the electric fields in vacuum are also obtained, which are also indispensable in elliptic estimates.

Cosmological study in loop quantum cosmology through dark energy model

The interacting generalized ghost version of pilgrim dark energy (GGPDE) is discussed in the framework of loop quantum cosmology (LQC). We analyze the behavior of cosmological parameters (Hubble, equation of state (EoS), deceleration) and cosmological planes ([Formula: see text] and [Formula: see text]-[Formula: see text]) in the present scenario ([Formula: see text] represents the EoS parameter and [Formula: see text] indicates the evolution of the EoS parameter, [Formula: see text],[Formula: see text] are statefinder parameters). It is observed that the deceleration parameter corresponds to the accelerated expansion of the universe. The EoS parameter lies in vacuum and phantom regions for all cases of [Formula: see text] (pilgrim dark energy (PDE) parameter). The [Formula: see text] plane lies in thawing region for all cases of [Formula: see text]. The [Formula: see text] plane corresponds to [Formula: see text] cold dark matter (CDM) and Chaplygin gas model. We have also mentioned the constraints on calculated cosmological parameters and found that all the trajectories of cosmological parameters and planes show the consistence behavior with the observational schemes.

Spacetime dynamics of a Higgs vacuum instability during inflation

A remarkable prediction of the Standard Model is that, in the absence of corrections lifting the energy density, the Higgs potential becomes negative at large field values. If the Higgs field samples this part of the potential during inflation, the negative energy density may locally destabilize the spacetime. We use numerical simulations of the Einstein equations to study the evolution of inflation-induced Higgs fluctuations as they grow towards the true (negative-energy) minimum. These simulations show that forming a single patch of true vacuum in our past light cone during inflation is incompatible with the existence of our Universe; the boundary of the true vacuum region grows outward in a causally disconnected manner from the crunching interior, which forms a black hole. We also find that these black hole horizons may be arbitrarily elongated---even forming black strings---in violation of the hoop conjecture. By extending the numerical solution of the Fokker-Planck equation to the exponentially suppressed tails of the field distribution at large field values, we derive a rigorous correlation between a future measurement of the tensor-to-scalar ratio and the scale at which the Higgs potential must receive stabilizing corrections in order for the Universe to have survived inflation until today.

A Comprehensive Cold Gas Performance Study of the Pocket Rocket Radiofrequency Electrothermal Microthruster

This paper presents computational fluid dynamics simulations of the cold gas operation of Pocket Rocket and Mini Pocket Rocket radiofrequency electrothermal microthrusters, replicating experiments performed in both sub-Torr and vacuum environments. This work takes advantage of flow velocity choking to circumvent the invalidity of modelling vacuum regions within a CFD simulation, while still preserving the accuracy of the desired results in the internal regions of the microthrusters. Simulated results of the plenum stagnation pressure is in precise agreement with experimental measurements when slip boundary conditions with the correct tangential momentum accommodation coefficients for each gas are used. Thrust and specific impulse is calculated by integrating the flow profiles at the exit of the microthrusters, and are in good agreement with experimental pendulum thrust balance measurements and theoretical expectations. For low thrust conditions where experimental instruments are not sufficiently sensitive, these cold gas simulations provide additional data points against which experimental results can be verified and extrapolated. The cold gas simulations presented in this paper will be used as a benchmark to compare with future plasma simulations of the Pocket Rocket microthruster.

The excitation and detection of a leaky surface electromagnetic wave on a high-index dielectric grating in a prism-coupler geometry

A periodically corrugated interface between vacuum and a high-index dielectric medium supports a p-polarized leaky surface electromagnetic wave whose sagittal plane is perpendicular to the generators of the interface. This wave is bound to the surface in the vacuum region, but radiates into the high-index dielectric medium. We study the excitation of this wave by p-polarized light incident from a prism on whose planar base the highindex dielectric medium in the form of a film is bonded. The unilluminated surface of the film is periodically corrugated, and is in contact with vacuum. Peaks and dips in the dependence of several low-order diffraction efficiencies on the angle of incidence (Wood anomalies) are the signatures of the excitation of the surface wave.

