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Pole skipping is a recently discovered subtle effect in the thermal energy density retarded two point function at a special point in the complex $(\omega,p)$ planes. We propose that pole skipping is determined by the stress tensor contribution to many-body chaos, and the special point is at $(\omega,p)_\text{p.s.}= i \lambda^{(T)}(1,1/u_B^{(T)})$, where $\lambda^{(T)}=2\pi/\beta$ and $u_B^{(T)}$ are the stress tensor contributions to the Lyapunov exponent and the butterfly velocity respectively. While this proposal is consistent with previous studies conducted for maximally chaotic theories, where the stress tensor dominates chaos, it clarifies that one cannot use pole skipping to extract the Lyapunov exponent of a theory, which obeys $\lambda\leq \lambda^{(T)}$. On the other hand, in a large class of strongly coupled but non-maximally chaotic theories $u_B^{(T)}$ is the true butterfly velocity and we conjecture that $u_B\leq u_B^{(T)}$ is a universal bound. While it remains a challenge to explain pole skipping in a general framework, we provide a stringent test of our proposal in the large-$q$ limit of the SYK chain, where we determine $\lambda,\, u_B,$ and the energy density two point function in closed form for all values of the coupling, interpolating between the free and maximally chaotic limits. Since such an explicit expression for a thermal correlator is one of a kind, we take the opportunity to analyze many of its properties: the coupling dependence of the diffusion constant, the dispersion relations of poles, and the convergence properties of all order hydrodynamics., Comment: 39 pages, 13 figures

The linear stability analysis has been analyzed for an electrified liquid sheet confined between two symmetric dielectric movable ambient gas. The present study aims to estimate the planer jet systems response when applying a tangential electric field. The dispersion relations for varicose and sinuous modes have been formulated. The electrical Euler number and some flow parameters have been tested for their influence on the electrified liquid sheet instability. In other words, the effects of electric field on the dominant wave number, and instability range (cutoff wave number) are discussed. The results clarify that the tangential electric field has a stabilizing effect for sinuous mode over the whole range of gas velocity ratio. On the other hand, for varicose mode, the electric field slightly improves the system stability to a certain limit, but it has a great role in stability for higher values of gas velocity ratio.

International audience; We report the observation of nonlinear three-wave resonant interactions between two different branches of the dispersion relation of hydrodynamic waves, namely the gravity-capillary and sloshing modes. These atypical interactions are investigated within a torus of fluid for which the sloshing mode can be easily excited. A triadic resonance instability is then observed due to this three-wave two-branch interaction mechanism. An exponential growth of the instability and phase locking are evidenced. The efficiency of this interaction is found to be maximal when the gravity-capillary phase velocity matches the group velocity of the sloshing mode. For a stronger forcing, additional waves are generated by a cascade of three-wave interactions populating the wave spectrum. Such a three-wave two-branch interaction mechanism is probably not restricted to hydrodynamics and could be of interest in other systems involving several propagation modes.

In this study, we propose a mechanical analysis for estimating the internal pressure of a finitely deformed spherical compartment from Lamb wave measurements. The proposed analysis produces a dispersion relation associating Lamb wave speed with pressure using limited material parameters (only a strain stiffening term). The analysis was validated on ultrasound bladder vibrometry (UBV) experiments collected from 9 ex vivo porcine bladders before and after formalin cross-linking. Estimated pressures were compared with pressures measured directly by a pressure transducer. The proposed analysis proved broadly effective at estimating pressure from UBV based Lamb wave without calibration as demonstrated by the observed concordance between estimated and measured pressures (Lin's CCC = 0.82 (0.66-0.91). Theoretical limitations and potential refinements to improve the accuracy and generality of the approach are discussed.

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.

Long wave evolution on viscous films flowing under gravity down an inclined plate in the presence of an electrostatic field acting normal to the plate is described using new nonlinear models. First, an asymptotic expansion is applied to derive a strongly nonlinear evolution equation for the interfacial position in the long-wave limit, which retains terms up to second order in a small film parameter ( e ) and thus brings in dispersive effects, inclination-angle corrections for hydrostatic pressure, second-order contributions to inertia and electric stresses as well as the interaction of the last two. Two weakly nonlinear models (WNMs) for the disturbances with O ( e 2 ) amplitude are then derived, which account for distinct effects of hydrostatic pressure, inertia and dispersion for shallow and steep angles. We compare the linear stability results based on the second-order electrified Benney equation (BE) and the WNMs with realistic parameter values. It is shown that the growth rates coincide, while the phase speed from the WNMs is a good approximation of that from the BE for small wavenumbers only. The comparison of exact dispersion relations from the Orr–Sommerfeld (OS) problem with the linear results of the second-order BE takes a step towards understanding the validity range of the BE with non-local terms that approximates the full electrohydrodynamic coupling system describing the inclined electrified film flow. The pertinent OS results demonstrate that a decrease in electrode distance can diminish the critical Reynolds number ( R e ). Furthermore, at subcritical R e with a slightly supercritical electric field, the finite wavelength of the least stable mode has been estimated using an energy balance, whose amplitude will be governed by two coupled Ginzburg–Landau (GL) equations, derived using a multiple-scale analysis by taking higher-order problems into account. The numerical solutions of the leading-order GL equation demonstrate that close to the bifurcation, it can fully govern the temporal behaviour of the system.

