Wavefront Research Articles

Dynamical structures of wave front to the fractional generalized equal width-Burgers model via two analytic schemes: Effects of parameters and fractionality

Abstract This work focuses on the fractional general equal width-Burger model, which describes one-dimensional wave transmission in nonlinear Kerr media with combined dispersive and dissipative effects. The unified and a novel form of the modified Kudryashov approaches are employed in this study to investigate various analytical wave solutions of the model, considering different powers of nonlinearity in the Kerr media. As a result, a wide range of structural solutions, including trigonometric, hyperbolic, rational, and logarithmic functions, are formulated. The achieved solutions present a kink wave, a collision of kink and periodic peaked soliton, exponentially increasing wave profiles, and shock with a dark peaked wave. The obtained solutions are numerically demonstrated for specific parameter values and general parametric powers of nonlinearity. We analyzed the effect of existing parameters on the obtained wave solutions with numerical graphics. Moreover, the stability of the model is analyzed with a perturbed system. Furthermore, a comparison with published results in the literature is provided, highlighting the differences and similarities. The achieved results showcase the diversity of structural solutions obtained through the proposed approaches.

Tunable full-space light field manipulation based on double-layer Ge2Sb2Te5 metasurfaces

Metasurfaces have the strong ability to reshape wave front and are attractive for a wide range of applications. However, metasurface based light field manipulation can be realized usually in either transmission or reflection space individually, which will limit its application scenario of metasuface. In this paper, we design a phase change material Ge2Sb2Te5 (GST) based double-layer dielectric metasurface in mid-infrared bands, which can achieve the light field manipulation in full space and dynamically control the focal intensity of reflected and transmitted light. As proof-of-concepts, two functional metasurfaces are designed and investigated: the first metasurface realizes the dynamically adjustable focus intensity in full-space under left circularly polarized (LCP) light incidence, the second metasurface is designed to provide spin-dependent bifocal in full space, which can generate custom designed two focal points under LCP or right circularly polarized (RCP) light incidence. Our proposed tunable full-space dielectric metasurfaces can be potentially applied for energy-harvesting, optical communication and optical imaging.

Ionic Mechanisms of Propagated Repolarization in a One-Dimensional Strand of Human Ventricular Myocyte Model.

Although repolarization has been suggested to propagate in cardiac tissue both theoretically and experimentally, it has been challenging to estimate how and to what extent the propagation of repolarization contributes to relaxation because repolarization only occurs in the course of membrane excitation in normal hearts. We established a mathematical model of a 1D strand of 600 myocytes stabilized at an equilibrium potential near the plateau potential level by introducing a sustained component of the late sodium current (INaL). By applying a hyperpolarizing stimulus to a small part of the strand, we succeeded in inducing repolarization which propagated along the strand at a velocity of 1~2 cm/s. The ionic mechanisms responsible for repolarization at the myocyte level, i.e., the deactivation of both the INaL and the L-type calcium current (ICaL), and the activation of the rapid component of delayed rectifier potassium current (IKr) and the inward rectifier potassium channel (IK1), were found to be important for the propagation of repolarization in the myocyte strand. Using an analogy with progressive activation of the sodium current (INa) in the propagation of excitation, regenerative activation of the predominant magnitude of IK1 makes the myocytes at the wave front start repolarization in succession through the electrical coupling via gap junction channels.

Active anisotropic polarization conversion meta-surface for 6G communication bandgap in the reflection mode

This paper investigates a single-layered active anisotropic meta-surface design capable of achieving high polarization conversion efficiency in the 6 G communication band gap. Additionally, the designed structure can convert the linear polarization of the incoming wave fronts to its cross-polarization and linear polarization to circular polarization in the reflection mode. The polarization conversion characteristic is achieved due to the strong anisotropic behavior of the meta-surface. Such a simple design can achieve a 90% to 100% cross-polarization conversion efficiency over a frequency region of [0.28–0.36] THz. The linear to circular polarization conversion is performed near 0.26 THz and 0.40 THz. Between these two frequencies, band linear to cross-polarization conversion is more prominent. The proposed design can be tuned from a half-wave plate (HWP) or linear polarization converter to a quarter-wave plate (QWP) or circular polarization converter using the chemical potential of graphene. The optical response of the meta-surface behaves differently from different incident angles. The proposed polarization converter can contribute to the development of active polarization device.

