Cutoff Wavenumber Research Articles

The properties of strong couple bound polaron in monolayer graphene

Based on the Hamiltonian of the interaction energy between electron on the surface of the graphene and longitudinal acoustic phonon on the surface of the substrate, the paper studies the properties of strong couple polaron in monolayer graphene considering the coulomb doping problem. The conventional Lee-Low-Pine unitary transformation method and linear combination operator method are used to calculate the ground state energy of the polaron. The results show that the ground state energy of the system has a linear relationship with the magnetic field strength, the cut-off wave number, the coulomb bound parameter, the distance between the graphene and the substrates, meanwhile, the ground state energy will split into two branches near the Dirac point.

The finite probe size effect in fluctuation measurements; application to dusty plasmas

The effect of the finite probe size in plasma fluctuation measurements is revisited for dusty plasmas, where it has been argued that dust leads to a significant low-frequency enhancement in the spectral densities of ion density fluctuations, which can constitute the physical basis of a dust diagnostic technique. Theoretical predictions for the spectral modifications are presented and the dust acoustic mode contribution is analysed. The finite probe size effect is treated within the volume average approach, which introduces geometry dependent form factors that are calculated for spherical and cylindrical probes. The volume average approach is compared with the typically employed cutoff wavenumber approximation for various dust and plasma parameters. The contribution of temperature fluctuations to the spectral density of current fluctuations is also evaluated.

Spatio-spectral concentration of convolutions

Differential equations may possess coefficients that vary on a spectrum of scales. Because coefficients are typically multiplicative in real space, they turn into convolution operators in spectral space, mixing all wavenumbers. However, in many applications, only the largest scales of the solution are of interest and so the question turns to whether it is possible to build effective coarse-scale models of the coefficients in such a manner that the large scales of the solution are left intact. Here we apply the method of numerical homogenization to deterministic linear equations to generate sub-grid-scale models of coefficients at desired frequency cutoffs. We use the Fourier basis to project, filter and compute correctors for the coefficients. The method is tested in 1D and 2D scenarios and found to reproduce the coarse scales of the solution to varying degrees of accuracy depending on the cutoff. We relate this method to mode-elimination Renormalization Group (RG) and discuss the connection between accuracy and the cutoff wavenumber. The tradeoff is governed by a form of the uncertainty principle for convolutions, which states that as the convolution operator is squeezed in the spectral domain, it broadens in real space. As a consequence, basis sparsity is a high virtue and the choice of the basis can be critical.

ALmost EXact boundary conditions for transient Schrödinger–Poisson system

For the Schrodinger-Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. 1, yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.

The Magnetic Effect of Polaron in Monolayer Graphene

The properties of the magnetopolaron in monolayer graphene are studied. The energies of the ground and first excited states of the monolayer graphene are obtained by linear combination operator and the conventional Lee–Low–Pine unitary transformation. Numerical calculations indicate that the energies will split into two branches, the ground splitting energy of polaron near the Dirac point will increase with increasing magnetic field strength and the Debye cut-off wavenumber (DCOW), and the first excited state energy will also increase with increasing magnetic field strength and the logarithm of the DCOWs.