An analytical study on the propagation characteristics of shear wave in a spherical layered structure comprising of an isotropic sandy material medium covered by a concentric spherical transversely isotropic sandy material layer of finite thickness has been carried out in the present work. The source of excitation for wave propagation is considered in the outer layer and the analytical treatment with contour integration and Fourier-Legendre Expansion theorem is utilized to accomplish closed form of dispersion relation. Further, Debye Asymptotic Expansion analysis is used to deal the complication caused by the inclusion of Bessel's function, Hankel's function and their derivatives in the solution procedure. With help of Debye Asymptotic Expansion analysis, the obtained dispersion relation converts in the form of elementary functions and found to be in well-agreement with pre-established and classical results through the particular cases. Numerical computations are done to illustrate the influence of the affecting parameters (anisotropy, sandiness and radii ratio) on dispersion curves graphically. Moreover, to expose the impact of anisotropy, numerical data of three distinct transversely isotropic materials (Magnesium, Zinc and Beryl) are taken into the account to establish the comparative study with isotropic material which serves the major highlights of the present study.

Deep-subwavelength periodic metallic structures, which are also called as plasmonic metamaterials, have received much attention due to their ability of supporting spoof surface plasmons polariton (SPP) modes. However, it is still difficult to obtain the dispersion relations of different modes for complicated plasmonic metamaterials with finite thickness. To solve the problem, we make further development of a field-network joint dispersion analysis method that was proposed recently, so that the method can be used to analyze the spoof SPP structures with certain thickness. The developed method not only allows us to predict the dispersion relations of complicated spoof SPP structures with finite thickness, but also can be used to find a series of intrinsic high-order modes of the periodic metallic structures. As an ex-ample, we present the theoretical dispersion curves of the fun-damental and high-order modes for a complicated spoof SPP structure, which have good agreements with the simulated re-sults. Meanwhile, the calculated near fields also match to the simulated and measured results well.

Examination of thermal expansion of two-dimensional (2D) nanomaterials is a challenging theoretical task with either ab-initio or classical molecular dynamics simulations. In this regard, while ab-initio molecular dynamics (AIMD) simulations offer extremely accurate predictions, but they are excessively demanding from computational point of view. On the other side, classical molecular dynamics simulations can be conducted with affordable computational costs, but without predictive accuracy needed to study novel materials and compositions. Herein, we explore the thermal expansion of several carbon-based nanosheets on the basis of machine-learning interatomic potentials (MLIPs). We show that passively trained MLIPs over inexpensive AIMD trajectories enable the examination of thermal expansion of complex nanomembranes over wide range of temperatures. Passively fitted MLIPs could also with outstanding accuracy reproduce the phonon dispersion relations predicted by density functional theory calculations. Our results highlight that the devised methodology on the basis of passively trained MLIPs is computationally efficient and versatile to accurately examine the thermal expansion of complex and novel materials and compositions using the molecular dynamics simulations.

The dispersion relation of torsional wave in a dissipative, incompressible cylindrical shell of infinite length incorporating initial stresses effects is investigated. The governing equation and closed form solutions are derived with the aid of Biot’s principle. Phase velocity and damping of torsional wave are obtained analytically and the influences of dissipation and initial stresses are studied in details.We proposed a new method for obtaining the phase and damping velocities of torsional wave in a complex form. Numerical results analyzing the torsional wave propagation incorporating initial stress effects are analyzed and presented in graphs. The analytical and numerical solutions reveal that, the dissipation as well as the initial stresses have notable impacts on the phase velocity of torsional wave in a pre-stressed dissipative cylindrical shell. The numerical results reveal that, the initial stresses and dissipation, considerably, effect the phase velocity of the torsional wave. It has been observed that, any change in dissipation parameter (?) produces a substantial change in damping velocity of torsional wave. In addition, it can be seen that, the phase velocity increases as the initial stress parameter increases. Finally, the result of numerical simulation illustrated the influence of dissipation and initial stresses on damping and phase velocities of torsional wave propagation. The conclusion made shown the consistency with the Biot’s incremental deformation theory, and the effective on model such as engineering mechanics and displacement of particles.