Is the invasive Rhododendron ponticum L. an emergent threat to mainland Atlantic forests? A population dynamics approach

Understanding the population dynamics of invasive species is essential for identifying the key parameters of their success and guiding management actions. European temperate forests of the Atlantic domain are prone to be invaded by the Pontic Rhododendron (Rhododendron ponticum L. subsp. baeticum (Boiss. & Reut.) Hand.-Mazz.), a shade-tolerate evergreen shrub native to the Iberian peninsula. While the invasion has a long history in Ireland and the British Isles, it is an emerging threat in mainland Europe. It is therefore a timely challenge to better understanding the invasive dynamics of this species in this context. We studied the population dynamics of R. ponticum in 27 invaded forests of north-western France, examining population structure, and individuals’ growth, fertility and fecundity among contrasted light conditions. All invasive populations were found on acidic soils. Irrespective of light conditions, R. ponticum exhibited a regular radial growth, with a clear increase since the 1990s. The majority of stems were younger than 38 years on average, indicating a recent increase in population density. Light availability strongly impacted R. ponticum’s canopy structure, with higher canopy cover and stem numbers under sun conditions. Despite the production of a huge number of viable seeds, the observed number of seedlings was always very low irrespective of light conditions, indicating recruitment limitation and thus a limited ability to establish new, distant populations. In contrast, vegetative propagation via intense layering at the invasion front wave ensured local population spread from initially planted individuals, especially on moist soils. We conclude that where it has been planted, R. ponticum is able to actively layer, thereby forming dense bushes in the forest understories as long as the soil is acidic and relatively moist. The establishment of new, distant populations appears a rare event since recruitment is limited to particular microhabitats related to forest management-associated disturbances. Such disturbance should thus be avoided in sites where the species has already established, unless a post-disturbance eradication of R. ponticum’s seedling can be implemented the following years. The plantation of R. ponticum in forest must be avoided when the soil is acidic and moist. Because R. ponticum’s growth performances are increasing since the 1990s, as a likely consequence of climate change, monitoring established populations is recommended to detect a possible increasing invasiveness.

Dynamics of crack front waves in three-dimensional material failure.

Crack front waves (FWs) are dynamic objects that propagate along moving crack fronts in three-dimensional (3D) materials. We study FW dynamics in the framework of a 3D phase-field platform that features a rate-dependent fracture energy Γ(v) (v is the crack propagation velocity) and intrinsic length scales, and quantitatively reproduces the high-speed oscillatory instability in the quasi-2D limit. We show that in-plane FWs feature a rather weak time dependence, with decay rate that increases with dΓ(v)/dv>0, and largely retain their properties upon FW-FW interactions, similarly to a related experimentally observed solitonic behavior. Driving in-plane FWs into the nonlinear regime, we find that they propagate slower than predicted by a linear perturbation theory. Finally, by introducing small out-of-plane symmetry-breaking perturbations, coupled in- and out-of-plane FWs are excited, but the out-of-plane component decays under pure tensile loading. Yet, including a small antiplane loading component gives rise to persistent coupled in- and out-of-plane FWs.

Mirror-coupled toroidal dipole bound states in the continuum for tunable narrowband perfect absorption

Metasurfaces have received a significant amount of attention in recent years as they offer novel ways for wave front control, subwavelength light focusing, and flat optics. Here, we employ sharp resonances in metasurfaces originated from the physics of bound states in the continuum (BICs) for both engineering and enhancing the absorption of light. Specifically, using temporal coupled-mode theory and numerical simulations, we demonstrate that an all-dielectric metasurface, of which the meta-atom consists of narrow-gap Si dimers with a monolayer graphene, can perfectly absorb the incident near-infrared light through critical coupling to the mirror-coupled toroidal dipole BIC. Due to unique loss engineering capabilities of the mode, multiple tuning knobs, including the narrow gap, meta-atom–mirror distance, and geometrical scaling factor, can be utilized for control over the coupling condition and the electric-field enhancement at the critical coupling condition. These results suggest that our platform could promise in on-chip optoelectronic applications.

Two-dimensional study of Rossby waves generated by an initial disturbance

Rossby waves are the fundamental time dependent large-scale motion of the ocean and atmosphere. In this article, we are interested to find analytical solution of Rossby waves produced by an initial disturbance. These waves, as we know, are archetypical low-frequency waves, which play a central role in defining meteorological and oceanographic conditions. Our purpose here is to analyze the properties of such waves in two dimension as a guide to the construction of the dynamical framework appropriate for low-frequency motion. As a precursor to our aim, we revisited the problem of Rossby wave generation in an ocean bounded by two imaginary latitudes for a particular type of external forcing. The characteristics of this motion are explored with the help of group velocity and phase velocity. Subsequently, the two-dimensional case of generation of Rossby wave by a general form of disturbance in an unbounded ocean is solved where the concept of stationary phase method is extensively used. The rules of governing the propagation of wave packet are discussed, and we found for a wave-like disturbance, Rossby wave is not a single wave train but rather several, which moves as a wave front with a definite direction-deviation. It is natural to question what role, if any, the source plays in explicit determination of these radiated waves and their asymptotic behavior. To address these and other concerns, we have developed an analytical model of generation of Rossby waves produced by an initial disturbance in two-dimensional open ocean with a considerable generality.

