Large Wavenumber Region Research Articles

Partial structure factors derived from coarse-grained phase-separation dynamics on a disordered lattice with density fluctuations

The simplest and most time-efficient phase-separation dynamics simulations are carried out on a disordered lattice to calculate the partial structure factors of coarse-grained A-B binary mixtures. The typical coarse-grained phase-separation models use regular lattices and can describe the local concentrations but cannot describe both local density and concentration fluctuations. To introduce fluctuation for local density in the model, the particle positions from a hard sphere fluid model are determined as disordered lattice points for the model. Then we place the local order parameter as the difference of the concentrations of A and B components on each lattice point. The concentration at each lattice point is time-evolved by discrete equations derived from the Cahn-Hilliard equation. From both fluctuations, Bhatia and Thornton’s structure factor can be accurately calculated. The structure factor for concentration fluctuations at the large wavenumber region gives us the correct mean concentrations of the components. Using the mean concentrations, partial structure factors can be converted from three of Bhatia and Thornton’s structure factors. The present model and procedures can provide a means of analysing the structural properties of many materials that exhibit complex morphological changes.

Spatial instability of double-layer viscoelastic liquid sheets in a viscous gas medium

The spatial instability of double-layer viscoelastic liquid sheets in a viscous gas medium is investigated. A linear stability analysis is used to simplify the governing equations and boundary conditions combined with the Oldroyd-B model for describing the viscoelastic liquid. The growth rate and the cut-off wavenumber have been studied by analyzing the dispersion curve which is based on the spectral collocation method. Moreover, we use the decomposition of growth rate to interpret some special cases. We conclude that the thickness ratio, the liquid density ratio, the liquid viscosity ratio, and the gas-to-liquid viscosity ratio stabilize the liquid sheets, while the gas-to-liquid density ratio, the Reynolds number, and the Weber number destabilize the liquid sheets. The dispersion curves are nearly-identical when the surface tension ratio is smaller than one, while the surface tension ratio is a stabilizing factor when the ratio is larger than one, but the second maximum and the counterintuitive destabilization exist in the large wavenumber region. As specific parameters concerning the viscoelasticity, the elasticity number transforms from the destabilizing factor into the stabilizing factor with the increased Reynolds number in the region nearby the cut-off wavenumber, because the relationship between the change rates of viscous dissipation terms and elasticity terms in the decomposition of the growth rate is varying. Besides, it is discovered that the trend of the change of the growth rate under the varying stress relaxation time ratio is non-monotonic and double-layer liquid sheets are most stable when the stress relaxation time ratio is near 3 (not 1), because the difference between the change rate of the viscous dissipation and the deformation retardation dissipation determines the most stable region (not the elasticity difference), which can also be interpreted with the variation of the energy terms.

Simulation of Acoustic Behavior of Bubbly Liquids with Hybrid Lattice Boltzmann and Homogeneous Equilibrium Models

AbstractHomogeneous equilibrium model (HEM) has been widely used in cavitating flow simulations. The major feature of this model is that a single equation of state (EOS) is proposed to describe the thermal behavior of bubbly liquid, where both kinematic and thermal equilibrium is assumed between two phases. In this paper, the HEM was coupled with multi-relaxation-time lattice Boltzmann model (MRT-LBM) and the acoustic behavior was simulated. Two approaches were applied alternatively: adjusting speed of sound (Buick, J. Phys. A, 2006, 39:13807-13815) and setting real gas EOS. Both approaches result in high accuracy in acoustic speed predictions for different void (gas) volume of fractions. It is demonstrated that LBM could be successfully applied as a Navier-Stokes equation solver for industrial applications. However, further dissipation and dispersion analysis shows that Shan-Chen type approaches of LBM are deficient, especially in large wave-number region.

