Discussion on“Dispersion characteristics of clayey soils containing waste rubber particles”[J Rock Mech Geotech Eng 15(2023)3050-3058]

We read with great interest the recent article by Erenson(2023)entitled“Dispersion characteristics of clayey soils containing waste rubber particles”.The author has studied the dispersion characteristics of clayey soils containing different percentages of waste rubber particles(WRPs)by performing several tests(viz.consistency limit,linear shrinkage limit,double hydrometer,crumb test and pinhole test)and scanning electron microscopy(SEM)analysis on five clayey(viz.Na-activated bentonite,refined ball clay,Ukrainian kaolin,Avanos kaolin and Afyon clay)samples containing 0%,5%,10%and 15%WRPs.It should be noted that Erenson(2023)has presented some interesting observations,but there are some serious issues that we want to share through this discussion and request the author of the original paper to address them to avoid their persistence in the scientific literature.

Love wave propagation in one-dimensional piezoelectric quasicrystal multilayered nanoplates with surface effects

The exact solutions for the propagation of Love waves in one-dimensional(1D)hexagonal piezoelectric quasicrystal(PQC)nanoplates with surface effects are derived.An electro-elastic model is developed to investigate the anti-plane strain problem of Love wave propagation.By introducing three shape functions,the wave equations and electric balance equations are decoupled into three uncorrelated problems.Satisfying the boundary conditions of the top surface on the covering layer,the interlayer interface,and the matrix,a dispersive equation with the influence of multi-physical field coupling is provided.A surface PQC model is developed to investigate the surface effects on the propagation behaviors of Love waves in quasicrystal(QC)multilayered structures with nanoscale thicknesses.A novel dispersion relation for the PQC structure is derived in an explicit closed form according to the non-classical mechanical and electric boundary conditions.Numerical examples are given to reveal the effects of the boundary conditions,stacking sequence,characteristic scale,and phason fluctuation characteristics on the dispersion curves of Love waves propagating in PQC nanoplates with surface effects.

A Comparative Study of Dispersion Characteristics Determination of a Trapezoidally Corrugated Slow Wave Structure Using Different Techniques

The linear dispersion relation of a trapezoidally corrugated slow wave structure （TCSWS） is analyzed and presented. The size parameters of the TCSWS are chosen in such a way that they operate in the x-band frequency range. The dispersion relation is solved by utilizing the Rayleigh-Fourier method by expressing the radial function in terms of the Fourier series. A highly accurate synthetic technique is also applied to determine the complete dispersion characteristics from experimentally measured resonances （cold test）. Periodic structures resonate at specific frequencies when the terminals are shorted numerical calculation, synthetic technique and cold appropriately. The dispersion characteristics obtained from test are compared, and an excellent agreement is achieved.

Plume dynamics and dispersion characteristics in oil horizontal release from damaged submarine pipeline

The dynamics model of plume for underwater oil spill is improved by considering the drag force of the plume.The comparisons between prediction and experiment show that the improved model is viable.The improved model combining the Lagrangian random walk method is used to simulate the entire oil transport process from release exit to water surface in underwater oil horizontal release and some new results are obtained.Firstly,the release rate,the current velocity and its direction have evident influence on plume dynamics.The plume length increases as release flow rate increases.For small oil release rate,the plume length is very short so that the plume stage can be ignored due to the small initial momentum.When the oil release in direction is the same as the current,the current will play a positive role in the plume motion and the plume will therefore extend a longer distance.In this case,the greater the current velocity is,the longer the plume extension length will be.And when the oil release in direction is opposite to the current,the plume first moves forward and then is reversed to move along the opposite direction.The position of the reversal point depends on the current velocity and the release rate.Secondly,the release rate and the current velocity also have a significant effect on oil droplet diffusion.For small oil release rate,the oil distribution area is narrow and the concentration near upper side of droplets moving path is relatively higher.As the release rate or current velocity increases,the oil droplet diffusion area expands away from the release point.Finally,the movement characteristics of oil droplets in the plume and diffusion stages will affect the time and location for oil droplets reaching the surface.In a small release rate as well as a small current velocity,the time for oil droplet reaching surface is very short and the horizontal position reaching surface is closer to release point.In this case,the time spent in the plume stage is extremely short compared to the time spent in the entire oil motion process.Therefore,the plume dynamics stage can be ignored in this case.With the increase of release rate or current velocity,the plume will be extended and the time spent in plume dynamics stage will also be longer,so the plume dynamics stage can no longer be ignored for larger release rate or current velocity.In the case of reverse current,as the plume momentum be partially consumed by the reverse current,the plume is reversed and decays quickly,the time taken in the plume dynamics stage is relatively shorter than that for positive current.Correspondingly,the total time is also somewhat shortened.

