Nonpropagating Mode Research Articles

Evolution of weak, homogeneous turbulence with rotation and stratification

This article concerns the time-evolution, spectral structure and scaling of weak turbulence subject to rotation and stable stratification. The flow is expressed as a combination of particular solutions, referred to as modes, of the linearised governing equations without viscosity or diffusion. Modes are of two types: oscillatory ones which represent inertial-gravity waves and time-independent ones that express a non-propagating (NP) component of the flow. The presence of the NP component, which plays an active role in the dynamics apart from in the case of pure rotation, renders wave-turbulence analysis problematic because the NP mode is non-dispersive. Equations are derived for the time evolution of the modal amplitudes, evolution which is due to nonlinearity and visco-diffusion. Subsequent analysis assumes that one or other (or both) of the Rossby and Froude numbers is small (weak turbulence). Given this assumption, the NP component is found to evolve independently of the wave one and a numerical scheme, similar to, though significantly different from classical direct numerical simulation, is used to determine its time evolution. The treatment of the wave component assumes its amplitude is large compared with the NP one, otherwise there are seemingly intractable difficulties of closure in the analysis. Given this further assumption, the wave component decouples from the NP one. Evolution equations for the wave spectra are derived using wave-turbulence analysis and are integrated numerically. As might be expected, these equations indicate that nonlinear coupling of wave modes is dominated by resonances. Results are given for both the NP and wave components.

Fabrication and Operation Analysis of a Surface-Plasmon Sensor Using a Nonpropagating Mode

Fabrication and Operation Analysis of a Surface-Plasmon Sensor Using a Nonpropagating Mode

Bifurcation Analysis and Propagation Conditions of Free-Surface Waves in Incompressible Viscous Fluids of Finite Depth

Viscous linear surface waves are studied at arbitrary wavelength, layer thickness, viscosity, and surface tension. We find that in shallow enough fluids no surface waves can propagate. This layer thickness is determined for some fluids, water, glycerin, and mercury. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for a given horizontal wave number. In contrast, there are two types of non-propagating modes. One kind of them exists at all wavelength and material parameters, and there are infinitely many such modes for a given wave number, distinguished by their decay rates. The other kind of non-propagating mode that is less attenuated may appear in zero, one, or two specimens. We notice the presence of two length scales as material parameters, one related to viscosity and the other to surface tension. We consider possible modes for a given material on the parameter plane layer thickness versus wave number and discuss bifurcations among different mode types. Motion of surface particles and time evolution of surface elevation is also studied at various parameters in glycerin, and a great variety of behaviour is found, including counterclockwise surface particle motion and negative group velocity in wave propagation.

Microphysically modified magnetosonic modes in collisionless, high-β plasmas

With the support of hybrid-kinetic simulations and analytic theory, we describe the nonlinear behaviour of long-wavelength non-propagating (NP) modes and fast magnetosonic waves in high-$\beta$collisionless plasmas, with particular attention to their excitation of and reaction to kinetic micro-instabilities. The perpendicularly pressure balanced polarization of NP modes produces an excess of perpendicular pressure over parallel pressure in regions where the plasma$\beta$is increased. For mode amplitudes$|\delta B/B_0| \gtrsim 0.3$, this excess excites the mirror instability. Particle scattering off these micro-scale mirrors frustrates the nonlinear saturation of transit-time damping, ensuring that large-amplitude NP modes continue their decay to small amplitudes. At asymptotically large wavelengths, we predict that the mirror-induced scattering will be large enough to interrupt transit-time damping entirely, isotropizing the pressure perturbations and morphing the collisionless NP mode into the magnetohydrodynamic (MHD) entropy mode. In fast waves, a fluctuating pressure anisotropy drives both mirror and firehose instabilities when the wave amplitude satisfies$|\delta B/B_0| \gtrsim 2\beta ^{-1}$. The induced particle scattering leads to delayed shock formation and MHD-like wave dynamics. Taken alongside prior work on self-interrupting Alfvén waves and self-sustaining ion-acoustic waves, our results establish a foundation for new theories of electromagnetic turbulence in low-collisionality, high-$\beta$plasmas such as the intracluster medium, radiatively inefficient accretion flows and the near-Earth solar wind.