The Electric Discharge Detection Method in the Low Vacuum Region of Vacuum Interrupter

SUMMARYThe vacuum circuit breaker (VCB) achieves the high current interrupting capability in the pressure lower than 10 Pa to 5 Pa. When gas pressure increases, the breakdown voltage of a VCB decreases according to Paschen's law, and in the case of small leak, the partial discharge will occur in the VCB and the high frequency electromagnetic waves are radiated. So, we have developed the partial discharge detection system using an antenna with the region from 200 MHz to 300 MHz placed inside the VCB. However, if the partial discharge occurs outside the VCB, the detection system leads to misdetection as the partial discharge inside the VCB. In order to improve the performance of partial discharge detection, the outputs of antenna voltages inside and outside the VCB are investigated.

Completion of metric reconstruction for a particle orbiting a Kerr black hole

Vacuum perturbations of the Kerr metric can be reconstructed from the corresponding perturbation in either of the two Weyl scalars $\psi_0$ or $\psi_4$, using a procedure described by Chrzanowski and others in the 1970s. More recent work, motivated within the context of self-force physics, extends the procedure to metric perturbations sourced by a particle in a bound geodesic orbit. However, the existing procedure leaves undetermined a certain stationary, axially-symmetric piece of the metric perturbation. In the vacuum region away from the particle, this "completion" piece corresponds simply to mass and angular-momentum perturbations of the Kerr background, with amplitudes that are, however, a priori unknown. Here we present and implement a rigorous method for finding the completion piece. The key idea is to impose continuity, off the particle, of certain gauge-invariant fields constructed from the full (completed) perturbation, in order to determine the unknown amplitude parameters of the completion piece. We implement this method in full for bound (eccentric) geodesic orbits in the equatorial plane of the Kerr black hole. Our results provide a rigorous underpinning of recent results by Friedman {\it et al.}\ for circular orbits, and extend them to non-circular orbits.

Electronic structure modulation of graphene edges by chemical functionalization

Using the density functional theory with the effective screening medium method, we study the electronic properties of graphene nanoribbons with zigzag edges that are terminated by hydrogen and ketone, hydroxyl, carbonyl, and carboxyl functional groups. Our calculations showed that the work function and electronic structures of the edges of the nanoribbons are sensitive to the functional groups attached to the edges. The nearly free electron state emerges in the vacuum region outside the hydroxylated edges and crosses the Fermi level, indicating the possibility of negative electron affinity at the edges.

Numerical analysis of terahertz surface plasmon polaritons propagating in a parallel plate configuration

In this paper, we present numerical analysis of terahertz (THz) surface plasmon polaritons propagating in a parallel plate configuration. A planar metal surface has the ability to support loosely bound surface waves, called Zenneck waves at terahertz frequencies. Two parallel metal plates separated by a narrow vacuum region can lead to the highly confined terahertz surface plasmon modes at specific frequencies. The frequency of the terahertz mode can be changed with a change in the gap between the plates. Further, we observed that the carrier concentration of plates strongly effect the frequency of the terahertz mode as well as its properties. We have examined in detail the dispersion properties of the terahertz surface plasmons supported by the parallel plate configuration with a varying gap width as well as carrier density of the plates.

Three-layer model for the surface second-harmonic generation yield including multiple reflections