A Viscous Potential Flow model for core-annular flow

Stability of core-annular flow has been studied extensively using spectral and pseudo-spectral methods. These methods, being computationally intensive, render the understanding of the role of each parameter on stability numerically cumbersome. Viscous Potential Flow (VPF) theory offers itself as an alternative analytical tool towards understanding stability of multiphase flows. VPF theory is known to successfully predict the stability features of capillary instability associated with jets flowing in an infinite ambient fluid analytically. In this work, we investigate the applicability of VPF theory in capturing the onset of capillary instability in core-annular flow (CAF). Here, first a VPF stability analysis of core-annular flow is performed for a base state satisfying VPF equations such that each phase has a uniform velocity (plug flow). This potential flow assumption of the base state as well as perturbed variables helps us to obtain a completely analytical dispersion relation to the problem. It is shown that the results of the analysis agree with the published literature of unconfined jets under different limiting conditions. Using VPF also helps to understand the effect of each parameter on the stability features of the system. To improve the accuracy of VPF analysis, we incorporate viscous pressure correction to ensure that continuity of tangential velocity and tangential stresses at the fluid–fluid interface are satisfied in an average sense. We show that the viscous correction to the irrotational pressure results in the same dispersion relation as that obtained by the method of energy dissipation. However, it is shown that this analytical dispersion relation is unable to predict the stability features of CAF even with the inclusion of pressure correction. Next, the stability of CAF is analyzed with laminar core-annular velocity profile as the base state. The results of this VPF analysis are compared with the stability of the complete CAF problem. It is shown that the predictions of the VPF stability analysis for the cut-off wavenumber and the fastest growing wavenumber associated with capillary instability are in close agreement with that of the complete problem for low Reynolds number and Weber number regimes.

Nonlocal response of hyperbolic metasurfaces.

We analyze and model the nonlocal response of ultrathin hyperbolic metasurfaces (HMTSs) by applying an effective medium approach. We show that the intrinsic spatial dispersion in the materials employed to realize the metasurfaces imposes a wavenumber cutoff on the hyperbolic isofrequency contour, inversely proportional to the Fermi velocity, and we compare it with the cutoff arising from the structure granularity. In the particular case of HTMSs implemented by an array of graphene nanostrips, we find that graphene nonlocality can become the dominant mechanism that closes the hyperbolic contour - imposing a wavenumber cutoff at around 300k(0) - in realistic configurations with periodicity L<π/(300k(0)), thus providing a practical design rule to implement HMTSs at THz and infrared frequencies. In contrast, more common plasmonic materials, such as noble metals, operate at much higher frequencies, and therefore their intrinsic nonlocal response is mainly relevant in hyperbolic metasurfaces and metamaterials with periodicity below a few nm, being very weak in practical scenarios. In addition, we investigate how spatial dispersion affects the spontaneous emission rate of emitters located close to HMTSs. Our results establish an upper bound set by nonlocality to the maximum field confinement and light-matter interactions achievable in practical HMTSs, and may find application in the practical development of hyperlenses, sensors and on-chip networks.

Gravity data inversion for Moho depth modeling in the Hellenic area

The main objective of this study is the determination of the Moho discontinuity in the Hellenic area based on gravity data inversion. High-resolution (2 arcmin) and accuracy (±2 to ±3 mGal) gravity data were used in the computations following the Parker–Oldenburg iterative method, and a low-pass filter was applied to gravity information towards the convergence of the final solution. To determine the cut-off wavenumber of the filter, we tested different mean depths and density contrasts of the crust and the mantle (Mohorovicic discontinuity). The selected density contrast and mean depth of the Mohorovicic discontinuity are those which agree with the Moho depth interpreted from deep seismic imaging data. By comparing the Moho depth estimated, covering both land and marine areas and including the Ionian and Aegean Sea, with those interpreted from previous studies, it is shown that our solution is consistent with the available seismic data interpretation. Moreover, the resolution of the gravity data and the appropriate filtering used in this study contributed to the representation of local features of the Moho discontinuity. Finally, area-dependent discrepancies detected between the Moho depths of the current solution and those derived from previous studies are extensively discussed.

Jeans instability of a dusty plasma with dust charge variations

The effect of the dust charge variations on the stability of a self-gravitating dusty plasma has been theoretically investigated. The dispersion relation for the dust-acoustic waves in a self-gravitating dusty plasma is obtained. It is shown that the dust charge variations have significant effects. It increases the growth rate of instability and the instability cutoff wavenumbers. It is found that by increasing the value of the ions temperature and the absolute value of the equilibrium dust charge, the cutoff wavenumber decreases and the stability region is extended.