Dispersion characteristics of seabed Scholte waves with variable velocity seawater in deep water

Acoustic velocity varies in deep-water environments.To obtain accurate inversion interpretations,it is necessary to develop a horizontally layered seawater–seabed(HLSS)model with continuously varying velocities.In this work,we used an HLSS model based on wave theory to deduce the Scholte wave dispersion equations and established an HLSS model based on the acoustic velocity profile and the submarine medium parameters of the South China Sea.We studied the dispersion characteristics of Scholte waves and theoretically calculated the amplitude–depth distribution.We also examined the influence of deep-water environments on the dispersion characteristics of Scholte waves.Using the real geological parameters of the Dongsha Islands in the South China Sea,we exploited the spectral element method to simulate seismic wave propagation in the fluid–solid interface and extracted the Scholte wave dispersion curves using multichannel analysis of surface waves(MASW).The consistent theoretical and extracted dispersion curve results verified the accuracy of our method.Numerical experiments showed that the dispersion characteristics of Scholte waves in deep water are weaker than those in shallow water.In addition to the seawater depth and the physical parameters of seabed sediments,the seawater’s variable velocity also influences Scholte wave dispersion characteristics.

Effects of Boundary Current on Electromagnetic Dispersion Characteristics for a Relativistic Electron Beam

With betatron oscillation characteristics of the electron beam and ion channel effect taken into account,dispersion characteristics of electrostatic modes and TM modes for a relativistic electron beam guided by ion channel are studied.Dispersion relations are derived and solved numerically to investigate the dependence of the dispersion characteristics for electrostatic modes and TM modes on the betatron oscillation frequency and the ratio of the relativistic electron beam radius to the waveguide radius.The effects of the boundary current on the dispersion characteristic of the TM modes and the interaction between the betatron modes and TM modes are analyzed.When considering the boundary current,for a strong ion channel,a new low-frequency branch of the TM modes arises and the interaction frequency between the betatron modes and the TM01modes is increased with the same parameters.

Research on Leak Location of Liquid-filled Pipe Based on Frequency Dispersion Characteristics

Due to the material problems and force majeure factors,the leakage will be occurred on the liquid-filled pipe resulting in waste of resources,environmental pollution and even endangering safety.Acoustic wave detection technology is widely used in buried pipeline leak detection,this technology mainly uses the wave(n=0,s=1)in the pipeline acoustic wave to locate the leak.When the leakage acoustic signal propagates along the liquid-filled pipe,the frequency dispersion characteristics can be obtained by wavelet decomposition.And there is a time delay(time difference)value between the leaky acoustic signals collected by the sensors at both ends of the leak.The outputs show that the results obtained by wavelet decomposition are in good agreement with the theoretical calculation results.Based on the obtained dispersion relation,the time delay values at different characteristic frequencies are analyzed by the cross-correlation method,and the leak location accuracy is discussed.This research content provides theoretical support and engineering application guidance for pipe leakage location technology.

Wave propagation analysis of porous functionally graded piezoelectric nanoplates with a visco-Pasternak foundation

This study investigates the size-dependent wave propagation behaviors under the thermoelectric loads of porous functionally graded piezoelectric(FGP) nanoplates deposited in a viscoelastic foundation.It is assumed that(i) the material parameters of the nanoplates obey a power-law variation in thickness and(ii) the uniform porosity exists in the nanoplates.The combined effects of viscoelasticity and shear deformation are considered by using the Kelvin-Voigt viscoelastic model and the refined higher-order shear deformation theory.The scale effects of the nanoplates are captured by employing nonlocal strain gradient theory(NSGT).The motion equations are calculated in accordance with Hamilton’s principle.Finally,the dispersion characteristics of the nanoplates are numerically determined by using a harmonic solution.The results indicate that the nonlocal parameters(NLPs) and length scale parameters(LSPs) have exactly the opposite effects on the wave frequency.In addition,it is found that the effect of porosity volume fractions(PVFs) on the wave frequency depends on the gradient indices and damping coefficients.When these two values are small,the wave frequency increases with the volume fraction.By contrast,at larger gradient index and damping coefficient values,the wave frequency decreases as the volume fraction increases.

ON FREE WAVE PROPAGATION IN ANISOTROPIC LAYERED MEDIA

The method of reverberation-ray matrix （MRRM） is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within the state space framework. The compatibility of physical variables in local dual coordinates gives the phase relation, from which exponentially growing functions are excluded. The interface and boundary conditions lead to the scattering relation, which avoids matrix inversion operation. Numerical examples are given to show the high accuracy of the present MRRM.

Comparative research on three types of coaxial slow wave structures

This paper studies three types of coaxial slow wave structures （SWSs）： （1） with ripples on both the inner and outer conductors; （2） with ripples on the outer conductor and smooth on the inner one; and （3） with ripples on the inner conductor and smooth on the outer one. The frequencies, coupling impedances, time growth rates and beam-wave interaction efficiencies of the three types of coaxial SWSs are obtained by theoretical analysis. Moreover, the relativistic Ccrenkov generators （RCGs） with the three types of coaxial SWSs are simulated with a fully electromagnetic particle- in-cell code, and the results verify the theoretical analysis. It is proved that the RCG with double-rippled coaxial SWS has the highest conversion efficiency and the shortest starting time.

