Search

Temperature effects on the electron trajectory and growth rate are investigated for a two-stream free-electron laser (FEL) with a helical wiggler along with a guide magnetic field. Both longitudinal and transverse components of the beam temperature are including providing the full beam temperature effects. Two different cases namely, conventional and reversed guide field are considered. Based on the fluid theory, the dispersion relation for the right hand polarized of the electromagnetic wave, including the important influence of temperature is obtained and solved numerically. Two resonances occur in this model: FEL and two-stream FEL (TS-FEL) resonances. It is shown that both of the peak growths of the resonances are reduced due to temperature. However, peak growth rates are substantially affected owing to transverse component of the beam temperature. The result shows, in the case of a reversed guide field the TS-FEL resonance has low thermal sensitivity with respect to the conventional guide field.

We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant $g_A$ in the neutron $\beta$-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function $g_1$, we determine the contribution from the $\gamma W$-box diagram to a precision better than $10^{-4}$. Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron $\beta$-decay are almost identical, i.e. the ratio $\lambda=g_A/g_V$ is almost unrenormalized. With this result, we predict the bare axial coupling constant to be {$\mathring{g}_A=-1.2754(13)_\mathrm{exp}(2)_\mathrm{RC}$} based on the PDG average $\lambda=-1.2756(13)$, Comment: Revised manuscript

The extensive arch-shaped features, solar prominences, are observed subtending high into the solar corona. Considering the prominences to be unbound, homogeneous and isothermal, invoking the background flow, in presence of the Newtonian radiation and turbulent viscosity, to investigate the spatial damping of compressional MHD waves, we derived a dispersion relation and solved it numerically for both the Kraichnan and Kolmogorov turbulences for a time span of 10 - 5 s to 10 5 s. For Kraichnan and Kolmogorov turbulences, we investigated the effect of background flow as well as variable physical parameters (e.g. electron density, magnetic field and angle between propagation vector and magnetic field) on the damping length of fast and slow modes. Our findings reveal that the background flow does not show any Doppler shift in the damping length of Fast as well as Slow modes for shorter periods. However, for the longer periods, the fast modes show significantly smaller Doppler shift but interestingly, we noticed that the slow modes exhibit a substantial Doppler shift.

The letter aims to generalize the second KP equation to a new one which still possesses a trilinear form. We construct Wronskian determinant solutions, based on its associated trilinear equation, instead of a Hirota bilinear form. Multi-soliton solutions are generated from the presented Wronskian formulation with higher-order dispersion relations. It is then shown that the extended second KP equation possesses resonant N -wave solutions. Moreover, generic one-lump and two-lump waves are built via the improved long wave limit procedure.

When compound jets are covered with surfactant on both interfaces, the property of those interfaces will be viscoelastic, unlike the Newtonian fluid interface. In this paper, the effects of surface viscoelasticity are principally studied through linear stability analysis and calculated using the Chebyshev spectral collocation method. Both surface elasticity and viscosity have properties to make the jet more stable, but the physical effects behind the two influencing mechanisms are different. When the inner and outer interfaces are separately covered with surfactant, the variations of surface viscoelastic parameters affect the growth rate and dominant wavenumber differently. In addition, the sensitivity of the maximum growth rate to the surface viscoelastic parameters depends on which interface the surfactant covers. A significant increase in the surface shear viscosity reduces the influence of surface elasticity on the maximum growth rate. The long-wave assumption was adopted to derive a one-dimensional dispersion equation in an algebraic form. The comparison between the simplified expression and the numerical results validated the applicability of the one-dimensional model in the vicinity of small wavenumber.

Wave propagation in a system of two arbitrary fluids separated by a contaminated interface in the form of an insoluble monolayer is investigated. The effects of four parameters (density ratio, R ; kinematic viscosity ratio, V ; Marangoni number, P ; and squared wave-Reynolds number, σ ) on the solutions of a comprehensive dispersion relation for these waves are analyzed. In the first part of the manuscript, several special cases are considered wherein the comprehensive dispersion relation is modified to a simple polynomial equation and its numerical solutions are obtained for σ ∈ [ 0 , 1 ] . A bifurcation is observed at σ = σ b in two of the solutions in each case; and the system is shown to be overdamped for σ σ b , and underdamped for σ > σ b . The relative influences of { R , V , P } on σ b are also analyzed, and it is found that in general, σ b is a strong function of { R , V } , but a weak function of P . In the second part of the manuscript, numerical solutions of the comprehensive dispersion relation are obtained for waves in a decane-water system, in the limit of { P ≫ 1 , σ ≫ 1 } ; and these solutions are classified to correspond to a transverse wave or to a longitudinal wave. The presence of a maximum/minimum in the frequency of oscillation and in the damping rate is observed for the transverse/longitudinal waves. For both the transverse and longitudinal wave modes, the relative deviation of the numerical solution (obtained from the comprehensive dispersion relation) from the respective approximate solution (obtained from a simple dispersion relation) is calculated. The relative deviation, though small, cannot be neglected because it accounts for the effects of elasticity and of capillarity/gravity; and disregarding it in the analyses will fail to yield the inherent maximum/minimum in the frequency of oscillation and in the damping rate for the transverse/longitudinal waves.