Aether scalar tensor theory: Linear stability on Minkowski space

We have recently proposed a simple relativistic theory which reduces to modified Newtonian dynamics for the weak-field quasistatic situations applied to galaxies, and to cosmological behavior as in the $\Lambda$CDM model, yielding a realistic cosmology in line with observations. A key requirement of any such model is that Minkowski space is stable against linear perturbations. We expand the theory action to second order in perturbations on a Minkowski background and show that it leads to healthy dispersion relations involving propagating massive modes in the vector and the scalar sector. We use Hamiltonian methods to eliminate constraints present, demonstrate that the massive modes have Hamiltonian bounded from below and show that a nonpropagating mode with a linear time dependence may have unbounded Hamiltonian for wave numbers $k< \mu$ and bounded otherwise. The scale $\mu$ is estimated to be $\lesssim \mathrm{Mpc}^{-1}$ so that the low momenta instability may only play a role on cosmological scales.

Avoidance of Strong Coupling in General Relativity Solutions with a Timelike Scalar Profile in a Class of Ghost-Free Scalar-Tensor Theories

Modified gravity theories can accommodate exact solutions, for which the metric has the same form as the one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is that perturbations around them exhibit strong coupling when the solutions are realized in degenerate higher-order scalar-tensor theories. We show that the strong coupling problem can be circumvented in the framework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a way that higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect is built-in in U-DHOST theories in general. There is an apparent Ostrogradsky mode in U-DHOST theories, but it does not propagate as it satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface. We also clarify how this nonpropagating mode, i.e., the "shadowy" mode shows up at the nonlinear level.

Propagation of longitudinal Pochhammer – Chree waves in cylindrical piles

The exact solutions of the linear Pochhammer – Chree equation for propagating harmonic waves in cylindrical piles, are analysed and reviewed emphasizing the role of both propagating and non-propagating wave modes. The notion of limiting wave velocities for the Pochhammer – Chree waves is discussed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes of the Pochhammer – Chree waves is performed, revealing existence of the non-propagating mode at the phase velocity coinciding with the c2 shear wave velocity. Analytical expressions for displacement fields are derived for both interior and exterior domains.

Subterahertz Longitudinal Phonon Modes Propagating in a Lipid Bilayer Immersed in an Aqueous Medium

The properties of subterahertz longitudinal acoustic phonon modes in the hydrophobic region of a lipid bilayer immersed in a compressible viscous aqueous medium are investigated theoretically. An approximate expression is obtained for the Mandelstam–Brillouin components of the dynamic structure factor of a bilayer. The analysis is based on a generalized hydrodynamic model of the “two-dimensional lipid bilayer + three-dimensional fluid medium” system, as well as on known sharp estimates for the frequencies and lifetimes of long-wavelength longitudinal acoustic phonons in a free hydrated lipid bilayer and in water, obtained from inelastic X-ray scattering experiments and molecular dynamics simulations. It is shown that, for characteristic values of the parameters of the membrane system, subterahertz longitudinal phonon-like excitations in the hydrophobic part of the bilayer are underdamped. In this case, the contribution of the viscous flow of the aqueous medium to the damping of a longitudinal membrane mode is small compared with the contribution of the lipid bilayer. Quantitative estimates of the damping ratio agree well with the experimental results for the vibration mode of the enzyme lysozyme in aqueous solution [1]. It is also shown that a coupling between longitudinal phonon modes of the bilayer and relaxation processes in its fluid environment gives rise to an additional peak in the scattering spectrum, which corresponds to a non-propagating mode.

