Density Corrugations Research Articles

Limit cycle oscillations, response time, and the time-dependent solution to the Lotka–Volterra predator–prey model

In this work, the time-dependent solution for the Lotka–Volterra predator–prey model is derived with the help of the Lambert W function. This allows an exact analytical expression for the period of the associated limit cycle oscillations and also for the response time between predator and prey population. These results are applied to the predator–prey interaction of zonal density corrugations and turbulent particle flux in gyrokinetic simulations of the collisionless trapped-electron mode turbulence. In the turbulence simulations, the response time is shown to increase when approaching the linear threshold, and the same trend is observed in the Lotka–Volterra model.

Formation of density corrugations due to zonal flow in wave-kinetic framework

The formation of density corrugation due to zonal flow, so-called zonal staircase, is investigated theoretically, based on the wave-kinetic framework. The wave-kinetic simulation is performed, considering the profile corrugation and the turbulence trapping mechanism, where the profile corrugation changes the growth rate and the dispersion relation of turbulence. The zonal density is generated by the modulation of particle transport. We obtain the analytical expression for the zonal density, which determines the staircase height. It is found that the amplitude normalized by the ambient density can be comparable to the zonal flow normalized by the diamagnetic drift velocity. The key effect that determines the turbulence profile is found to be the phenomenon of turbulence trapping by zonal flow, while the profile corrugation due to zonal density has weaker effects. Thus, turbulence is localized where the flow curvature is negative, which leads to a flattening of the density profile through the enhancement of particle transport. This fact clearly shows that the effect of turbulence trapping dominates the density gradient dependence of the local linear instability.

A unified theory of zonal flow shears and density corrugations in drift wave turbulence

A unified theory of zonal flow shears and density corrugations in drift wave turbulence is presented. Polarization and density advection beat excitation are studied in combination with modulational response. Noise is driven by two-time flux correlation. While the effective zonal flow eddy viscosity can go negative, the zonal diffusivity is positive definite. There is no inverse cascade of density corrugation. The connection between avalanches and corrugations is discussed. The zonal cross-correlation is identified and calculated. Conditions for alignment of zonal shears and corrugation gradients are determined, and the implications for staircase structure are discussed. We show that the synergy of beat noise and modulational effects is stronger than either alone. Strong zonal flows can be excited well below the modulational instability threshold. In the context of L–H transition, zonal noise quenches turbulence overshoot by eliminating the threshold for zonal flow excitation. The power threshold for L–H transition is lowered.

Zonal profile corrugations and staircase formation: Role of the transport crossphase

Recently, quasi-stationary structures called E × B staircases were observed in gyrokinetic simulations, in all transport channels [Dif-Pradalier et al. Phys. Rev. Lett. 114, 085004 (2015)]. We present a novel analytical theory—supported by collisional drift-wave fluid simulations—for the generation of density profile corrugations (staircase), independent of the action of zonal flows: turbulent fluctuations self-organize to generate quasi-stationary radial modulations Δθk(r,t) of the transport crossphase θk between density and electric potential fluctuations. The radial modulations of the associated particle flux drive zonal corrugations of the density profile via a modulational instability. In turn, zonal density corrugations regulate the turbulence via nonlinear damping of the fluctuations.

Three-dimensional modeling of chromospheric spectral lines in a simulated active region