Planar metasurfaces provide exceptional wavefront manipulation at the subwavelength scale by controlling the phase of the light. Here, we introduce an out-of-plane nanohole-based metasurface design with the implementation of a unique self-rolling technique. The photoresist-based technique enables the fabrication of the metasurface formed by nanohole arrays on gold (Au) and silicon dioxide (SiO2) rolled-up microtubes. The curved nature of the tube allows the fabrication of an out-of-plane metasurface that can effectively control the wavefront compared to the common planar counterparts. This effect is verified by the spectral measurements of the fabricated samples. In addition, we analytically calculated the dispersion relation to identify the resonance wavelength of the structure and numerically calculate the phase of the transmitted light through the holes with different sizes. Our work forms the basis for the unique platform to introduce a new feature to the metasurfaces, which may find many applications from stacked metasurface layers to optical trapping particles inside the tube. publishedVersion

Love waves propagation in a viscoelastic waveguide loaded on its surface with viscoelastic fluids of finite thickness is investigated in this paper. The Maxwell and Kelvin-Voigt constitutive equations are employed in order to describe the fluid viscoelasticity. By solving the equations of motion in the different media (viscoelastic fluid, viscoelastic waveguide and elastic substrate) and imposing the suitable boundary conditions, an accurate and simple generalized complex dispersion equation is established for Love waves. Subsequently, a comparison is made with the published complex dispersion equations in the literature in some particular cases, and a very good agreement is showed. A detailed study was conducted by varying key parameters such as operating frequency, waveguide thickness and fluid thickness. The waveguide surface was subjected to various glycerol concentrations, with a wide range of dynamic viscosity, representing both Newtonian and viscoelastic behaviors. Theoretical analysis shows that to reasonably predict the characteristics responses of Love waves, the Maxwell fluid is more appropriate for low glycerol concentration and, the Kelvin-Voigt fluid is more suitable for high glycerol concentration and at high frequency. Results also evaluated the influence of layer thickness on the dispersion curves. The obtained results can be very useful in the design and optimization of Love wave fluid sensors.

In this paper, the propagation properties of in-plane elastic waves in a nano-scale N-type piezoelectric semiconductor material/piezoelectric dielectric material layered periodic composite are theoretically investigated. Under the background of classical continuum mechanics of solids, the transfer matrix method and the Bloch theorem, the transfer matrices of the N-type piezoelectric semiconductor material, the piezoelectric dielectric material and the interface and the dispersion equation of in-plane Bloch waves are derived mathematically. Basing on the numerical calculation results, we investigate the physical influences of the semiconductor effect, biasing electric fields and the interface effect on the dispersion curves of in-plane elastic waves. It is found that the electron carrier mobility and diffusion will reduce the equivalent rigidity of the N-type piezoelectric semiconductor material, which will be limited by the existence of biasing electric fields. On the basis of the propagation of in-plane elastic waves, both the mathematical model and the physical mechanisms are fundamental to the analysis and optimization of nano-scale energy harvesters.

The thermal convection of a plasma in porous medium is investigated to include simultaneously the effect of rotation and the finiteness of the ion Larmor radius (FLR) in the presence of a vertical magnetic field. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of a uniform rotation, finite Larmor radius and magnetic field introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, finite Larmor radius, rotation, medium permeability and magnetic field are found to have stabilizing (or destabilizing) effects under certain conditions. In the absence of rotation, finite Larmor radius has stabilizing effect on the thermal instability of the system whereas the medium permeability and the magnetic field may have stabilizing or destabilizing effect under certain conditions. The conditions κ

An Electromagnetic (EM) pulse falling on a plasma medium from vacuum can either reflect or propagate inside the plasma depending on whether it is overdense or underdense. In a magnetised plasma, however, there are usually several pass and stop bands for the EM wave depending on the orientation of the magnetic field with respect to the propagation direction. The EM wave while propagating in a plasma can excite electrostatic disturbances in the plasma [1, 2]. In this work Particle - In - Cell simulations have been carried out to illustrate the complete transparency of the EM wave propagation inside a strongly magnetised plasma. The external magnetic field is chosen to be perpendicular to both the wave propagation direction and the electric field of the EM wave, which is the X mode configuration. Despite the presence of charged electron and ion species the plasma medium behaves like a vacuum. The observation is understood with the help of particle drifts. It is shown that though the two particle species move under the influence of EM fields their motion does not lead to any charge or current source to alter the dispersion relation of the EM wave propagating in the medium. Furthermore, it is also shown that the stop band for EM wave in this regime shrinks to a zero width as both the resonance and cut-off points approach each other. Thus transparency to the EM radiation in such a strongly magnetised case appears to be a norm. This may have important implications in astrophysical scenarios. For instance, the plasma surrounding objects like pulsars and magnetars is often threaded with strong magnetic fields.

We make a physical–mathematical analysis of the implications that the presence of a large number of tiny bubbles may have, when present, on the thin upper layer of the sea. In our oceanographic example, the bubbles are due to intense rain. It was found that the bubbles increase momentum dissipation in the near surface and affect the surface tension force. For short waves, the implications of increased vorticity are momentum exchanges between wave and mean flow and modifications to the wave dispersion relation. For the direct effect we have analyzed, the implications are estimated to be non-significant when compared to other processes of the ocean. However, we hint at the possibility that our analysis may be useful in other areas of research or practical application.

Imaging polariton dynamics Two-dimensional (2D) materials can confine light to volumes much shorter than the wavelength, and, together, the long propagation lengths make them attractive materials for developing nanophotonic platforms. Characterizing the spatiotemporal control of 2D polariton wave packets has been hindered for the same reasons that make their potential applications exciting: They have extremely small wavelengths and are strongly confined inside the material. Kurman et al. developed a new pump-probe technique based on electron emission that provides access to the spatiotemporal dynamics of 2D polaritons. The nanometric spatial resolution and femtosecond temporal resolution will be useful for probing the excitation dynamics of these materials. Science , abg9015, this issue p. 1181

Distributions different from those predicted by equilibrium statistical mechanics are commonplace in a number of physical situations, such as plasmas and self-gravitating systems. The best strategy for probing these distributions and unavailing their origins consists in combining theoretical knowledge with experiments, involving both direct and indirect measurements, as those associated with dispersion relations. This paper addresses, in a quite general context, the signature of nonequilibrium distributions in dispersion relations. We consider the very general scenario of distributions corresponding to a superposition of equilibrium distributions, that are well-suited for systems exhibiting only local equilibrium, and discuss the general context of systems obeying the combination of the Schrödinger and Poisson equations, while allowing the Planck’s constant to smoothly go to zero, yielding the classical kinetic regime. Examples of media where this approach is applicable are plasmas, gravitational systems, and optical molasses. We analyse in more depth the case of classical dispersion relations for a pair plasma. We also discuss a possible experimental setup, based on spectroscopic methods, to directly observe these classes of distributions.

