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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.

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 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.

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