Context. Because of the complex physics that governs the formation of chromospheric lines, interpretation of solar chromospheric observations is difficult. The origin and characteristics of many chromospheric features are, because of this, unresolved. Aims. We focus on studying two prominent features: long fibrils and flare ribbons. To model these features, we use a 3D magnetohydrodynamic simulation of an active region, which self-consistently reproduces both of these features. Methods. We modeled the Hα, Mg II k, Ca II K, and Ca II 8542 Å lines using the 3D non-LTE radiative transfer code Multi3D. To obtain non-LTE electron densities, we solved the statistical equilibrium equations for hydrogen simultaneously with the charge conservation equation. We treated the Ca II K and Mg II k lines with partially coherent scattering. Results. This simulation reproduces long fibrils that span between the opposite-polarity sunspots and go up to 4 Mm in height. They can be traced in all lines owing to density corrugation. In contrast to previous studies, Hα, Mg II h&k, and Ca II H&K are formed at similar height in this model. Although some of the high fibrils are also visible in the Ca II 8542 Å line, this line tends to sample loops and shocks lower in the chromosphere. Magnetic field lines are aligned with the Hα fibrils, but the latter holds to a lesser extent for the Ca II 8542 Å line. The simulation shows structures in the Hα line core that look like flare ribbons. The emission in the ribbons is caused by a dense chromosphere and a transition region at high column mass. The ribbons are visible in all chromospheric lines, but least prominent in Ca II 8542 Å line. In some pixels, broad asymmetric profiles with a single emission peak are produced similar to the profiles observed in flare ribbons. They are caused by a deep onset of the chromospheric temperature rise and large velocity gradients. Conclusions. The simulation produces long fibrils similar to what is seen in observations. It also produces structures similar to flare ribbons despite the lack of nonthermal electrons in the simulation. The latter suggests that thermal conduction might be a significant agent in transporting flare energy to the chromosphere in addition to nonthermal electrons.

Quantum Ferrofluid Turbulence.

We study the elementary characteristics of turbulence in a quantum ferrofluid through the context of a dipolar Bose gas condensing from a highly nonequilibrium thermal state. Our simulations reveal that the dipolar interactions drive the emergence of polarized turbulence and density corrugations. The superfluid vortex lines and density fluctuations adopt a columnar or stratified configuration, depending on the sign of the dipolar interactions, with the vortices tending to form in the low-density regions to minimize kinetic energy. When the interactions are dominantly dipolar, the decay of the vortex line length is enhanced, closely following a t^{-3/2} behavior. This system poses exciting prospects for realizing stratified quantum turbulence and new levels of generating and controlling turbulence using magnetic fields.

The non–storm time corrugated upper thermosphere: What is beyond MSIS?

AbstractObservations in the recent decade have revealed many thermospheric density corrugations/perturbations under nonstorm conditions (Kp < 2). They are generally not captured by empirical models like Mass Spectrometer Incoherent Scatter (MSIS) but are operationally important for long‐term orbital evolution of Low Earth Orbiting satellites and theoretically for coupling processes in the atmosphere‐ionosphere system. We review these density corrugations by classifying them into three types which are driven respectively by the lower atmosphere, ionosphere, and solar wind/magnetosphere. Model capabilities in capturing these features are discussed. A summary table of these corrugations is included to provide a quick guide on their magnitudes, occurring latitude, local time, and season.

Graphene on Ni(111): Electronic Corrugation and Dynamics from Helium Atom Scattering.

Using helium atom scattering, we have studied the structure and dynamics of a graphene layer prepared in situ on a Ni(111) surface. Graphene/Ni(111) exhibits a helium reflectivity of ∼20% for a thermal helium atom beam and a particularly small surface electron density corrugation ((0.06 ± 0.02) Å peak to peak height). The Debye–Waller attenuation of the elastic diffraction peaks of graphene/Ni(111) and Ni(111) was measured at surface temperatures between 150 and 740 K. A surface Debye temperature of θD = (784 ± 14) K is determined for the graphene/Ni(111) system and θD = (388 ± 7) K for Ni(111), suggesting that the interlayer interaction between graphene and the Ni substrate is intermediary between those for strongly interacting systems like graphene/Ru(0001) and weakly interacting systems like graphene/Pt(111). In addition we present measurements of low frequency surface phonon modes on graphene/Ni(111) where the phonon modes of the Ni(111) substrate can be clearly observed. The similarity of these findings with the graphene/Ru(0001) system indicates that the bonding of graphene to a metal substrate alters the dynamic properties of the graphene surface strongly and is responsible for the high helium reflectivity of these systems.