The current study aims to study the velocity profile of torsional surface waves in a three-layer model consisting of sand-dunes deposit sandwiched between the watery-porous layer and the orthotropic half-space. The top and the middle layers exhibit irregular interfaces employing various geometrical shapes such as parabolic, rectangular, and triangular notch. The main objective is to analyze the effect of these irregular interfaces on torsional wave propagation. Furthermore, the three-layer model involves inhomogeneity through gravity, initial stress, rigidity, and medium density. These inhomogeneity parameters, coupled with irregularity, bears a remarkable impact on the velocity-profile. The generalized dispersion relation has been derived, and one particular case has been deduced to validate the current work. Detailed numerical simulation has been performed to characterize the computations, and graphical illustrations have been exhibited to support the mathematical investigation.

We present the approach that unifies the analytical description and a new model of the cylindrical plasma produced and sustained by а weakly damped surface-wave. This approach includes the use of a fixed-point magnetic-current model. An analytical expression is reported for the normalized power of a surface plasma wave, Q ˜ . This power is determined as a function of the normalized wavenumber X. We show that the absorbance of the power has a clear maximum at around X ∼ 3 – for the parameters used; the magnitude of the maximum depends on dielectric losses such that Q ˜ generally increases with the increase of t g δ . Analysis of the formula for normalized power of surface electron plasma wave has shown the necessity for evaluating the dispersion relation. Since this equation is very complex and implicit, the calculations are not clearly seen. In this paper, an attempt has been made in order to overcome the difficulties, by applying the fixed convergent iteration algorithm. We show in this paper that the fixed-point method is efficient and can be adapted for computations performed here.

The current article is concerned with a nonlinear stability analysis of cylindrical Walters B' fluids. The system is pervaded by an axial time periodic electric field. A cylindrical interface is supposed to be disconnected from two dielectric fluids. The fluids are fully saturated in porous media. The motivation to scrutinize this area is attributed to the great attention it receives in many practical situations in physics and engineering applications. The implementation of the appropriate nonlinear boundary conditions of the linearized equations of motion yields a nonlinear characteristic dispersion equation. This equation manages the surface deflection of the surface waves. The use of the non-dimensional analysis resulted in various well-known non-dimensional numbers. A new approach to the characteristic equation is inspected by employing the Homotopy perturbation method (HPM). This new methodology resulted in a Klein-Gordon equation. Utilizing a travelling-wave solution to the linear part of the characteristic equation, a new restriction of the stability analysis appears. The investigation reveals the non-resonance as well as the resonance cases, and the stability criteria are established in both arguments. A set of diagrams is plotted to display the influence of various non-dimensional physical numbers on the stability profile and shows interesting features.

We investigated the dispersion relations of the triple-chambered cochlea separated by the basilar membrane and the Reissner's membrane. The slow waves can propagate on the basilar membrane (basilar membrane mode), and also on the Reissner’s membrane (Reisnner’s membrane mode). Most of the previous studies have focused on the mechanics of vibration of the basilar membrane and there are only a few studies on the wave propagation on Reissner’s membrane. In this study, we focused particularly on the Reissner's membrane mode among the many propagation modes and evanescent modes that the structure supports. We analyzed the dispersion of the Reissner’s membrane mode and the basilar membrane mode, and studied their dependency on the position along the cochlea. We also studied how the distance between the Reissner's membrane and the basilar membrane affects the dispersion relations.

The dispersion and dielectric attenuation characteristics of a double-staggered grating waveguide (DSGW) are two crucial features related to the output characteristics of a sheet-beam traveling-wave amplifier and have been previously studied by using theoretical analysis and simulations. In this work, these two characteristics are both experimentally studied. Two ${H}$ -band (220–325 GHz) DSGW circuit prototypes with and without dielectric attenuators made of the BeO-TiO2 composite ceramic were machined by using nanocomputer numerical control milling. Experimental studies of the dispersion property were performed successfully where the measurement results were in good agreement with those predicted by simulations, exhibiting a wide passband of 70 GHz (230–300 GHz). The measured transmission coefficient has been decreased from −5 to −55 dB after the introduction of dielectric attenuators, experimentally verifying the feasibility of the adopted methodology. The effects of the variations of dispersion relation and transmission loss on the beam-wave interaction stability were also investigated.