Tunable surface plasmon instability leading to emission of radiation

We propose a new approach for energy conversion from a dc electric field to tunable terahertz emission based on hybrid semiconductors by combining two-dimensional (2D) crystalline layers and a thick conducting material with possible applications for chemical analysis, security scanning, medical (single-molecule) imaging, and telecommunications. The hybrid nano-structure may consist of a single or pair of sheets of graphene, silicene, or a 2D electron gas. When an electric current is passed through a 2D layer, we discover that two low-energy plasmon branches exhibit a characteristic loop in their dispersion before they merge into an unstable region beyond a critical wave vector qc. This finite qc gives rise to a wavenumber cutoff in the emission dispersion of the surface plasmon induced instability and emission of radiation (spiler). However, there is no instability for a single driven layer far from the conductor, and the instability of an isolated pair of 2D layers occurs without a wavenumber cutoff. The wavenumber cutoff is found to depend on the conductor electron density, layer separation, distances of layers from the conductor surface, and the driving-current strength.

Complex plasma in g×B configurations: Stability switching and stationary structure

In a low-pressure magneto-gravitated complex plasma, the stability state of dust gravitational drift wave is switched at a critical wavenumber and the propagating dust magneto-gravitational drift wave is transformed into an aperiodic stationary structure at a cut-off wavenumber. In this paper, two analytical formulas have been derived for the critical wavenumber of stability switching and the cut-off wavenumber of stationary structure. The critical wavenumber is equal to the ratio of ion plasma frequency to ion streaming velocity and the cut-off wavenumber is proportional to the ratio of dust plasma frequency to dust g×B drift velocity. These scaling formulas are in excellent agreement with exact numerical solutions of dispersion relations. These scenarios are expected to be observed in fully magnetized dusty plasma experiments as the next frontier for complex plasma research.

Phonon Transport Characteristics in a Thin Silicon Film

Phonon transport characteristics in thin silicon film are investigated due to temperature disturbance at the film edges. Phonon intensity distribution ratio , where Iomax is the maximum equilibrium intensity, I is the phonon intensity corresponding to acoustics branch at any location and time in the film) and phonon wavelength ratio , where k is the wavenumber, , and kcutoff is the cutoff wavenumber based on the film length, are introduced to assess the effects of quasi-ballistic and ballistic phonons on the film thermal conductivity and specific heat. It is found that phonon intensity ratio due to longitudinal acoustic branch is considerably higher than that of transverse acoustics branch. The influence of phonon wavelength ratio is not significantly high on the intensity ratio due to longitudinal acoustics branch. Reducing the wavelength ratio creates the size effect in the film while lowering thermal conductivity and specific heat of the film, which is more pronounced when the reduction becomes more than 20%.

Effect of Péclet number on miscible rectilinear displacement in a Hele-Shaw cell.

The influence of fluid dispersion on the Saffman-Taylor instability in miscible fluids has been investigated in both the linear and the nonlinear regimes. The convective characteristic scales are used for the dimensionless formulation that incorporates the Péclet number (Pe) into the governing equations as a measure for the fluid dispersion. A linear stability analysis (LSA) is performed in a similarity transformation domain using the quasi-steady-state approximation. LSA results confirm that a flow with a large Pe has a higher growth rate than a flow with a small Pe. The critical Péclet number (Pec) for the onset of instability for all possible wave numbers and also a power-law relation of the onset time and most unstable wave number with Pe are observed. Unlike the radial source flow, Pec is found to vary with t0. A Fourier spectral method is used for direct numerical simulations (DNS) of the fully nonlinear system. The power-law dependence of the onset of instability ton on Pe is obtained from the DNS and found to be inversely proportional to Pe and it is in good agreement with that obtained from the LSA. The influence of the anisotropic dispersion is analyzed in both the linear and the nonlinear regimes. The results obtained confirm that for a weak transverse dispersion merging happens slowly and hence the small wave perturbations become unstable. We also observ that the onset of instability sets in early when the transverse dispersion is weak and varies with the anisotropic dispersion coefficient, ε, as ∼√[ε], in compliance with the LSA. The combined effect of the Korteweg stress and Pe in the linear regime is pursued. It is observed that, depending on various flow parameters, a fluid system with a larger Pe exhibits a lower instantaneous growth rate than a system with a smaller Pe, which is contrary to the results when such stresses are absent.