Tunable and efficient terahertz radiation generation by photomixing of two super Gaussian laser pulses in a corrugated magnetized plasma

A scheme of terahertz (THz) radiation generation is investigated by photo-mixing of two super Gaussian laser beams having different frequencies (ω1, ω2) and wave numbers (k→1, k→2) in a performed corrugated plasma embedded with transverse dc magnetic field. Lasers exert a nonlinear ponderomotive force, imparting an oscillatory velocity to plasma electrons that couples with the density corrugations (n′=nα0eiαz) to generate a strong transient nonlinear current, that resonantly derives THz radiation of frequency ∼ωh (upper hybrid frequency). The periodicity of density corrugations is suitably chosen to transfer maximum momentum from lasers to THz radiation at phase matching conditions ω=ω1−ω2 and k→=k→1−k→2+α→. The efficiency, power, beam quality, and tunability of the present scheme exhibit high dependency upon the applied transverse dc magnetic field along with q-indices and beam width parameters (a0) of super Gaussian lasers. In the present scheme, efficiency ∼10−2 is achieved with the optimization of all these parameters.

Helium-surface interaction potential of Sb(111) from scattering experiments and close-coupling calculations

Helium atom scattering (HAS) was used to study the antimony Sb(111) surface beyond the hard-wall model. HAS angular distributions and drift spectra show a number of selective adsorption resonance features, which correspond to five bound-state energies for He atoms trapped in the surface-averaged He-Sb(111) potential. As their best representation, a 9-3 potential with a depth of $4.4\ifmmode\pm\else\textpm\fi{}0.1$ meV was determined. Furthermore, the charge density corrugation of the surface was analyzed using close-coupling calculations. By using a hybrid potential, consisting of a corrugated Morse potential (short range) and a 9-3 potential (long range), a peak-to-peak corrugation of 17% was obtained. The kinematic focusing effects that occurred were in good agreement with surface phonon dispersion curves from already published density functional perturbation theory calculations.

Corrugations in the Disk of the Edge‐On Spiral Galaxy IC 2233

We recently reported the discovery of a regular corrugation pattern in the H I disk of the isolated, edge-on spiral galaxy IC 2233. Here we present measurements of the vertical structure of this galaxy at several additional wavelengths, ranging from the far-ultraviolet to the far-infrared. We find that undular patterns with amplitude -->5'' ( 250 pc) are visible in a variety of Population I tracers in IC 2233, including the young to intermediate-age stars, the H II regions, and the dust. However, the vertical excursions become less pronounced in the older stellar populations traced by the mid-infrared light. This suggests that the process leading to the vertical displacements may be linked with the regulation of star formation in the galaxy. We have also identified a relationship between the locations of the density corrugations and small-amplitude ( 5 km s?1) velocity undulations in the H I rotation curve. We are able to exclude several possible mechanisms for the origin of the observed corrugations, including tidal interaction from a companion, Parker instabilities, or a galactic bore. Global gravitational instabilities appear to be the most likely explanation, although local perturbations may also be important.

Atomistic Scale Modeling of Factors Affecting the Channel Mobility in 4H-SiC MOSFETs

We have identified the crystal planes of 4H-SiC, interfacing with gate oxide, which will lead to minimum defect density and lowest interface corrugations. The atomic surface density, surface energy, and surface roughness of various crystal planes of 4H-SiC have been computationally characterized using Molecular Dynamics simulations. We have also investigated the screening distances of defects in SiO2 and SiC using a multiscale approach.

Electronic density corrugation and crystal azimuthal orientation effects on energy losses of hydrogen ions in grazing scattering on a Ag(110) surface

We present a detailed study of the energy losses of hydrogen ions that are scattered off an Ag(110) single-crystal surface for primary energies between 1 and 4 keV. We performed measurements for grazing angles as a function of crystal azimuthal orientation, which show large differences in energy losses. Experimental results are discussed by means of trajectory calculations of protons scattered under grazing-incidence conditions on the surface. Using nonlinear models for the stopping power, ab initio crystal structure calculations of the electronic density, and semiclassical simulations, we obtain data that are in very good agreement with experimental results. These simulations allow us to properly take into account the variations of the surface electronic density and hence obtain an accurate description of the energy loss processes for ion scattering along various azimuthal orientations of the target.

Hyperfine spectra of trapped bosons in optical lattices

We calculate the interaction induced inhomogeneous broadening of spectral lines in a trapped Bose gas as a function of the depth of a three-dimensional cubic optical lattice. As observed in recent experiments, we find that the terraced "wedding-cake" structure of Mott plateaus splits the spectrum into a series of discrete peaks. The spectra are extremely sensitive to density corrugations and trap anharmonicities. For example, even when the majority of the cloud is superfluid the spectrum displays discrete peaks.