The Kelvin-Helmholtz instability (KHI) occurs at the interface amongst two fluids, which are in relative motion with a common boundary. The growth rate of waves occurs whenever the relative velocity is greater as compared with the critical relative velocity. In the present paper, the influence of boundary roughness on KHI under the impact magnetic field in a couple-stress fluid layer bounded by a rigid surface at the lower side and upper side by a fluid saturated porous layer. Using suitable surface and boundary conditions, we have derived the dispersion relation and results are depicted graphically. As observed in presence of sharp interface, magnetic field exhibits stabilizing effect however, destabilizing effect is shown by the buoyancy force on KHI. Also, noted that the growth rate of interface reduces, as there is a rise in roughness parameter value.

We study the hydrodynamic excitations of backreacted holographic superfluids by computing the full set of quasinormal modes (QNMs) at finite momentum and matching them to the existing hydrodynamic theory of superfluids. Additionally, we analyze the behavior of the low-energy excitations in real frequency and complex momentum, going beyond the standard QNM picture. Finally, we carry out a novel type of study of the model by computing the support of the hydrodynamic modes across the phase diagram. We achieve this by determining the support of the corresponding QNMs on the different operators in the dual theory, both in complex frequency and complex momentum space. From the support, we are able to reconstruct the hydrodynamic dispersion relations using the hydrodynamic constitutive relations. Our analysis rules out a role-reversal phenomenon between first and second sound in this model, contrary to results obtained in a weakly coupled field theory framework., v3: matches version published in JHEP; v2: added fig. 7 and discussion about incoherent limit plus new appendix C; 26 pages + 10, 15 figures

A design method of the non-periodic meander line slow-wave structure (ML-SWS) and folded-waveguide slow-wave structure (FW-SWS) for traveling-wave tubes (TWTs) is proposed based on effective phase velocity synchronization. For the non-periodic ML-SWS and FW-SWS, the unified effective axial phase velocity seen by electrons, the dispersion equation, and the ideal beam-wave synchronization voltage are derived. The theoretical results demonstrate that the non-periodic ML-SWS and FW-SWS reported to date are consistent with the proposed method. Furthermore, two examples are presented as applications for the proposed method to the non-periodic SWS design, including the concentric arc FW-SWS and the zigzag ML-SWS. In addition, the simulated results of the two examples are in good agreement with the theoretical ones.

Sigma model in AdS3× S3 background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for N-spike strings moving in AdS3× S1 with angular momentum J in S1 ⊂ S5 in the presence of mixed flux. We observe that the addition of angular momentum J or winding number m results in the spikes getting rounded off and not end in cusp. The presence of flux shows no alteration to the rounding-off nature of the spikes. We also consider the large N-limit of N-spike string in AdS3× S1 in the presence of flux and show that the so-called Energy-Spin dispersion relation is analogous to the solution we get for the periodic-spike in AdS3− pp-wave ×S1 background with flux.

An effective overmoded circuit is proposed to support efficient interaction with two beams for the development of high power extended interaction oscillators (EIOs) toward sub-terahertz (THz) and higher frequency. The circuit design focuses on the effect of the frequency-determining parameter on mode characteristics of the $\mathrm{TM}_{{1} {n}}$ sequence. Frequency equivalence between $\mathrm{TM}_{{1} {n}}$ modes with different ${n}$ supports the mode selection for two-beam interaction. Accordingly, the TM13 mode is selected to duplicate the dispersion relation around the axial mode of $2\pi $ and ohmic loss of conventional TM11 mode used in conventional single-beam circuits. On this basis, the overmoded circuit is formed with two beams based on the TM13 mode. In order to verify its effectiveness, a 0.22-THz EIO is designed with the overmoded circuit and, most importantly, the effect of the uniformity of two beams on the EIO performance is simulated. When the current of one beam is assumed to be constant and that of another beam is increased, the power is increased linearly and then tends to be saturation. This shows good capability of the EIO in interacting with nonuniform two beams, which is critical for its stable operation. Simulation results have shown the achievement of the average power of 0.22-THz wave over 1.26 kW with double beams at 23 kV and each current of 0.2 A.