Wave observations are as yet an important technique to resolve fine structures in the plasma that cannot be identified by different instruments. In this way, we proposed the generation of electrostatic solitary waves during the interaction between the solar wind particles and Venus’s atmosphere at high altitude. The plasma system is treated as a multicomponent unmagnetized plasma consists of background electrons, positive ions (H+ and O+), and streaming solar wind electrons and protons. The dispersion relation is derived for linear waves and the stability/instability of electrostatic wavepackets is investigated. The dependence of the instability growth rate on the ion beam speed has been analyzed. Stability analysis reveals the occurrence of an imaginary frequency part in three regions. Using the reductive perturbation theory, the set of fluid equations is reduced to the Korteweg-de Vries (KdV) equation to describe the evolution of small but finite amplitude soliton waves. The model predicts the propagation of electrostatic soliton waves with an electric field of 1.2 mV/m and a time duration of 0.4 ms. The output of the fast Fourier transform of the electric field pulse is a broadband in the frequency range of ~ 3.2 to 199.5 kHz. It is proposed that the model can be a decent possibility for clarifying the observation of a wide variety of plasma oscillations by Galileo flyby of Venus.

Phasor diagrams are utilized to plot and analyze thermoacoustic modes in a duct with ideal closed/open acoustic boundary conditions that contains a velocity-sensitive flame. Inspection of phasor diagrams that represent fluctuations of velocity, pressure, heat release rate and characteristic wave amplitudes at the flame elicits characteristic features of marginally stable, intrinsic thermoacoustic (ITA) modes: the sign of velocity fluctuations and the sign of the gradient of pressure fluctuations change across the flame. These sign changes result from a reversal of direction of the velocity phasor across the flame, affected by unsteady heat release exactly out-of-phase with respect to upstream velocity fluctuations and of sufficient strength. Unlike alternative methods proposed for the identification of ITA modes, the proposed categorization does not involve a parameter sweep, but relies on an analogy with the structure of ITA modes in an anechoic environment. The phasor diagram also elucidates that continuous transitions from acoustic to ITA modes and vice versa can be achieved by an increase or decrease of the gain of the flame transfer function. The representation of acoustic wave propagation in terms of phasors facilitates the formulation of a compact dispersion relation of the thermoacoustic configuration under consideration. The value of the transitional gain of the flame transfer function, where acoustic/ITA transitions occur, may be deduced easily from the dispersion relation. A plot of solution branches of acoustic and ITA modes illustrates how the respective mode transitions, and how they can be related to the well-known quarter wave modes of a closed/open resonator. It is observed that under variation of transfer function gain and phase, marginally stable eigenmodes may occur at almost any frequency, not only at frequencies that correspond to the quarter-wave modes.

In this paper, a pre-compressed one-dimensional granular crystal model is studied. The bright analytic single and multiple solitary wave solutions in more general forms than those obtained the KdV system in the previous studies are derived by using the homogeneous balance principle and Hirota’s bilinear method. The difference between the present solutions and those from the KdV system are investigated both analytically and numerically. By analyzing the dispersion relation and the collision process of solitary waves, we find that there are two types of double-solitary waves in the pre-compressed granular crystal model. The geometric and numerical analysis of dynamic behaviors of the solutions is presented with emphasis on the relation between the double-solitary waves and elastic collision between single-solitary waves. We find that the opposite collision between single-solitary waves may be stable and thus generate a stable double-solitary wave. It is concluded that the collision is a special stable double-solitary wave solution. We further propose a possible way to determine the stability of multiple solitary waves qualitatively. The results of this paper provide a theoretical basis for finding stable multiple solitary wave solutions.

The study presents an analysis of free induction decay (FID) in the diluted magnetic composite using the model of spin waves in continuous media. It takes into account the dipole–dipole interaction of the bulk lattice atoms and between them and ferromagnetic dopant ions, and also the indirect exchange interaction of the dopants. A dispersion relation of the magnetic waves is evaluated from the magnetization evolution equation. There are two spectrum branches of spin waves. Their basic frequencies are determined by the gyromagnetic ratio and interaction parameters of the dopant ions and bulk lattice atoms, and by the dopant concentration. The FID asymptotic behaviour is evaluated.

The present investigation deals with the study of higher-order nonlinearity and dispersion to electron-acoustic waves in an unmagnetized and collisionless plasma system incorporating immobile ions, cool adiabatic electrons and nonthermal-Tsallis distributed hot electrons. Employing proper stretched coordinates and Reductive Perturbation Method (RPM), dispersion relation and Korteweg de-Vries (KdV) equation have been derived to the lower-order potential. An inhomogeneous KdV-type equation emerges to the next higher order that accounts for fifth-order dispersion. This study focuses on revealing the dependency of the behaviour of dressed electron-acoustic waves on nonthermal parameter (β), hot-to-cool electron density ratio (α), hot-to-cool electron temperature ratio (θ), Mach number ( $${{\Delta} M}$$ ) and nonextensive parameter (q). Only negative potential structures are reported for which the numerical results are interpreted in the form of two and three-dimensional profiles. The numerical results reflect the decrease in the amplitude of dressed solitary structures, thus obliging simulation of electron-acoustic solitary behaviour in the auroral regions and magnetosphere of Earth.