Landau damping in a bounded magnetized plasma column

The damping decrement of Landau damping and the effect of thermal velocity on the frequency spectrum of a propagating wave in a bounded plasma column are investigated.The magnetized plasma column partially filling a cylindrical metallic tube is considered to be collisionless and non-degenerate.The Landau damping is due to the thermal motion of charge carriers and appears whenever the phase velocity of the plasma waves exceeds the thermal velocity of carriers.The analysis is based on a self-consistent kinetic theory and the solutions of the wave equation in a cylindrical plasma waveguide are presented using Vlasov and Maxwell equations.The hybrid mode dispersion equation for the cylindrical plasma waveguide is obtained through the application of appropriate boundary conditions to the plasma-vacuum interface.The dependence of Landau damping on plasma parameters and the effects of the metallic tube boundary on the dispersion characteristics of plasma and waveguide modes are investigated in detail through numerical calculations.

Theoretical analysis of a relativistic travelling wave tube filled with plasma

A cold and uniform plasma-filled travelling wave tube with sinusoidally corrugated slow wave structure is driven by a finite thick annular intense relativistic electron beam with the entire system immersed in a strong longitudinal magnetic field. By means of the linear field theory, the dispersion relation for the relativistic travelling wave tube （RTWT） is derived. By numerical computation, the dispersion characteristics of the RTWT are analysed in different cases of various geometric parameters of the slow wave structure and plasma densities. Also the gain versus frequency for three different plasma densities and the peak gain of the tube versus plasma density are analysed. Some useful results are obtained on the basis of the discussion.

Variational analysis of the disc-loaded waveguide slow-wave structures

The variational method is applied to calculate the dispersion characteristics of disc-loaded waveguide slow-wave structures. The parameters describing the waveguide discontinuities in disc-loaded waveguide are calculated by the variational method. Then the dispersion characteristics of slow-wave structures are obtained using lossless microwave quadrupole theory. Good agreement was observed between results of the Variational method and those of field matching method and high frequency structure simulator. In the case of broad band, results of the variational method are better than those of field matching method.

Accurate analysis of arbitrarily-shaped helical groove waveguide

This paper presents a theory on accurately analysing the dispersion relation and the interaction impedance of electromagnetic waves propagating through a helical groove waveguide with arbitrary groove shape, in which the complex groove profile is synthesized by a series of rectangular steps. By introducing the influence of high-order evanescent modes on the connection of any two neighbouring steps by an equivalent susceptance under a modified admittance matching condition, the assumption of the neglecting discontinuity capacitance in previously published analysis is avoided, and the accurate dispersion equation is obtained by means of a combination of field-matching method and admittancematching technique. The validity of this theory is proved by comparison between the measurements and the numerical calculations for two kinds of helical groove waveguides with different groove shapes.

An open-styled dielectric-lined azimuthally periodic circular waveguide for a millimeter wave traveling-wave tube

An open-styled dielectric-lined azimuthMly periodic circular waveguide （ODLAP-CW） for a millimeter-wave traveling-wave tube （TWT） is proposed, which is a modified form of a dielectric-lined azimuthally periodic circular waveguide （DLAP-CW）. The slow-wave characteristics of the open-styled DLAP-CW are studied by using the spatial harmonics method, which includes normalized phase velocity and interaction impedance. The complicated dispersion equations are numerically solved with MATLAB and the results are in good agreement with the simulation results obtained from HFSS. The influence of structural parameters on the RF properties is investigated based on our theory. The numerical results show that the optimal thickness of the metal rod can increase the interaction impedance, with the dielectric constant held fixed. Finally, the slow-wave characteristics and transmission properties of an open-styled structure are compared with those of the DLAP-CW. The results validate that the mode competition is eliminated in the improved structure with only a slight influence on the dispersion characteristics, which may significantly improve the stability of an open-styled DLAP-CW-based TWT, and the interaction efficiency is also improved.

Theoretical study of wave propagation along the coaxial waveguide filled with moving magnetized plasma

This paper presents detailed theoretical study on the theory of wave propagation along the coaxial waveguide filled with moving magnetized plasma （CWMMP）. Making use of the Lorentz transformation and the constitutive transformation, Maxwell＇s equations lead to the coupled non-homogeneous differential equations which govern the wave propagation in CWMMP, and then analytical solutions have been obtained. The discussion about the eigenvalues of the waves and detailed studies on the fields are carried out. It finds that the fields of the CWMMP are composed of two parts with different eigenvalues. Numerical calculations show that because of Doppler shift effect, the eigenvalues of the modes in such a case is quite different from those of the CWMMP. And a detailed discussion on the dispersion characteristic of CWMMP is presented.

Cold-Test Experimental Research of an S-Band Broadband High Power CCTWT

Cold-test experiment of an S-band broadband high power coupled-cavity traveling-wave tube(CCTWT)is introduced in this paper.The dispersion characteristic,the synchronous voltage and the interaction impedance of this S-band CCTWT are measured.The experimental results are in agreement with the numerical simulation values.