Transverse spin angular momentum of light is a key concept in recent nanophotonics to realize unidirectional light transport in waveguides by spin-momentum locking. Herein we theoretically propose subwavelength nanoparticle chain waveguides that efficiently sort optical spins with engineerable spin density distributions. By arranging high-refractive-index nanospheres of different sizes in a zigzag manner, directional optical spin propagation is realized. The origin of the efficient spin transport is revealed by analyzing the dispersion relation and spin angular momentum density distributions. In contrast to conventional waveguides, the proposed asymmetric waveguide can spatially separate up- and down-spins and locate one parity inside and the other outside the structure. Moreover, robustness against bending the waveguide and its application as an optical spin sorter are presented. Compared to previous reports on spatial engineering of local spins in photonic crystal waveguides, we achieved substantial miniaturization of the entire footprint down to subwavelength scale., 20 pages, 5 figures

Shear horizontal surface acoustic waves (SAW) propagation in an ultra-thin functionally graded piezoelectric (FGP) layer bonded to a homogeneous substrate is analytically formulated in the mathematical framework of surface/interface elasticity theory. It is assumed that the FGP over-layer is made of a hexagonal 6-mm crystal with a single axis of rotational symmetry coinciding with the axis of polarization. The mechanical and piezoelectric properties of the layer are assumed to vary linearly with thickness. The half-space is made of a transversely isotropic material. It should be mentioned that this model is of great interest in investigating SAW devices at high frequencies. Accounting for the surface/interface effects, the pertinent electromechanical dispersion relation for both cases of the electrically open and short surfaces is derived analytically using Wentzel–Kramers–Brillouin singular perturbation theory. The effects of the surface/interface parameters and the gradient parameter which indicate the variation of the piezoelectric properties of the FGP layer on the dispersion relation, the electromechanical coupling factor, displacement field, electric potential function, electric displacement field, and stress field are studied numerically, and the results are compared with those obtained from classical theory.

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

Accurate Rayleigh scattering and absorption cross sections of atmospheric gases are essential for understanding the propagation of electromagnetic radiation in planetary atmospheres. Accurate extinction cross sections are also essential for calibrating high-finesse optical cavities and differential optical absorption spectroscopy and for accurate remote sensing. In this study, we measured the scattering and absorption cross sections of carbon dioxide, nitrous oxide, sulfur hexafluoride, oxygen, and methane in the continuous wavelength range of 307–725 nm using broadband cavity-enhanced spectroscopy (BBCES). The experimentally derived Rayleigh scattering cross sections for CO2, N2O, SF6, O2, and CH4 agree with refractive index-based calculations, with a difference of (0.4 ± 1.2) %, (−0.6 ± 1.1) %, (0.9 ± 1.4) %, (2.8 ± 1.2) %, and (0.9 ± 2.2) %, respectively. The O2–O2 collision-induced absorption and absorption by methane are obtained with high precision at the 0.8 nm resolution of our BBCES instrument in the 307–725 nm wavelength range. New dispersion relations for N2O, SF6, and CH4 were derived using data in the UV–vis wavelength range. This study provides dispersion relations for refractive indices, n-based Rayleigh scattering cross sections, and absorption cross sections based on more continuous and more extended wavelength ranges than available in the current literature.

Using the Born–von Karman model, we have constructed a simple analytic theory of dispersion of flexural vibrations in graphene, which makes it possible to take into account any number of configuration spheres. In the framework of this theory, the quadratic dispersion of flexural acoustic phonons in graphene has been analyzed. It is shown that such a dispersion of flexural vibrations in graphene is the interaction of each atom with not only nearest neighbors, but also with more distant atoms. The signs of effective force constants corresponding to different coordination spheres must be various, preserving the system stability. We have obtained analytic relations between elastic constants, for which flexural vibrations can propagate in the plane of graphene. In the “critical” relation derived in this study, negative elastic constants of the second and third coordination sphere compensate the positive contribution from the first coordination sphere almost completely. As a result, the propagation of low-frequency flexural acoustic waves with conventional linear dispersion in a narrow interval of wavevector values near k = 0 turns out to be impossible. We have determined the conditions in which the dispersion relation of flexural modes in graphene becomes quadratic, which is typical of flexural vibrations in thin macroscopic membranes.

The propagating characteristics of the water and muddy waves are one of the concerns of theoretical studies because of the following facts: (1) With the development of the economy in the estuaries, local residents and government paid increasing attention to the ecological environment of the estuarine beaches The propagating characteristics of the water and muddy waves are closely related to the ecological environment, the concern of the government and the residents. (2) The propagating characteristics of the mud are the bottleneck of the study of the coastal and beach dynamics because of the complicated constitutive relation of the mud. The different constitutive models may lead to different explanations of its mechanism. Hence, the proper selection of the model is one of the keys to reveal the true kinematic properties of the mud in the estuaries. This paper first establishes a power law model of the constitutive relation of the mud. Based on this model, a gravity wave theory is proposed. According to the mechanism of the mud wave transportation, the coupled mud-water wave field can be divided into two layers. The upper layer is described as the viscous Newtonian fluid, whereas the lower high-concentration mud layer is described as the power law fluid. Next, the equations of the proposed model are discretized and the calculations are made by using the difference method. Then, the propagating characteristics are discussed, and the dispersion relations of the water and mud waves are analyzed in detail.