Nonlinear propagation of magnetoacoustic waves in magnetized, collisionless, warm bi-ion plasmas with positive and negative ions of different masses and charge states are investigated. The two-fluid model is used here. Using reductive perturbation technique, the Korteweg-de Vries equation is derived as nonlinear dispersion relation, and its solution for the magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is obtained. Using experimental values for the plasma parameters, magnetoacoustic soliton structures for K-fullerene plasma are illustrated along with some other useful alkali-fullerene plasmas.

We propose a three-dimensional mathematical model to describe dynamical processes of membrane fission. The model is based on a phase field equation that includes the Gaussian curvature contribution to the bending energy. With the addition of the Gaussian curvature energy term numerical simulations agree with the predictions that tubular shapes can break down into multiple vesicles. A dispersion relation obtained with linear analysis predicts the wavelength of the instability and the number of formed vesicles. Finally, a membrane shape diagram is obtained for the different Gaussian and bending modulus, showing different shape regimes.

Analytical hybrid-mode dispersion relations of a lossy coaxial waveguide were rigorously analyzed using a mode-matching technique. In order to model a practical coaxial line with inevitable losses, we adopted an all-dielectric coaxial waveguide surrounded by the perfect electric conductor (PEC) boundary. The rigorous dispersion characteristics of the TM01, TE01, and EH11 modes were investigated for lossy coaxial waveguides filled with different electrical conductivities. Based on the exact solutions, approximate but accurate dispersion equations were proposed for the TM0p, TE0p , EHmp, and HEmp modes in order to estimate and compare the behaviors of complex propagation constants in the microwave and visible spectra.

Using the linearized Vlasov–Maxwell model and the polarization tensor components for weakly magnetized ( $$\left| \omega -{\mathbf {k}}\cdot {\mathbf {v}}\right| >\varOmega $$ ) electron plasma the dispersion relations of parallel and perpendicular propagating electromagnetic modes are evaluated under high frequency/long wavelength limit (i.e., $$\omega >{\mathbf{k }}\cdot {\mathbf{v }}$$ ). The propagation characteristics of R–L and ordinary waves are discussed in the presence of isotropic Fermi–Dirac distribution function in a relativistic regime. The Polylog functions that arise due to arbitrary/partial degeneracy are examined in various degeneracy and relativistic limits. The graphical results are also extracted in the presence of quantum non-degenerate, degenerate and fully degenerate regimes due to the variation in relativistic parameter $$(\frac{T}{ m_{0}c^{2}})$$ , Lorentz factor ( $$\gamma $$ ) and degeneracy parameter $$(\frac{\mu }{T})$$ in weakly and strongly relativistic limits. Furthermore, the derived results are found to be in complete agreement with the previous investigations.

We use the Hamiltonian structure of equatorial wave-current interactions in the case of non-zero constant vorticity in the near-surface homogeneous layer, studying the dispersion relation for linear long waves outrunning the currents (downstream waves). We also investigate the behavior of the lifespan of the solution of the evolution equation for nonlinear long internal waves with respect to vorticity values.

In this paper, propagation of surface waves in nonlocal transversely isotropic liquid-saturated porous solid half-space has been investigated. The model is proposed for two different situations of which one is for excluding fluid nonlocal effect, and the other is for including fluid nonlocal effect. The existence of a new wave that arises due to the presence of nonlocality parameter in the medium as well as some critical circular frequencies is derived. Dispersion equation for the propagation of Rayleigh-type surface waves and their conditions of existence at the free surface of transversely isotropic liquid-saturated porous solids has been obtained. The boundary may be opened surface pores or sealed surface pores. Dependence of the velocities of surface waves, Rayleigh wave type on the direction of propagation and frequency has been illustrated. These numerical results report the phenomena such as anomalous negative dispersion of wave velocities with frequency.

To realize the refractive index dispersion accurately is essential for the design of optical devices. In this paper, we study hexagonal ZnO microrod cavities. We measure angle-resolved photolumines...

Wavefield decomposition can be used to extract effective information in reverse time migration and full-waveform inversion. The wavefield decomposition methods based on the Hilbert transform (HTWD) and the Poynting vector (PVWD) are the most commonly used. The HTWD needs to save the wavefields at all time steps or introduce additional numerical simulation, which increases the computational cost. PVWD cannot handle multiwave arrivals, and its performance is poor in complex situations. We have developed an efficient wavefield decomposition method based on the Hilbert transform (EHTWD). EHTWD constructs two wavefields to replace the original wavefield and the wavefield after the Hilbert transform. The first wavefield is obtained by using the dispersion relation to modify the frequency components. The other wavefield is obtained by time difference approximation. Therefore, there is a 90° phase change between the two wavefields. In EHTWD, we only need two wavefields at different moments, which avoids the need for additional numerical simulation. EHTWD is also suitable for wavefield decomposition in arbitrary directions. Compared to HTWD, the computational complexity can be greatly reduced with the decrease of the number of imaging time slices. The numerical examples of wavefield decomposition demonstrate that our method can realize wavefield decomposition in any direction. The examples of imaging decomposition and real data also indicate that EHTWD suppresses imaging noise effectively.