Finite Larmor radius magnetohydrodynamic analysis of the Rayleigh-Taylor instability in Z pinches with sheared axial flow

The Rayleigh-Taylor (RT) instability in Z pinches with sheared axial flow (SAF) is analyzed using finite Larmor radius (FLR) magnetohydrodynamic theory, in whose momentum equation the FLR effect (also referred to as the effect of gyroviscosity) is introduced through an anisotropic ion (FLR) stress tensor. A dispersion relation is derived for the linear RT instability. Both analytical and numerical solutions of the dispersion equation are given. The results indicate that the short-wavelength modes of the RT instability can be stabilized by a sufficient FLR, whereas the long-wavelength modes can be stabilized by a sufficient SAF. In the small-wavenumber region, for normalized wavenumber K<2.4, the hybrid RT/KH (Kelvin-Helmholtz) instability is shown to be the most difficult to stabilize. However the synergistic effect of the SAF and gyroviscosity can mitigate both the RT instability in the large-wavenumber region (K>2.4) and the hybrid RT/KH instability in the small-wavenumber region. In addition, this synergistic effect can compress the RT instability to a narrow wavenumber region. Even the thorough stabilization of the RT instability in the large-wavenumber region is possible with a sufficient SAF and a sufficient gyroviscosity.

Anisotropy of the horizontal velocity fluctuation field in the large wavenumber region

This paper utilizes meridional and zonal velocity data measured by chaff rockets at a high resolution of 25 m in the 67—96 km region during the MAC/SINE campaign to study the characteristics of the spectra of the meridional and zonal velocity fluctuations. Results suggest that the mean vertical wavenumber spectra have a forked point near vertical wavenumber k = 0.001 m −1 . In the vertical wavenumber region smaller than the forked point, the spectra of the meridional and zonal velocities have approximately the same spectral slope, amplitude, and characteristic vertical wavelength, and agree well with the linear saturated spectral model. In the vertical wavenumber region larger than the forked point, however, the meridional and zonal spectra are inconsistent not only in both slope and amplitude, but also in spectral structure. The differences between the observed meridional and zonal spectra provide observational evidence of azimuthal anisotropy of the velocity fluctuation field in the large vertical wavenumber region in mean sense.

The Scaling Law of Quasi-Geostrophic Turbulence with Weak Energy Dissipation

When a problem without viscosity is considered as an ideal case, a small dissipation term is necessary in many numerical calculations. Quasi-geostrophic turbulence, which is described by the barotropic version of quasi-geostrophic potential vorticity equation, (also called Charney-Hasegawa-Mima equation as an equivalent) is one of these situations: a dissipation term must be added in order to prevent the energy from piling up in the large wavenumber region. Consequently, the total energy decreases gradually, which should be conserved in an ideal situation. In this article, the total energy dissipation rate in quasi-geostrophic turbulence is estimated, based on the assumption that the energy dissipated in this system is equal to the energy transported to the large wavenumber region. This estimation complements the dynamic scaling laws for the quasi-geostrophic turbulence developed by Watanabe et al. (1998): the parameter expressing the total energy dissipation, which was determined from the result of the numerical calculation in their study, is derived from the parameters of the setting of the numerical calculation. This estimation also suggests the means to determine the appropriate artificial hyperviscosity coefficient used in numerical simulations.

Comparison Between Mitigation Effects of the Finite Larmor Radius and Sheared Axial Flow on Rayleigh-Taylor Instability in Z-Pinch Implosions

A magnetohydrodynamic (MHD) formulation is derived to investigate and compare the mitigation effects of both the sheared axial flow and finite Larmor radius (FLR) on the Rayleigh-Taylor (RT) instability in Z-pinch implosions. The sheared axial flow is introduced into MHD equations in a conventional way and the FLR effect into the equations via ∂/∂t → -i(ω + ik2⊥ρ2iΩi), as proposed in our previous paper [Chin. Phys. Lett. 2002 19 217], where k2⊥ ρ2i is referred to FLR effect from the general kinetic theory of magnetized plasma. Therefore the linearized continuity and momentum equations for the perturbed mass-density and velocity include both the sheared axial flow and the FLR effect. It is found that the effect of sheared axial flow with a lower peak velocity can mitigate RT instability in the whole wavenumber region and the effect of sheared axial flow with a higher one can mitigate RT instability only in the large wavenumber region (for normalized wavenumber κ > 2.4): The effect of FLR can mitigate RT instability in the whole wavenumber region and the mitigation effect is stronger than that of the sheared axial flow with a lower peak velocity in the almost whole wavenumber region.