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 theory of electromagnetic eigenwaves of a cylindrical plasma waveguide located in a constant coaxial magnetic field is developed. The dispersion equation for a waveguide with high electronic conductivity is obtained. It is shown that the waveguide supports the propagation of bulk and bulk-surface hybrid waves of helicon origin. The nonreciprocity effect of waveguide eigenwaves with the identical field distributions, but differing in the direction of propagation along the azimuthal coordinate and also when the direction of the external magnetic field is reversed, is discovered.

This paper studies magnetic line defects in the Wilson-Fisher $O(N)$ model. A powerful method to probe the system is to consider mixed two-point functions of the order parameter and the energy operator in the presence of the defect. A recently developed dispersion relation allows us to bootstrap these mixed correlators to leading order in the $\epsilon$-expansion. We also carry out explicit diagrammatic calculations, finding perfect agreement with the bootstrap, and we conclude extracting the new CFT data predicted by the two-point functions., Comment: 35 pages + appendix

A class of problems of wave propagation in waveguides consisting of one or several layers that are characterized by linear variation of the squared refractive index along the normal to the interfaces between them is considered in this paper. In various problems arising in practical applications, it is necessary to efficiently solve the dispersion relations for such waveguides in order to compute horizontal wavenumbers for different frequencies. Such relations are transcendental equations written in terms of Airy functions, and their numerical solutions may require significant computational effort. A procedure that allows one to reduce a dispersion relation to an ordinary differential equation written in terms of elementary functions exclusively is proposed. The proposed technique is illustrated on two cases of waveguides with both compact and non-compact cross-sections. The developed reduction method can be used in applications such as geoacoustic inversion.

Generalized Kramers–Kronig (K–K) type dispersion relations and sum rules are derived in the static limit for the moments of the degenerate four wave mixing susceptibility. The degenerate nonlinear susceptibility is different from a typical use of the conventional K–K dispersion relations, which assume absence of complex poles of a function in the upper half of complex frequency plane, whereas degenerate susceptibility has simultaneous poles in both half planes. In the derivation of the generalized K–K relations the poles and their order are taken into account by utilization of the theorem of residues. The conventional K–K relations can be used to estimate the real and imaginary parts of the second and higher powers of the susceptibility as the effect of the poles is reduced due to a faster convergence of the dispersion relations. The present theory is directly applicable to higher order susceptibilities and can be used in testing of theoretical models describing the degenerate four wave mixing susceptibility in nonlinear optical and terahertz spectroscopy.

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.

Waves of different geometries (plane, cylindrical and spherical) in a porous medium saturated by a three-phase fluid: water, oil and gas is considered. Unified dispersion relations for waves with different geometries are obtained. It is shown that the dependence of phase velocities on frequency is the same for plane, cylindrical and spherical waves (with axial symmetry) and independent of the geometry of the process.

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.

This paper is dedicated to the mathematical modeling of torsional surface waves in a heterogeneous monoclinic crystal cladded with a void type porous layer and gravitating viscous-sandy-elastic semi infinite substratum subjected to imperfect corrugated boundary surface. The model is solved analytically by using an implicit separable variable technique together with a Whittaker’s function and Bessel’s functions. This study focused on the determination of dispersion equation constituents from displacement components of the media by using suitable boundary conditions. The isotropic limit tests expose strong symphony together with the isotropic results attainable in literature. Detailed analysis through numerical simulations and graphical illustration of the dispersion equation includes discussion on the various rheological parameters such as shape of the irregular surfaces, Biot’s gravity parameter, sandy parameter, heterogeneity parameter, dissipation factor etc., on the dispersion curves of torsional wave.