We present the three-layer model to calculate the surface second-harmonic generation (SSHG) yield. This model considers that the surface is represented by three regions or layers. The first layer is the vacuum region with a dielectric function ${\ensuremath{\epsilon}}_{v}(\ensuremath{\omega})=1$ from where the fundamental electric field impinges on the material. The second layer is a thin layer $(\ensuremath{\ell})$ of thickness $d$ characterized by a dielectric function ${\ensuremath{\epsilon}}_{\ensuremath{\ell}}(\ensuremath{\omega})$, and it is in this layer where the SSHG takes place. The third layer is the bulk region denoted by $b$ and characterized by ${\ensuremath{\epsilon}}_{b}(\ensuremath{\omega})$. Both the vacuum and bulk layers are semi-infinite. The model includes the multiple reflections of both the fundamental and the second-harmonic (SH) fields that take place at the thin layer $\ensuremath{\ell}$. We obtain explicit expressions for the SSHG yield for the commonly used $s$ and $p$ polarizations of the incoming $1\ensuremath{\omega}$ and outgoing $2\ensuremath{\omega}$ electric fields, where no assumptions for the symmetry of the surface are made. These symmetry assumptions ultimately determine which components of the surface nonlinear second-order susceptibility tensor $\mathbf{\ensuremath{\chi}}(\ensuremath{-}2\ensuremath{\omega};\ensuremath{\omega},\ensuremath{\omega})$ are different from zero, and thus contribute to the SSHG yield. Then, we particularize the results for the most commonly investigated surfaces, the (001), (110), and (111) crystallographic faces, taking their symmetries into account. We use the three-layer model and compare it against the experimental results of a Si(111)$(1\ifmmode\times\else\texttimes\fi{}1)$:H surface, as a test case, and use it to predict the SSHG yield of a Si(001)$(2\ifmmode\times\else\texttimes\fi{}1)$ surface.

Growth of CdTe on Si(100) surface by ionized cluster beam technique: Experimental and molecular dynamics simulation

II–VI semiconductor CdTe was grown on the Si(100) substrate surface by the ionized cluster beam (ICB) technique. In the ICB method, when vapors of solid materials such as CdTe were ejected through a nozzle of a heated crucible into a vacuum region, nanoclusters were created by an adiabatic expansion phenomenon. The clusters thus obtained were partially ionized by electron bombardment and then accelerated onto the silicon substrate at 473K by high potentials. The cluster size was determined using a retarding field energy analyzer. The results of X-ray diffraction measurements indicate the cubic zinc blende (ZB) crystalline structure of the CdTe thin film on the silicon substrate. The CdTe thin film prepared by the ICB method had high crystalline quality. The microscopic processes involved in the ICB deposition technique, such as impact and coalescence processes, have been studied in detail by molecular dynamics (MD) simulation.

On plasma edge ideal MHD stability/instability condition in Mercier stable magnetic hill configurations

The stability of peeling modes in zero net current stellarator plasma is studied in high poloidal mode number m 1 approximation. The vacuum region solution is taken into account. Under these conditions in Mercier stable magnetic hill plasmas internal peeling modes are stable. External peeling modes can be unstable, but several limitations on them are found. It is shown that an analytically derived pressure gradient threshold is in reasonable agreement with the experimental observations and numerical calculations. The threshold decreases with increasing poloidal mode number m. It is shown, however, that higher modes may be stabilized due to finite ion Larmor radius effects. For the sake of definiteness, we have investigated peeling mode behavior in Mercier unstable plasma. It is shown that both external and internal peeling modes can be unstable in this regime. However, external and internal peeling modes in this case are definitely different.

(Invited) A First-Principles Molecular Dynamics Study on Active Sites on Metal Nano Particles: Application of the Compressed Gas Model

The first-principles Molecular Dynamics (FPMD) is applied to investigate gas adsorption onto surfaces of metal nano particles. Herein we focus on catalytic reactions for ammonia synthesis and decomposition. Some Ru nano clusters are prepared as a model of the catalyst, and gas adrosptions of the H2, N2, and NH3 molecules are investigated. In order to do a conceptually unbiased mechanistic study, a natural and reasonable strategy would be to make many models to be investigated by “electronic-structure simulations”. In this study, we apply the compressed gas model in which distribution of gas molecule in high pressure simulations are taken into account. The compressed gas cluster is inserted in the simulation box containing a metal nano particle. Because of the compressed nature of the “ball” of the gas molecules, they automatically diffuse into the vacuum region and hit on the nano particle surface with velocity. By repeating this simulation, we could identify some characteristics of the adsorption sites on the metal nano particle and the gas molecule dependence in the adsorption behavior. It was found that the H2 adsorption should be structure insensitive, while the N2 and NH3 adsorptions should be structure sensitive. In the simulation of the NH3 adsorption, we observed formation of the H2 molecule from NH­ 3. It was found that the kink plays an important role as a reaction center of the H2 formation. In the simulation, H2 was yielded in a mechanism similar to the Eley-Rideal mechanism.