Enhancement of cyclotron absorption of plasma oscillations excited by powerful radio wave below multiple electron gyroharmonics

Theoretical research of increase in the cyclotron absorption of upper-hybrid plasma oscillations generated by a powerful radio wave is presented. Such increase occurs at pump frequencies below the harmonic of electron gyrofrequency due to the transformation of the plasma wave energy into a large wave number region which is formed in a magnetized ionospheric plasma under the action of the spatial dispersion. We suppose that proposed mechanism can result in the experimentally observed effect of additional ionosphere ionization appearance below the electron gyroharmonics and can lead to corresponding asymmetry in the effects of ionosphere artificial airglow and plasma noise enhancement caused by accelerated electrons.

Harmonic wave propagation along a non-principal direction in a pre-stressed elastic plate

In this paper harmonic wave propagation in a pre-stressed, incompressible elastic plate is investigated. Specifically the problem in which one principal direction of the primary deformation is normal to the plate and the direction of propagation is at an angle θ to one of the in-plane principal direction is considered. The dispersion relation is derived in respect of a general strain energy function and numerical solutions presented for a Mooney–Rivlin material. The dispersion curves are shown to be more complex in nature than those associated with propagation along an in-plane principal direction, as the solution arising from the horizontally polarised shear wave does not uncouple. An asymptotic analysis, for high and low wave number, is carried out with the high wave number expansions providing a good approximation to the numerical solution over a large wave number region. The paper also includes an investigation of the effects of changes in the normal Cauchy stress and direction of propagation on the existence of surface waves.

SMALL AMPLITUDE VIBRATIONS OF AN INTERNALLY CONSTRAINED ELASTIC LAYER

Small amplitude vibrations, in the form of infinitesimal harmonic waves, in an incompressible elastic layer are considered. When the layer is additionally subject to the constraint of restricted shear and the associated preferred planes are parallel to the free surface, it is shown that the order of the governing equations of motion is reduced. The implication is that traction free boundary conditions at the upper and lower surfaces of the plate cannot be satisfied. Unlike previous studies, involving fibre inextensibility, it seems that no simple physical interpretation is possible. In an attempt to resolve this anomaly and satisfy the boundary conditions, the constraint is relaxed slightly and the strain energy function expanded as a Taylor series. However, it is found that even in this case the dispersion relation has no solutions above a certain wave speed, this usually occurring in the low wavenumber regime. It is verified analytically that no low wavenumber phase speed limit exists. It is postulated that the reason for this rather unusual behaviour is attributable to the rate of shearing. In the high wavenumber regime asymptotic expansions are obtained which give phase speed as a function of wavenumber and harmonic number. These expansions are shown to provide excellent agreement with the numerical solution over a remarkably large wavenumber region.

Charge Excitations in Doped Mott Insulator in One Dimension

The doped Mott insulator in one dimension has been studied based on the phase Hamiltonian with the Umklapp scattering process, in which the charge degree of freedom is described by the quantum sine-Gordon model. The well-known equivalence between the quantum sine-Gordon model and the massive Thirring model for the spinless fermion makes it clear that the Mott-Hubbard gap originates from the Umklapp scattering process as was indicated by Emery and Giamarchi. Compressibility, density-density correlation function, frequency dependence of optical conductivity and Drude weight have been calculated in the presence of the impurity scattering treated in the self-consistent Born approximation. It is seen that there exists a crossover behavior in the spectral weight of charge excitations: the acoustic mode is dominant in small wave number region while the optical excitations across the Mott-Hubbard gap lie in large wave number region and that this crossover wave number is reduced as the Mott transition is approached.