This paper reports dynamical effects in one-dimensional locally resonant piezoelectric metastructures leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The nonlinear electromechanical unit cell is built upon a linear host oscillator coupled to a nonlinear electrical circuit via piezoelectricity. Semi-analytical harmonic balance (HB)-based dispersion relations are derived to predict the location and edges of the nonlinear attenuation band. Numerical responses show that weakly and moderately nonlinear piezoelectric metastructures (NPMSs) promote a class of nonlinear attenuation band where a bandgap and a wave supratransmission band coexist, while also imparting nonlinear attenuation at the resonances around the underlying linear bandgap. Besides, strongly nonlinear regimes are shown to elicit broadband chaotic attenuation. Negative capacitance (NC)-based essentially cubic piezoelectric attachments are found to expand the aforementioned effects over a broader bandwidth. Excellent agreement is found between the predictions of the HB-based dispersion relations and the nonlinear transmissibility functions of undamped and weakly damped NPMSs at weakly and moderately nonlinear regimes, even in the presence of NC circuits. This research is expected to pave the way toward fully tunable smart periodic metastructures for vibration control via nonlinear piezoelectric attachments.

The narrow band gap width caused by local resonance is the shackle for the further development of conventional metamaterials. In this paper, a novel type of hierarchical metamaterial containing parallel multiple resonators is presented, whose ultra-broadband vibration suppression property originates from a rational gradient design. Characterization of dispersion relations and bandgap characteristics of the one-dimensional outward-hierarchical lattice system reveals the variation of bandgap boundaries with relevant parameters. Thus, two gradient design approaches are proposed to overlap and merge the bandgaps. These designs are verified on the analogous continuum models by finite element simulations, and the ultra-wide wave/vibration attenuation band is consistent with the prediction of band gap diagram. Moreover, the range of the total band gap is determined by the boundary parameters of the gradient design, and its integrity is affected by the setting of gradient interval. In particular, the relationship between the gradient interval setting and the generation of overlapping gaps is analyzed. The gradient outward-hierarchical metamaterial is demonstrated to be an effective solution for elastic wave bandgap engineering, which can also be considered as a complement to existing inward-hierarchical configurations.

This paper addresses the wave propagation problem within the context of the theory of materials with triple porosity under local thermal non-equilibrium. The time-harmonic wave solution is studied and the dispersion relation is explicitly established as an eighth-degree algebraic equation. It is shown that there are two shear waves undamped in time, that are non-dispersive and unaltered by the presence of the pore system or by thermal effects. Also, there are seven longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave, three longitudinal quasi-pore standing waves and three other longitudinal quasi-thermal standing waves. An illustrative simulation on a material like Berea sandstone shows that the effects of coupling triple porosity with local thermal imbalance and mechanical deformations leads to an increase in the propagation speed of the longitudinal quasi-elastic wave accompanied by an increase in its rate of decrease over time, as well as to a relaxation of the decrease in time for the quasi-pore and quasi-thermal standing waves.

Построена полностью нелинейная слабо дисперсионная модель волновой гидродинамики четвертого порядка длинноволновой аппроксимации. За скорость в модели взята усредненная по глубине горизонтальная составляющая скорости трехмерного течения. Учтена подвижность дна. Выполненная модификация модели обеспечивает шестой и восьмой порядки точности аппроксимации дисперсионного соотношения трехмерной модели потенциальных течений. In the numerical simulation of medium-length surface waves in the framework of nonlinear dispersive (NLD) models, an increased accuracy of reproducing the characteristics of the simulated processes is required. A number of works (Kirby (2016), e.g.) describe approaches to improve the known NLD-models. In particular, NLD-models of the fourth order of the long-wave approximation have been proposed and, based on a comparison of numerical results with experimental data, their high accuracy has been demonstrated (Ataie-Ashtiani and Najafi-Jilani (2007); Zhou and Teng (2010)). In these new models, the horizontal component of the velocity vector of the threedimensional (FNPF-) model of potential flows at a certain surface located between the bottom and the free boundary was chosen as the velocity vector. The result was a very cumbersome form of equations. In addition, the laws of conservation of mass and momentum do not hold for these models. The main result of this work is the derivation of a two-parameter fully nonlinear weakly dispersive (mSGN4) model of the fourth order of the long-wave approximation, which is a generalization of the well-known Serre-Green-Naghdi (SGN) second order model. In the derivation, the velocity averaged over the thickness of the liquid layer was used. The assumption about the potentiality of the three-dimensional flow was used only at the stage of closing the model. The movement of the bottom is taken into account. For the derived model, the law of conservation of mass is satisfied, and the law of conservation of total momentum is satisfied in the case of a horizontal stationary bottom. The equations of the mSGN4-model are invariant under the Galilean transformation and are presented in a compact form similar to the equations of gas dynamics. The dispersion relation of the mSGN4-model has the fourth order of accuracy in the long wave region and satisfactorily approximates the dispersion relation of the FNPF-model in the short wave region. Moreover, with a special choice of the values of the model parameters, an increased accuracy of approximating the dispersion relation of the FNPF-model at long waves (sixth or eighth order) is achieved. Analysis of the deviations of the values of the phase velocity of the mSGN4 model from the values of the “reference” speed of the FNPF model in the entire wavelength range showed that the most preferable is the mSGN4 model with the parameter values corresponding to the Pad’e approximant (2,4).