This article proposes a scannable leaky-wave antenna (LWA). The antenna consists of a ferrite-blade waveguide with a longitudinal slot on the upper wall, which has a tunable composite right-/left-handed (CRLH) property. The left-handed (LH) behavior of this structure is based on the negative effective permeability of the ferrite material and the negative effective permittivity of the waveguide excited below its cutoff frequency. First, based on the modal analysis and calculated dispersion relation, the unbalanced CRLH response of the ferrite-blade waveguide is investigated. Second, an LWA is presented by using a longitudinal slot on the upper wall of the proposed ferrite-blade waveguide, where the tunable balance CRLH response is achieved and analyzed by the transverse resonance method (TRM). The proposed LWA can provide backward, broadside, and forward radiations by a change in the operation frequency or the magnetic bias, independently. The given results show a +59° to −57° sweep in the radiation beam when the magnetic bias of the ferrite changed from 1400 to 1600 Oe at the sampling frequency of 6.4 GHz. Moreover, the results show that the frequency tuning range is more than 600 MHz (6.2–6.8 GHz). The peak gain and efficiency of the proposed antenna are 7.1 dBi and 78.5% at 6.6 GHz, respectively.

The electrostatic twisted ion-acoustic waves with finite orbital angular momentum states and associated kinetic instability are investigated in an electron-ion plasma. The plasma consisting of superthermal electrons and ions is modeled by using a non-gyrotropic Kappa distribution function in which the free energy source for wave excitation is provided by the relative directed motion of streaming electrons with respect to the ions. In the frame work of kinetic theory, the Vlasov-Poisson equations are employed to derive the expressions for dispersion relation and Landau damping rate under paraxial approximation. The results are analyzed for threshold condition of wave dispersion and instability growth rate in the presence of helical electric field structure. The relevance of study to the observed situations is also described.

Head-on collisional phenomena of ion acoustic (IA) waves in electron–positron–ion magnetized plasmas are investigated through linear and nonlinear analyses. The plasma system is considered collisionless and comprising cold ions, kappa distributed cold electrons, and positrons. Dispersion relation is derived with the aid of the linear perturbation method. The two sided nonlinear Korteweg-de Vries (KdV) equations are derived employing extended Poincare-Lighthill-Kuo (ePLK) method. The effects of wave frequency on linear group velocity with species density ratio are studied. Further, the production of ion acoustic solitons in terms of ion gyrofrequency ( $${\omega }_{\mathrm{g}}$$ ), superthermality parameters for electrons ( $${\kappa }_{\mathrm{e}}$$ ), and positrons ( $${\kappa }_{\mathrm{p}}$$ ) is investigated. Additionally, the effects of obliqueness (angle between magnetic field and wave propagation vector) on nonlinearity coefficient and phase shifts with density ratios (positron to electron and ion to electron) are demonstrated.

Polycrystalline textured thin films with distinct pleochroism and birefringence comprising oriented rotational domains of the orthorhombic polymorph of an anilino squaraine with isobutyl side chains (SQIB) are analyzed by imaging Mueller matrix ellipsometry to obtain the biaxial dielectric tensor. Simultaneous fitting of transmission and oblique incidence reflection Mueller matrix scans combined with the spatial resolution of an optical microscope allows to accurately determine the full biaxial dielectric tensor from a single crystallographic sample orientation. Oscillator dispersion relations model well the dielectric tensor components. Strong intermolecular interactions cause the real permittivity for all three directions to become strongly negative near the excitonic resonances, which is appealing for nanophotonic applications.

A prospective method to assess thermo-acoustic instabilities based on two reflection coefficients measured from the upstream side of the burner is presented and experimentally validated. In order to compose a model which allows predicting the onset of thermo-acoustic instability of combustion in a practical appliance, one has to characterize the thermo-acoustic properties of the burner including the flame as an acoustically active element and acoustic properties of all other (usually passive) components of the combustion appliance both upstream as well as downstream of the burner. This kind of modeling strategy usually faces serious practical problems related to the need of measurements/modeling at the hot downstream part of the system. In the present work, we propose a measurement and a system modeling approach which relies on two acoustic measurements, namely reflection coefficients, only at the cold (burner upstream) part of the combustion appliance. Both reflection coefficients, termed upstream and input, can be readily measured using standard acoustic techniques. The need to measure the input reflection coefficient of an acoustically active subsystem may impose difficulties related to the acoustic instability of the measurement setup itself. The approach and technical solution to handle this problem via a special modification of the excitation source (loudspeaker box) is proposed. The dispersion relation to search for system eigen frequencies is represented in a form that couples the reflection coefficients of the upstream part of the appliance and input reflection coefficient from the downstream part as observed through the burner with flame. This form of the dispersion relation is commonly used in the theory of radio-frequency circuits and recently introduced for thermo-acoustic problems. The proposed method is applied to burners with premixed burner-stabilized Bunsen-type flames. The observed instability conditions and oscillation frequencies are compared with predictions of the proposed modeling approach and reveal good correspondence.

Within the framework of Tsallis nonextensive statistics, the criteria for the Jeans gravitational instability are derived for a self-gravitating protoplanetary disk, whose substance consists of a mixture of a conducting ideal q-gas and modified radiation of a photon gas. The instability criteria are derived from the corresponding dispersion relations written for both neutral disk matter and magnetized plasma with modified blackbody radiation. The thermodynamics of a photon gas are constructed based on the nonextensive Tsallis quantum entropy, which depends on the deformation parameter. It is shown that blackbody q-radiation can stabilize the state of a nonextensive medium for a purely gaseous disk, and for an electrically conducting disk, the Jeans instability criterion is modified by the magnetic field and radiation pressure only in the transverse propagation mode of the disturbance wave.

In this paper, we report our numerical study of transverse mode phonon polaritons generated on magnetoelectric multiferroic films. The mathematical models of the dispersion relation for both surface and guided-wave modes were derived by solving the Maxwell equations. Then, numerical calculations were performed for various thicknesses using parameters suitable for illustrating magnetoelectric multiferroic BaMnF4. It was found that around the thicknesses of 0.1 mm–1 mm, the guided-wave modes were discreet. The surface phonon polaritons were obtained at the region between ferroelectric resonant frequency ω e and intercept frequency ω i. These surface modes were reciprocal, i.e., ω( k ) = ω(− k ). These results were in good agreement with the calculated attenuated total reflection spectra. It was also found numerically that the application of a magnetic field was able to shift the frequency of the surface phonon polaritons.