The Effect of Deformation Potential Magnetopolaron in Graphene

The effects of a deformation potential on a magnetopolaron in monolayer graphene are investigated using the method of linear-combination operators and a simple unitary transformation based on the carrier–acoustic phonon coupling. We find that the splitting of the zero-energy Landau level occurs due to the magnetopolaron effect. The magnitude of splitting energy as functions of the magnetic field and the Debye cut-off wave number of acoustic phonon are discussed in the weak and strong coupling limit, respectively. The obtained results are meaningful for understanding the important role of carrier–phonon coupling in determining the fundamental properties of graphene.

Broadband, non‐destructive characterisation of PEC‐backed materials using a dual‐ridged‐waveguide probe

A new probe which utilises a dual-ridged waveguide to provide broadband, non-destructive (ND) material characterisation measurements of a perfect electric conductor (PEC)-backed material is introduced. The new probe possesses a bandwidth similar to existing coaxial probes and is structurally robust like rectangular waveguide probes. The combinations of these two qualities make it especially attractive for ND inspection/evaluation applications in the field. The theoretical development of the dual-ridged-waveguide probe is discussed. A magnetic field integral equation is derived by applying Love's equivalence theorem and enforcing the continuity of transverse fields at the dual-ridged-waveguide aperture. The magnetic field integral equation is then solved for the theoretical reflection coefficient using the method of moments. The permittivity and permeability of the material under test are found by minimising the root-mean-square difference between the theoretical and measured reflection coefficients using non-linear least squares. To validate the new probe, experimental results are presented of a magnetic absorbing material comparing results obtained using the new probe with those obtained using a traditional, destructive technique. The probe's sensitivity to sample thickness, flange-plate thickness, cutoff wavenumber and measured S-parameter uncertainties is also investigated.

Inertial effects of miscible viscous fingering in a Hele-Shaw cell

The effects of inertia on miscible displacements in a Hele-Shaw cell are analyzed. Both linear stability analysis and nonlinear simulations are performed. The results reveal that inertia tends to attenuate viscous fingering. An analysis based on the quasi-steady-state approximation (QSSA) revealed that the growth rate at initial time decreases monotonically as a modified Reynolds number Re* increases, while the most dangerous wavenumber tends to shift toward smaller values. It was also found that the cutoff wavenumber is not affected by inertia and that inertial effects are very limited for longwave instabilities. Initial value calculations extended the QSSA and confirmed the decrease of the growth rate with Re* for long times. Full nonlinear simulations based on a spectral method showed that inertial effects tend to delay the initial development of the instability and result in wider fingers at later breakthrough times. Furthermore, a quantitative analysis of the mixing area shows that inertia can extend the dispersive regime. A re-scaling of the mixing area and time is proposed and the curves at any Peclet and modified Reynolds numbers were superposed onto a single universal curve. With this, the mixing area of any flow with different inertial effects can be predicted.

Length scale of density waves in the gravitational flow of fine grains in pipes

Gravitational flow of grains in pipes is frequently encountered in industry. When the grains and pipes are size-constrained, granular flow may result in density waves consisting of alternate high- and low-compactness regions. This paper discusses the length scale of density waves that appear when fine grains fall vertically in pipes. A one-dimensional model and a linear stability analysis of the model are presented. The analysis suggests the presence of long-wavelength instability for the most unstable mode, moreover, a cut-off wavenumber from which the length scale is estimated. Finally, the model results are compared to experimental data.