Electronic stopping of keV nitrogen ions interacting with a Pt(110)(1 × 2) surface—a tool to characterize electronic surfaces

AbstractIon channeling is used to investigate the electronic density corrugation at surfaces by analysing the electronic stopping behaviour of ions scattering grazingly off a clean single crystalline Pt(110)(1 × 2) surface. We use the fact that under these conditions the elastic contribution can be separated from the inelastic energy‐loss processes, which are closely related to the electronic density sampled along the projectiles trajectories. Therefore, we have a direct probe of the surface electronic density structure. Here, experiments and their theoretical interpretation for N+ ions at primary ion energies of 1–10 keV are presented. Multi‐peak features of the energy spectra, depending on the azimuthal surface orientation, are attributed to different particle trajectories. A detailed analysis of trajectory calculations affords an unambiguous assignment of the observed peak structures to three trajectory classes, each sampling specific energy losses. The comparison of the experimental energy‐loss values with results obtained from a surface‐adapted energy‐loss model for ion scattering that includes the electron density allows us to investigate the electronic surface of the sample. The results are compared with calculated surface electron density contours. Reasonable agreement is obtained, showing that the presented method is suitable to characterize the electronic density structure at crystalline surfaces. Copyright © 2005 John Wiley & Sons, Ltd.

On the origin of the surface anisotropy in optical second harmonic generation from stepped Al(001) surfaces

A microscopic calculation of the anisotropic nonlinear optical surface response of vicinal Al(001) is performed within a two-band model. As previously found for flat Al(111), the tangential surface current exhibits a surprisingly large penetration depth. This large penetration depth, however, does not necessarily imply a weak sensitivity of the anisotropic response to surface conditions. The anisotropy resulting from the nonsymmetric stacking of the lattice planes parallel to the macroscopic surface is very much larger than the anisotropy due to the nonsymmetric density corrugation at stepped jellium surfaces.

Evidence of Quantum Motion of Hydrogen on Pd(111) in He-Diffraction data

ABSTRACTWe present elastic He-beam scattering data of the Pd(111)/H system. Diffraction intensities were measured as a function of surface temperature in the range 140°K–320°K. Two remarkable features are observed : the first is the presence of C3v symmetry at (1 × 1) saturation coverage (140°K) and its transformation to C6v symmetry at lower coverages (270°K). The second feature is the anomalous attenuation of the specular He beam accompanying this transformation. Taken together these features provide strong evidence of a fundamental change in the surface charge density corrugation. A classical interpretation of the motion of hydrogen either fails to reproduce the measured attenuation or leads to contradictory and unphysical conclusions regarding the H-metal bond length or surface equilibrium. An alternative quantum mechanical interpretation is developed and is shown to provide consistent and satisfactory explanation of the measurements.

Effect of lattice vibrations on scanning tunnelling microscope images

Tersoff and Hamann's theory of the scanning tunnelling microscope is used in a preliminary investigation of the effect of lattice vibrations on the atomic scale contour maps generated with this instrument. It is found that appreciable errors in inferred charge density corrugation amplitudes can arise if the mean-square atomic displacements vary significantly across the sample surface.

The interpretation of experimentally derived helium-metal interaction potentials

We show that existing theories which relate the helium-metal potential to the metallic surface charge density do not lead to a unique prediction for the surface charge density profile for a given experimental potential. A simple calculation of the corrugation of the attractive van der Waals potential for Cu(110) and Ag(110) shows that this is a contributary factor and that its inclusion improves the agreement between theories and also between experimental and calculated values for the charge density corrugation amplitude.

The interpretation of experimentally derived helium-metal interaction potentials

We show that existing theories which relate the helium-metal potential to the metallic surface charge density do not lead to a unique prediction for the surface charge density profile for a given experimental potential. A simple calculation of the corrugation of the attractive van der Waals potential for Cu(110) and Ag(110) shows that this is a contributary factor and that its inclusion improves the agreement between theories and also between experimental and calculated values for the charge density corrugation amplitude.