The dispersion relation for capillary waves of an arbitrary azimuthal symmetry on an elliptic cross-section jet in a uniform electrostatic field which is perpendicular to the axis of symmetry of the jet is derived. The stability of the first three azimuthal modes is investigated. It is shown that the stability of capillary waves on the jet reduces with increase in the external electrostatic field strength and the related eccentricity of transverse jet cross-section, as well as with increase in the polarization charge on the jet surface. Comparison with a jet in a radial electrostatic field is carried out. In the case of the transverse electrostatic field the instability growth rates of the capillary waves of any symmetry on the jet surface are turned out to be significantly higher than those in the case of the radial electrostatic field.

We analyze the chirality of dispersion relations and propagation lengths of two fundamental modes (m=0 and 1) in single silver nanowire coated by chiral TDBC. The systems of both Ag nanowires only coated by left TDBC (ALM) and right TDBC (ARM) are considered, respectively. Finite-difference time-domain method is used to do the mode analysis. The results show that the dispersion relations curves of both ALM and ARM are similar to magnetic hysteresis loops. There is a dip in the propagation length of ALM or ARM versus the incident frequency at the resonant frequency of left TDBC or right TDBC. The propagation length is reduced shapely in chiral TDBC due to the dissipation of TDBC. The difference of the propagation length $$|\Delta L|$$ becomes larger with the incident frequency far away from the resonant frequency of chiral TDBC for these two modes. The maximum difference of the real part of the effective index between ALM and ARM ( $$\Delta n'$$ ) is the linear function of m and the radius of Ag nanowire. With the radius decreasing from 100nm to 10nm, the propagation length for m=0 decreases and the propagation length for m=1 increases. Also, the maximum difference of the propagation length for m=1 increases. The maximum normalized difference between Ag nanowires coated by left TDBC and right TDBC in both the dispersion relation for $$m=0$$ (0.024) and the propagation length for $$m=1$$ (0.16) are quite larger than the one of only chiral TDBC (1/3000). According to our analysis, chiral molecules can be distinguished in either the dispersion relation or the propagation length, and our proposed structure has potential applications in chiral molecules detecting.

Artificial materials, known as phononic crystals (PCs) and acoustics/elastic metamaterials (AMs/EMs), have been proved to have band-gaps within which no flexural wave can propagate through, which have received great attentions. Among AMs/EMs, locally resonant (LR) beams are frequently encountered in the field of mechanical, civil and aeronautical engineering. However, the analysis of finite LR beams lacks of an efficient and exact approach. The primary objective of this study is to employ and develop an exact and efficient wave-based vibration analysis approach to study a finite Timoshenko LR beam carrying periodic separated force and moment type resonators. The proposed wave-based analysis approach is a powerful method that provides the exact solution in vibration analysis for structural waves that propagate along uniform structural elements and reflect and transmit at structural discontinuities. With the approach, the modeling and analysis process can be well simplified, which improves the efficiency in the design and analysis of finite LR beams. The frequency response results with three sets of resonators obtained through wave-based analysis approach show great agreements with both simulation and experimental results. Moreover, the measured results of the resonator with higher natural frequency show the promising advantage in achieving broader band-gap in low-frequency range, because the propagation attenuation in the experiment causes the absence of the narrow pass-bands which exists in the theoretical results. This paper proves that the wave-based vibration analysis approach was an exact and efficient method in solving complex vibration problem in finite periodic LR structures. In addition, the rich dispersion relation and wide band-gap property of the separated force and moment type resonators are demonstrated with the theoretical, simulation, and experimental results.

The current paper is concerned with the nonlinear stability analysis of rotating magnetic fluid columns. The rotation sources are a mixture of both uniform and oscillating behavior. The motivation behind tackling this topic is the increasing interest in atmospheric and oceanic motions. The system consists of two magnetic phase fluid that fills two infinite vertical cylinders. An azimuthal uniform magnetic field is penetrated on the system. The governing equations of motion, in terms of the Coriolis force and reduced pressure, along with Maxwell’s equation in the quasi-static approximations are considered. Consequently, the disturbance of the interface has an azimuthal behavior. The fluids are fully saturated in porous media. In light of the implication of the nonlinear boundary conditions, the solutions of the linearized equations of motion resulted in a nonlinear characteristic dispersion equation. Utilizing the homotopy perturbation technique, this equation is analyzed. A modification of the latter equation is made to seem like a nonlinear Klein–Gordon equation. The stability criteria are realized in linear as well as nonlinear approaches. A set of diagrams is graphed to illustrate the effects of several non-dimensional numbers on the stability profile in resonance as well as non-resonance cases.

A simplified second strain gradient Euler–Bernoulli beam theory with two non-classical elastic coefficients in addition to the classical constants is presented. The governing equation and the associated classical and non-classical boundary conditions are derived with the aid of variational principles. The simplified second strain gradient theory is governed by an eighth-order differential equation with displacement, slope, curvature and triple derivative of displacement as degrees of freedom. This theory can be reduced to the first strain gradient and classical Euler–Bernoulli beam theories. Analytical solutions for static behaviour, free vibration and stability analyses are presented for different boundary conditions and length scale parameters. Using the numerical Laplace transform, a spectral element is developed for dynamic analysis of a cantilever beam subjected to a Gaussian pulse. Further, spectrum and dispersion relations are derived to study wave propagation characteristics. The gradient effects on the structural response are assessed and compared with the corresponding first strain gradient and classical beam theories. Observations show that the second strain gradient theory exhibiting stiffer behaviour in comparison to the first strain gradient and classical theories. The beam deflection decreases whereas frequencies and buckling load increase for increasing values of the gradient coefficient in comparison to the first strain gradient and classical theories. The forced response for a finite beam reveals a decrease in the amplitude and a shift to smaller time values with an increase in the value of length scale parameter. Additionally, the second strain gradient beam shows a dispersive behaviour, and for a given frequency the wavenumber decreases and the phase speed increases with an increase in the length scale parameter as compared to the first strain gradient beam theory.