Coupled transverse modulational instability of electron cyclotron waves

Transverse modulation instabilities for single and double electron cyclotron waves in finite and infinite media are investigated. This research shows that there is a intensity threshold that depends on the strength of external magnetic field. The growth rate of instability decreases as the external magnetic field strength increases. In finite media, the threshold for absolute transverse modulational instability of counterpropagating waves is increased by the external magnetic field in the small transverse wave number region. However, in large wave number region, the threshold depends scarcely on the external magnetic field.

Self-organization in three-dimensional compressible magnetohydrodynamic flow

A three-dimensional self-organization process of a compressible dissipative plasma with a velocity-magnetic field correlation is investigated in detail by means of a variational method and a magnetohydrodynamic simulation. There are two types of relaxation, i.e., fast relaxation in which the cross helicity is not conserved and slow relaxation in which the cross helicity is conserved approximately. In the slow relaxation case the cross helicity consists of two components with opposite sign that have almost the same amplitude in the large wavenumber region. In both cases the system approaches a high correlation state, dependent on the initial condition. These results are consistent with observational data of the solar wind. Selective dissipation of magnetic energy, normal cascade of magnetic energy spectrum, and inverse cascade of magnetic helicity spectrum are observed for the sub-Alfvénic flow case, as was observed previously for the zero-flow case. When the flow velocity is super-Alfvénic, the relaxation process is altered significantly from the zero-flow case.

Three‐dimensional ray tracing of electrostatic cyclotron harmonic waves and Z mode electromagnetic waves in the magnetosphere

Three dimensional ray tracing is made for electrostatic electron cyclotron harmonic waves and Z mode electromagnetic waves in the earth magnetosphere, using the hot plasma dispersion relation. For a large wave number region, the so‐called electrostatic approximation for the dispersion relation can be used to trace the ray paths. The necessary initial conditions for an electrostatic electron cyclotron harmonic mode wave to be continuously converted to a Z mode electromagnetic mode wave can be investigated by the electrostatic approximation. Only the waves generated in the very vicinity of the geomagnetic equatorial plane can propagate over a long distance. The waves can be converted to Z mode if the initial wave normal direction lies near the geomagnetic meridian plane. The algorithm of ray tracing using the full hot plasma dispersion relation is also developed. A complete traverse of the wave starting from the electrostatic electron cyclotron harmonic mode to the Z mode can only be confirmed by the ray tracing based on the full hot plasma dispersion relation. A possibility of conversion from the electrostatic mode finally to a free space electromagnetic mode can also be investigated by this ray tracing. These results are not contradictory with the conversion mechanism for the generation of escaping continuum radiation in the earth magnetosphere.

Two-Photon Polarization Spectroscopy in CuCl

Highly sensitive momentum-space spectroscopy, named two-photon polarization spectroscopy (TPPS), is presented in the Z 3 exciton resonant region of CuCl. This spectroscopy is based on the induced optical anisotropy associated with the formation of \( \varGamma_{1}\) excitonic molecules (EM's). By this method the following facts are confirmed: the upper branch polaritons (UBP's) and the lower branch polaritons (LBP's) coexist in the wide energy range above the longitudinal exciton energy; the conversion of UBP into LBP occurs in the reflection at the sample boundary; the EM relaxation depends on the wave number in the large wave number region. From the quantitative analysis of the spectra, it has been found that the damping of the Z 3 exciton depends strongly on its energy in the L-T gap region. The prospects of the ABC problem are also discussed.

Application of Kubo's Modified Theory of Brownian Motion to a Plasma

Kubo's modified theory of Brownian motion is used to calculate the friction experienced by a plasma electron. It is found that the spectral decomposition of the average Coulomb interaction is similar in functional form to the Landau damping decrement. It is also shown that when this friction is summed over the large wavenumber region of the spectrum the usual collision frequencies result.