On Kinetic Slow Modes, Fluid Slow Modes, and Pressure-balanced Structures in the Solar Wind

Abstract Observations in the solar wind suggest that the compressive component of inertial-range solar-wind turbulence is dominated by slow modes. The low collisionality of the solar wind allows for nonthermal features to survive, which suggests the requirement of a kinetic plasma description. The least-damped kinetic slow mode is associated with the ion-acoustic (IA) wave and a nonpropagating (NP) mode. We derive analytical expressions for the IA-wave dispersion relation in an anisotropic plasma in the framework of gyrokinetics and then compare them to fully kinetic numerical calculations, results from two-fluid theory, and magnetohydrodynamics (MHD). This comparison shows major discrepancies in the predicted wave phase speeds from MHD and kinetic theory at moderate to high β. MHD and kinetic theory also dictate that all plasma normal modes exhibit a unique signature in terms of their polarization. We quantify the relative amplitude of fluctuations in the three lowest particle velocity moments associated with IA and NP modes in the gyrokinetic limit and compare these predictions with MHD results and in situ observations of the solar-wind turbulence. The agreement between the observations of the wave polarization and our MHD predictions is better than the kinetic predictions, which suggests that the plasma behaves more like a fluid in the solar wind than expected.

Analysis of defects in externally driven dust-density wavefronts in cogenerated dusty plasma using the time-resolved Hilbert–Huang transform

Analysis of defects in externally driven dust-density wavefronts (DDWs) in cogenerated dusty plasma has been carried out. The DDWs are excited for threshold positive bias through another T-shaped electrode which is placed inbetween two main discharge electrodes. Spatiotemporal evolution of the DDWs reveals a wave defect and non-propagating wave mode in the DDW field. A space-time plot and the time-resolved Hilbert–Huang transform (HHT) were employed to analyze the spatiotemporal wave data at a specific location in the wave field.

Evolution of Indian Ocean dipole and its forcing mechanisms in the absence of ENSO

The evolution of Indian Ocean dipole (IOD) and its forcing mechanisms are examined based on the analysis of coupled model simulations that allow or suppress the El Nino-Southern Oscillation (ENSO) mode of variability. The model can reproduce the most salient observed features of IOD even without ENSO, including the relationships between the eastern and western poles at both the surface and subsurface, as well as their seasonality. This suggests that ENSO is not fundamental for the existence of IOD. It is demonstrated that cold (warm) sea surface temperature (SST) anomalies in the eastern Indian Ocean associated with IOD can be initiated by springtime Indonesian rainfall deficit (surplus) through local surface wind response. The growth of the SST anomalies depends on the initial local subsurface condition. Both the air–sea interaction and surface–subsurface interaction contribute to the development of IOD. The evolution of IOD can be represented by two leading extended empirical orthogonal function (EEOF) modes of tropical surface–subsurface Indian Ocean temperatures; one stationary and the other non-stationary. The onset, growth, and termination of IOD, as well as the transition to an opposite phase, can be interpreted as alternations between the non-propagating mode (EEOF1) and the eastward-propagating Kelvin wave (EEOF2). The evolution of IOD is also accompanied by a westward-propagating Rossby wave which is captured in the EEOF1 of the subtropical surface–subsurface Indian Ocean temperatures. Therefore, both Bjerknes feedback and a delayed oscillator operate during the evolution of IOD in the absence of ENSO also.

Experimental study of ultra shallow water acoustic wave propagation

The sound propagation in ultra shallow water was studied experimentally. The investigation was carried out in the nature pond approximately 300 × 20 m in size. Its depth was about 1 m. For such a pond critical frequency is about 700 Hz that is easy to emit and receive. The main purpose was to study the process of acoustic wave propagation in case of strong bottom influence and to restore some bottom parameters. The signal was radiated by the transducer and recorded by a set of point receivers located at different distances from the transducer. The signal was linear frequency modulated in 100 Hz–10 kHz band and was 10 s in duration. Its correlation with the recorded signal defines the pond response function. The modes representation was used. The group velocity frequency dependence was obtained by use of this method and it was very close to the theoretical one considering a soft bottom. The critical frequency also corresponded to the soft bottom model. The attenuation of sound was also studied in a wide frequency range including non-propagating mode. The results are very sensitive to the signal-to-noise ratio. It was shown that the used correlation method significantly improved the quality of obtained characteristics.