A van der Waals bonded moire bilayer formed by sequential growth of TiSe2 and TiTe2 monolayers exhibits emergent electronic structure as evidenced by angle-resolved photoemission band mapping. The two monolayers adopt the same lattice orientation but incommensurate lattice constants. Despite the lack of translational symmetry, sharp dispersive bands are observed. The dispersion relations appear distinct from those for the component monolayers alone. Theoretical calculations illustrate the formation of composite bands by coherent electronic coupling despite the weak interlayer bonding, which leads to band renormalization and energy shifts.

The growth of magneto-hydrodynamic fluctuations relevant to cosmic ray confinement in and near their sources, and the effects of local plasma conditions is revisited. We consider cases where cosmic rays penetrate a medium which may contain a fraction of neutral particles, and explore the possible effects of high-order cosmic-ray anisotropies. An algorithm for calculating the dispersion relation for arbitrary distributions, and anisotropies is presented, and a general solution for power-law cosmic-ray distributions is provided. Implications for the resulting instabilities near to strong Galactic cosmic-ray sources are discussed. We argue that cosmic-ray streaming in weakly ionised plasmas eliminates the need for the existence of an evanescent band in the dispersion relation, a conclusion which may be confirmed by gamma-ray observations. The necessity for additional multi-scale numerical simulations is highlighted, as understanding the non-linear behaviour is crucial., Accepted to MNRAS

Purpose . Propagation of a shear wave in sandy marine sediments is considered. The acoustic properties of a shear wave are the phase velocity and the attenuation coefficient. It is known that in dry sandy sediments, the attenuation coefficient is directly proportional to frequency. In the saturated mediums, there are the deviations from this law that implies existence of two physical mechanisms of losses – the intergranular friction and viscous loss. The study is aimed at developing a two-phase theoretical model of the shear wave propagation in the unconsolidated marine sediments, and at identifying the dissipative effects caused by the fluid relative movement in the pore space. Methods and Results . The intergranular friction is modeled using a springpot, which represents an element combing conservative properties of a spring and dissipative ones of a dashpot. The equation of motion is applied, where a part of fluid is assumed to be associated with the media solid phase and another part is considered to be mobile. For a harmonic displacement, the equations of state and the equation of motion yield a new two-phase dispersion relation (the theory of Grain Shearing + + Effective Density , or GS + EDs , for short). The results of the GS + EDs theory are compared with the data of the velocity and attenuation measurements taken from the open sources. It is shown that during propagation of the compressional and shear waves, the mechanisms of interaction between the granules, and between the granules and fluid are not similar. Character of the changes in the grain-to-grain friction parameters when the pore space is saturated with fluid, is analyzed. Conclusion . Manifestation of the dissipative effects resulting from the pore saturation with fluid depends on the density of the granules packing. In case of a dense packing, there are no conditions for the fluid relative movement, and the sandy sediments exhibit the property of a constant Q -factor. If the packing is loose, the viscous losses make a significant contribution, and the attenuation frequency dependence is nonlinear. The effective pore sizes for the compression and shear waves do not coincide.

This paper presents a theoretical study on the propagation of electromagnetic surface waves supported by the metamaterial-filled bi-layered graphene structure. The effective surface conductivity approach based upon the Kubo’s formalism is used to model the atomically thick graphene layer, while the analytical modeling of the metamaterials used the framework of causality principle-based Kramers-Kroing relations. With respect to the index of refraction, the two configurations of metamaterials have been considered—i.e., double positive (DPS) and double negative (DNG). The impedance boundary conditions (IBCs) have been employed at the interface for the computation of characteristics equations of odd and even surface modes under DPS and DNG configurations. The numerical results regarding the dispersion relations, effective mode index, and phase speed for the odd and even modes of electromagnetic surface waves supported by each configuration of structure have been presented. Further, the influence of chemical potential and thickness of metamaterial filling in parallel graphene layers on the wave propagation characteristics has been analyzed. To check the accuracy of the numerical results, special conditions were employed, which converge to the published results. The proposed work may have potential applications in plasmonic based logic designs, renewable energy devices, THz surface wave guides, and near-field communication devices.

We analyse near-extremal black brane configurations in asymptotically $\mathrm{AdS}_4$ spacetime with the temperature $T$, chemical potential $\mu$, and three-velocity $u^\nu$, varying slowly. We consider a low-temperature limit where the rate of variation is much slower than $\mu$, but much bigger than $T$. This limit is different from the one considered for conventional fluid-mechanics in which the rate of variation is much smaller than both $T$, $\mu$. We find that in our limit, as well, the Einstein-Maxwell equations can be solved in a systematic perturbative expansion. At first order, in the rate of variation, the resulting constitutive relations for the stress tensor and charge current are local in the boundary theory and can be easily calculated. At higher orders, we show that these relations become non-local in time but the perturbative expansion is still valid. We find that there are four linearised modes in this limit; these are similar to the hydrodynamic modes found in conventional fluid mechanics with the same dispersion relations. We also study some linearised time independent perturbations exhibiting attractor behaviour at the horizon - these arise in the presence of external driving forces in the boundary theory., Comment: 85 pages, 4 appendices. v2: A few corrections, additional comments, one new appendix and additional references v3: Version published in JHEP