Fast-sausage oscillations in coronal loops with smooth boundary

Aims. The effect of the transition layer (shell) in nonuniform coronal loops with a continuous radial density profile on the properties of fast-sausage modes are studied analytically and numerically. Methods. We modeled the coronal waveguide as a structured tube consisting of a cord and a transition region (shell) embedded within a magnetic uniform environment. The derived general dispersion relation was investigated analytically and numerically in the context of frequency, cut-off wave number, and the damping rate of fast-sausage oscillations for various values of loop parameters. Results. The frequency of the global fast-sausage mode in the loops with a diffuse (or smooth) boundary is determined mainly by the external Alfven speed and longitudinal wave number. The damping rate of such a mode can be relatively low. The model of coronal loop with diffuse boundary can support a comparatively low-frequency, global fast-sausage mode of detectable quality without involving extremely low values of the density contrast. The effect of thin transition layer (corresponds to the loops with steep boundary) is negligible and produces small reductions of oscillation frequency and relative damping rate in comparison with the case of step-function density profile. Seismological application of obtained results gives the estimated Alfven speed outside the flaring loop about 3.25 Mm/s.

Investigation of numerical viscosities and dissipation rates of second-order TVD-MUSCL schemes for implicit large-eddy simulation

Monotonically integrated large-eddy simulation (MILES) approach utilizes the dissipation inherent to shock-capturing schemes to emulate the role played by explicit subgrid-scale eddy diffusivity at the high-wavenumber end of the turbulent energy spectrum. In the current study, a novel formulation is presented for quantifying the numerical viscosity inherent to Roe-based second-order TVD-MUSCL schemes for the Euler equations. Using this formulation, the effects of numerical viscosity and dissipation rate on implicit large-eddy simulations of turbulent flows are investigated. At first, the three-dimensional (3-D) finite-volume extension of the original Roe's flux, including Roe's Jacobian matrix, is presented. The fluxes are then extended to second-order using van Leer's MUSCL extrapolation technique. Starting from the 3-D Roe-MUSCL flux, an expression is derived for the numerical viscosity as a function of flux limiter and characteristic speed for each conserved variable, distance between adjacent cell centers, and a scaling parameter. Motivated by Thornber et al. [16] study, the high numerical viscosity inherent to TVD-MUSCL schemes is mitigated using a z-factor that depends on local Mach number. The TVD limiters, along with the z-factor, were initially applied to the 1-D shock-tube and 2-D inviscid supersonic wedge flows. Spatial profiles of numerical viscosities are plotted, which provide insights into the role of these limiters in controlling the dissipative nature of Roe's flux while maintaining monotonicity and stability in regions of high gradients. Subsequently, a detailed investigation was performed of decaying homogeneous isotropic turbulence with varying degrees of compressibility. Spectra of numerical viscosity and dissipation rate are presented, which clearly demonstrate the effectiveness of the z-factor both in narrowing the wavenumber range in which dissipation occurs, and in shifting the location of dissipation peak closer to the cut-off wavenumber. The present z-factor approach of limiting numerical viscosities is shown to perform as well as, or even better in some cases, than the Thornber et al. approach of directly limiting velocity jumps at a cell interface.

Dust magneto-gravitational drift wave in g×B configuration

The dispersion relation of electrostatic waves in a magnetized complex plasma under gravity is presented. It is assumed that the waves propagate perpendicular to the external fields. The effects of weak electric field, neutral drag force, and ion drag force are also taken into account. The dispersion relation is numerically examined in an appropriate parameter space in which the gravity plays the dominant role in the dynamics of magnetized microparticles. The numerical results show that an unstable low frequency drift wave can be developed in the long wavelength limit. This unstable mode is transformed into an aperiodic stationary structure at a cut-off wavenumber. Furthermore, the influence of the external fields on the dispersion properties is analyzed. It is shown that the instability is essentially due to the E×B drift motion of plasma particles. However, in the absence of weak electric field, the g×B drift motion of microparticles can cause the instability in a wide range of wavenumbers. It is also found that by increasing the magnetic field strength, the wave frequency is first increased and then decreased. This behaviour is explained by the existence of an extremum point in the dust magneto-gravitational drift velocity.