Visualization of non-propagating Lamb wave modes for fatigue crack evaluation

This article develops a non-propagating Lamb wave mode (NPL) imaging technique for fatigue crack visualization. NPL has a great potential for crack evaluation in that it significantly contributes local mode amplitudes in the vicinity of a crack without spatial propagation. Such unique physical phenomenon is theoretically proven and experimentally measured through laser scanning. Although its measurement is a quite challenging work due to the fact that it is quite localized and coexists with complex propagating Lamb wave modes, a NPL filter proposed in this article overcomes the technical challenge by eliminating all propagating Lamb modes from laser scanned full Lamb wavefields. Through the NPL filtering process, only fatigue crack-induced NPLs can be measured and retained. To verify such physical observation and the corresponding NPL filter, a real micro fatigue crack is created by applying repeated tensile loading, and its detectability is tested using a surface-mounted piezoelectric transducer for generating Lamb waves and a laser Doppler vibrometer for measuring the corresponding responses. The experimental results confirm that even an invisible fatigue crack can be instantaneously visualized and effectively evaluated through the proposed NPL measurement and filtering processes.

Investigation of dominant spin wave modes by domain walls collision

Spin wave emission due to field-driven domain wall (DW) collision has been investigated numerically and analytically in permalloy nanowires. The spin wave modes generated are diagonally symmetric with respect to the collision point. The non-propagating mode has the highest amplitude along the middle of the width. The frequency of this mode is strongly correlated to the nanowire geometrical dimensions and is independent of the strength of applied field within the range of 0.1 mT to 1 mT. For nanowire with film thickness below 5 nm, a second spin wave harmonic mode is observed. The decay coefficient of the spin wave power suggests that the DWs in a memory device should be at least 300 nm apart for them to be free of interference from the spin waves.

INTRINSIC LOCALIZED MODES IN QUANTUM FERROMAGNETIC ISING–HEISENBERG CHAINS WITH SINGLE-ION UNIAXIAL ANISOTROPY

Based on the coherent-state method combined with the Dyson–Maleev representation of spin operators, the existence and properties of intrinsic localized spin-wave modes in quantum ferromagnetic Ising–Heisenberg chains with single-ion uniaxial anisotropy are investigated analytically in the semiclassical limit. With the help of the multiple-scale method combined with semidiscrete approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, a bright type intrinsic localized spin-wave mode can exist below the bottom of the linear spin-wave spectrum. Besides, we show that, at the boundary of the Brillouin zone, a dark type intrinsic localized spin-wave mode appears above the top of the linear spin-wave spectrum, which is different from the resonant nonpropagating kink mode.

Spatiotemporal evolution of dielectric driven cogenerated dust density waves

An experimental observation of spatiotemporal evolution of dust density waves (DDWs) in cogenerated dusty plasma in the presence of modified field induced by glass plate is reported. Various DDWs, such as vertical, oblique, and stationary, were detected simultaneously for the first time. Evolution of spatiotemporal complexity like bifurcation in propagating wavefronts is also observed. As dust concentration reaches extremely high value, the DDW collapses. Also, the oblique and nonpropagating mode vanishes when we increase the number of glass plates, while dust particles were trapped above each glass plates showing only vertical DDWs.