Dispersion of a passive tracer by water waves is of significant importance for many scientific and technological problems including bio-diversity of marine life, ecological impact of anthropogenic incidents, planning of rescue operation and global oceanic transport. Formally, turbulent dispersion of a passive tracer by surface waves is a Brownian motion caused by a prescribed noise, viz., random fluctuations of the wave field. From this perspective, it is similar to the conventional dispersion by tracer particles by turbulent flows initially described in the seminal work of Richardson, Taylor and Obukhov. The additional challenges of this problem are imposed by the complexity of the underlining wave field—different dispersion relations and correlation structure, directionality and its spread, wave breaking—and this complexity necessitates further theoretical and experimental research. The aim of the present study is experimental validation of scaling relations for the mean drift and mean variance of tracer particles predicted by the wave turbulence theory. We report results of a set of targeted experiments in a large three-dimensional wave tank where the positions of the tracer particles—modelled as surface drifters—were tracked down with optical cameras. The experimental data are analysed and discussed in the light of the weak turbulence theory.

By employing Mindlin’s Form II gradient elasticity theory (strain gradient elasticity theory), we investigate the SH surface wave propagating in a strain-gradient layered half-space. The dispersion equation of the SH surface wave is derived analytically. For the general case where both the surface layer and the half-space are strain-gradient elastic materials, the dispersion equation involves 10 material constants. The dispersion equation of the general case can degenerate to that of several special cases by dropping some material parameters. The existence regions of the dispersion curves are discussed in detail. The effects of strain-gradient elastic constants on the dispersion curves are examined. It is seen that the features of SH surface waves in strain-gradient elastic materials are much richer than those in classical elastic materials. Ministry of Education (MOE) The authors would like to thank the financial support from Singapore Ministry of Education Academic Research Fund Tier 1 (RG185/18). Jianmin Long also acknowledges the support from the National Natural Science Foundation of China (11702081) and the Fundamental Research Funds for the Central Universities, Hohai University (2019B08714).

The propagation of dust-acoustic waves in a dusty plasma bounded in finite symmetrical cylindrical geometry has been theoretically investigated. By using the reductive perturbation method, we obtain a quasi-nonlinear Schrodinger equation. It is shown that there is a dark envelope soliton under certain conditions, while its amplitude will decrease with the time. The dependence of both the dispersion relation and group velocity of envelope solitary waves on the radius of cylinder has been given. Moreover, we define the duration time of dark envelope solitons and give the theoretical ones. It is found that the duration time increases as the radius of cylinder increases, while it decreases as the viscosity coefficient of dusty plasmas increases.

Nowadays, the viscoelastic carbon nanotubes (CNTs) have been used as one of the most promising candidates for nanodevices (or nanoelectronics) and super-strong reinforcement fibers in polymer nanocomposites. In recent years there have been many papers that considered the effects of material length scales in the investigations of the material constants related on the structural parameters on the wave propagation in the viscoelastic CNTs. By using different approaches, for examples, Eringen’s differential nonlocal model, modified couple stress theory, and strain gradient theories, the stiffness softening or strengthening effect can be well predicted. However, the influence of the rapid stiffness enhancing effect on the wave characteristics of the viscoelastic CNTs is still not reported. To deal with such problem, this work aims to investigate the transverse wave propagation in viscoelastic single-walled carbon nanotubes (SWCNTs) adhered by surface material based on the nonlocal second-order strain gradient elasticity theory. The characteristic equation of wave motion of the viscoelastic SWCNTs with surface effect is systematically formulated to achieve the analytical dispersion relation between the wave frequency (or phase velocity) and the wave number. In the end, some most important conclusions are concluded.

Two-dimensional van der Waals (vdW) crystals can sustain various types of polaritons with strong electromagnetic confinements, making them highly attractive for nanoscale photonic and optoelectronic applications. While extensive experimental and numerical studies have been devoted to the polaritons of the vdW crystals, analytical models are sparse. Particularly, applying the model to describe polariton behaviors that are visualized by state of the art near-field optical microscopy requires further investigations. In this study, we develop an analytical waveguide model to describe polariton propagations in vdW crystals. The dispersion contours, dispersion relations, and localized electromagnetic field distributions of polariton waveguide modes are derived. The model is verified by real-space optical nano-imaging and numerical simulation of phonon polaritons in α-MoO3, which is a vdW biaxial crystal. Although we focus on α-MoO3, the proposed model is valid for other polaritonic crystals within the vdW family given the corresponding dielectric substitutions. Our model therefore provides an analytical rationale for describing and understanding the localized electromagnetic fields in vdW crystals that are associated with polaritons.

—The effect of hot anisotropic plasma on the development of cyclotron instability in the near-Earth space plasma at finite plasma pressure $${{\beta }_{ \bot }}$$ is studied. It is shown that the finiteness of $${{\beta }_{ \bot }}$$ ​ does not only modify the imaginary part of the dispersion equation which is associated with the amplification of waves but also changes the real part of this equation which describes wave propagation along the magnetic field lines. This leads to a change in the cyclotron instability increment and causes variations in the parameters of propagation of electromagnetic ion-cyclotron (EMIC) waves along a field line. The obtained results suggest that for the generation of EMIC waves in the near-Earth plasma, small values of perpendicular proton plasma pressure ( $${{\beta }_{ \bot }}$$ ), large anisotropy values ( $$A$$ ), and large values of $${{{{v}_{{\parallel h}}}} \mathord{\left/ {\vphantom {{{{v}_{{\parallel h}}}} {{{c}_{A}}}}} \right. \kern-0em} {{{c}_{A}}}}$$ ratio are preferable.