The correlation between electrical properties and surface plasmon resonance (SPR) wavelength was discussed using ITO grating coupler. ITO films were prepared on SiO $$_{2}$$ /Si substrate by RF sputtering with thermal annealing, and the grating was directly fabricated on the sample surface by focused ion beam. Electron density and mobility were evaluated by fitting optical reflection spectra according to Drude model, and then SPR wavelength was estimated from the dispersion relation of surface plasmon. Characteristic SPR dip was observed in polarized reflection spectrum, however, measured wavelength was different from theoretically estimated value. The discrepancy was explained by introducing the assumption based on effective medium theory, in which the grating is assumed as a thin film with effective refractive index.

In this work we investigate the influence of the material’s internal characteristic length parameters on the dispersion relations for the surface shear waves in the piezoelectric materials. We derive semi-analytical solution for the dynamic anti-plane problem of the second gradient electroelasticity taking into account the elastic, electric field and inertia gradient effects. We found that in opposite to the known solutions of the second gradient elasticity, in the presented coupled field theory we can obtain a solution for the second (‘‘optical’’) branch of the dispersion relations. However, this solution should be abandoned since it has non-decaying behavior with purely imaginary attenuation coefficient. Also it is shown that gradient piezoelectric modulus that defines the high order piezoelectric effect, i.e. the coupling between the strain gradients and the electric field gradients, can be insignificant in the assessments on the spatial dispersion effects for the electroacoustic surface 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.

The surface current density of charge carriers in two-dimensional doubly periodic n-type semiconductor superlattices in an external magnetic field in the presence of temperature gradient has been calculated in the single-electron approximation. The magnetic field was assumed to be permanent, homogeneous, and oriented perpendicular to the electron-gas plane. A joint solution of the Schrodinger equation and kinetic Boltzmann equation showed that the dependences of the surface density of transverse current on temperature and temperature-gradient magnitude are significantly nonlinear and contain portions with negative transverse differential conductivity. The dependence of the relaxation time on the electron quasi-momentum is phenomenologically taken into account in the model via the dispersion relation for carriers in magnetic subbands.

We present new two-sided constraints on Lorentz Invariance violation energy scale for photons with quartic dispersion relation from recent gamma ray observations by Tibet-AS$\gamma$ and LHAASO experiments. The constraints are based on the consideration of the processes of photon triple splitting (superluminal scenario) and the suppression of shower formation (subluminal). The constraints in subluminal scenario are better than the pair production constraints and are the strongest in the literature., Comment: 11 pages, 2 figures, 1 table. v2: the effect of pair production on CMB has been added

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 physical and optical properties of plasmas are depended on dynamics of species in the discharge volume. Then, the presence of an electron beam, as a separate component, in a dusty plasma can modify the plasma structures through altering the discharge parameters. In this report, the linear propagation of acoustic modes in a collisionless dusty plasma contains electrons, ions and charged dust grains is investigated in the presence of an electron beam. Our analysis indicates that the electron beam can modify the dispersion relations of dust acoustic modes which resulted different data transportation in dusty plasmas. The obtained results are also examined for negative and positive charged dust grains with different number densities. The charge of dust grains represents an important role in the dynamics of the low frequency waves. Additionally, our findings reveal that the propagation of acoustic waves in dusty plasmas can be controlled by adjusting the electron number density of the beam and the cathode potential. Lastly, we obtian the destabilizing effects, originated from dust charge fluctuation, by reconsidering the dispersion relations of both dust acoustic modes.

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

We present results of the analysis of Brillouin light-scattering (BLS) measurements of spin waves performed on ultrathin single and multirepeat CoFeB layers with adjacent heavy metal layers. From a detailed study of the spin-wave dispersion relation, we independently extract the Heisenberg exchange interaction (also referred to as symmetric exchange interaction), the Dzyaloshinskii–Moriya interaction (DMI, also referred to as antisymmetric exchange interaction), and the anisotropy field. We find a large DMI in CoFeB thin films adjacent to a Pt layer and nearly vanishing DMI for CoFeB films adjacent to a W layer. Furthermore, the influence of the dipolar interaction on the dispersion relation and on the evaluation of the Heisenberg exchange parameter is demonstrated. Eventually, an experimental analysis of the impact of the DMI on the spin-wave lifetime is presented.