Physical mechanisms for electron mirror and field swelling modes

Ion mirror instability is dominant in planetary and cometary magnetosheaths and other high-beta plasmas where the ions are hotter than the electrons. It is associated with a zero-frequency non-propagating mode with the wave vector nearly perpendicular to the ambient magnetic field. The counterparts of this instability in hot electron plasmas are the field swelling and electron mirror instabilities. A theory for these instabilities was developed more than two decades ago (Basu B and Coppi B 1982 Phys. Rev. Lett.48 799, 1984 Phys. Fluids27 1187) within the framework of a fluid model. The connection between the two types of instabilities has been analyzed in (Migliuolo S 1986 J. Geophys. Res.91 7981). In contrast to these papers, we shall here adopt the standard quasi-hydrodynamic approach that is usually used for the study of mirror instabilities. To analyze the electron mirror and field swelling instabilities, we will only use the perpendicular balance condition and the Liouville theorem. We have found that such a description is easier to understand and gives us increased physical insight into the basic physical features of both these instabilities.

MRI: A Possible Mechanism for Funnel Flows?

ABSTRACTMagnetorotational instability (MRI) has been suggested to have an important role on the dynamics of accretion disks. We investigate MRI as an alternative way for guiding plasma from the disk to the funnel flow at the disk-magnetosphere boundary of classical T Tauri stars (CTTSs) by considering the diamagnetic effects. We solve the magnetohydrodynamic equations by including the effect of both the magnetic field gradient and the perpendicular (to the field) velocity gradient produced by the magnetization current at the disk-magnetosphere boundary for the first time. Diamagnetic current modified MRI produces a nonpropagating mode which may lift the plasma from the disk towards the vertical magnetic field lines. Our model also shows that the diamagnetic effects play an important role in triggering the MRI. The instability becomes more powerful with the inclusion of the gradient in the magnetic field and the perpendicular velocity.

Boundary attenuation angles for inhomogeneous plane waves in anisotropic dissipative media

We study behavior of attenuation (inhomogeneity) angles [Formula: see text], i.e., angles between real and imaginary parts of the slowness vectors of inhomogeneous plane waves propagating in isotropic or anisotropic, perfectly elastic or viscoelastic, unbounded media. The angle [Formula: see text] never exceeds the boundary attenuation angle [Formula: see text]. In isotropic viscoelastic media [Formula: see text]; in anisotropic viscoelastic media [Formula: see text] may be greater than, equal to, or less than [Formula: see text]. Plane waves with [Formula: see text] do not exist. Because [Formula: see text] in anisotropic viscoelastic media is usually not known a priori, the commonly used specification of an inhomogeneous plane wave by the attenuation angle [Formula: see text] may lead to serious problems. If [Formula: see text] is chosen close to [Formula: see text] or even larger, indeterminate, unstable or even nonphysical results are obtained. We study properties of [Formula: see text] and show that the approach based on the mixed specification of the slowness vector fully avoids the problems mentioned above. The approach allows exact determination of [Formula: see text] and removes instabilities known from the use of the specification of the slowness vector by [Formula: see text]. For [Formula: see text], the approach yields zero phase velocity, i.e., the corresponding wave is a nonpropagating wave mode. The use of the mixed specification leads to the explanation of the deviation of [Formula: see text] from [Formula: see text] as a consequence of different orientations of energy-flux and propagation vectors in anisotropic media. The approach is universal; it may be used for isotropic or anisotropic, perfectly elastic or viscoelastic media, and for homogeneous and inhomogeneous waves, including strongly inhomogeneous waves, like evanescent waves.

Collective properties of water confined in carbon nanotubes: A computer simulation study

The collective properties of water confined in the (10,10), (8,8) and (6,6) carbon nanotubes are studied by analysing the longitudinal-current autocorrelation function, calculated from computer-simulated trajectories. The corresponding spectra clearly show the presence of two excitations, but their behaviour is quite different from that observed in the case of bulk water. Instead of the strong positive dispersion of the hydrodynamic sound mode characteristic of bulk water (the fast-sound phenomenon), the sound dispersion relation of confined water is observed to flatten into a non-propagating mode, while a second excitation appears at a higher frequency. This behaviour is analysed in terms of the localized oscillation modes of the hydrogen-bond network.