Acoustic black hole designs for circular beams under axial loading

Acoustic Black Hole (ABH), as a non-reflecting wave effect, has been realised in beams and plates by locally changing their thickness. Geometrical ABH designs stem from their transverse-load bearing properties, assuming isotropic material properties associated with engineering materials (e.g., steels). The underlying physics is to manipulate stiffness locally for a transversely-loaded structure, leading to a change in the elastic wave speed. However, the same ABH would have limitations for axial loading, i.e., slender beams for which longitudinal waves dominate. Here, we present a wave propagation approach using wavefront tracking to identify a potential ABH for axially-loaded circular beams. We study wave propagation in three exponential designs of finite length, monitoring the wave-travel time. Indicative of an effective ABH in finite length sections, the wave-travel time increases compared to the case of a beam without ABH. By employing the wave front tracking method for the design of an ABH with axial loading, it is possible to verify the effectiveness of ABHs. Also, various material models, e.g., orthotropic materials such as wood, and different loading conditions can be considered, which opens a new avenue in applications of ABH phenomena beyond conventional vibro-acoustic control problems.

Multi-Conductor Cable Modeling With Inclusion of Measured Coaxial Wave Propagation Characteristics

The prediction of voltage stresses in transformer and machine windings requires the ability to calculate pulse propagation effects on the feeding cable with sufficient accuracy. The use of commonly available cable models in electromagnetic transient (EMT) programs can lead to voltage wave fronts with too weak damping at very high frequencies. This work shows a method for improving the accuracy of such models by usage of measured coaxial mode propagation characteristics. The information is introduced into a wide-band multi-conductor cable model at high frequencies by a merging procedure, with only a minor impact on the non-coaxial modes of propagation. The application of the developed model is demonstrated for cases where the metallic sheaths are grounded at one end only, or are cross-bonded.

On coherently processing multiple arrays in underwater environments with spatial coherence losses from random medium effects and sensor position uncertainties

Under ideal circumstances coherently beamforming multiple distributed arrays should provide improvements over the standard approach of processing the arrays individually and combining them incoherently. These include improved directivity and higher gain. However, two major challenges when coherently processing spatially separated arrays in a real ocean are dealing with coherence losses or wave front distortions caused by random medium effects like internal waves and uncertainties in sensor locations. Some of the consequences are degraded beampatterns and poorer array directivity. In this paper, we perform a simulation-based study utilizing numerical propagation models along with theory examining the effects of wave front distortions induced by random medium effects like internal waves and sensor position uncertainties on coherently beamforming distributed arrays in representative ocean waveguides. Realistic realizations of wave front distortions are generated from actual internal wave measurements and models. The sensitivities of coherent processing to these effects are characterized by resultant beampatterns and losses in array directivity along with a quantification of the tolerances.

Role of alpha particles in penetration of solar wind diamagnetic structures into the magnetosphere

We present the results of studies showing the presence of simultaneous jumps in the density of protons (N2/N1)p and alpha particles (N2/N1)α at the boundaries of diamagnetic structures (DS) of various types both in the quasi-stationary slow solar wind (SW) and in sporadic SW. For DS of quasi-stationary slow SW, associated with streamer belt or chains, in the statistics considered in the paper there is a single linear dependence of (N2/N1)α on (N2/N1)p. This means that these jumps have the same physical nature and are related to diamagnetism at the boundaries of DS of quasi-stationary SW streams of various types.
 At the front of interplanetary shock waves (ISW), the (N2/N1)α jump is approximately twice as large as the (N2/N1)p jump. This reflects the features of the collective collisionless plasma heating at ISW fronts and requires further studies. A maximum excess (almost 3 times) of the increase in the alpha-particle density (N2/N1)α over the increase in the proton density (N2/N1)p is observed in eruptive prominences.
 The magnetospheric response in such phenomena as auroras, proton and alpha particle fluxes, geomagnetic field, and geomagnetic pulsations is similar under the influence of DS of various types and ISW. The detected features of the magnetospheric response to the contact with DS of different types and ISW can be interpreted as impulsive passage of the DS matter (plasmoid) into the magnetosphere.
 The results of studies of the (N2/N1)α jumps can be used as an additional important argument in identifying cases of impulsive penetration of DS into the magnetosphere and in examining the physical nature of these penetrations.

Анализ параметров ударных волн на стенке взрывной полости при преломлении детонационных волн через воздушную и водную среду

Анализ параметров ударных волн на стенке взрывной полости при преломлении детонационных волн через воздушную и водную среду

Роль альфа-частиц в проникновении диамагнитных структур солнечного ветра внутрь магнитосферы

We present the results of studies showing the presence of simultaneous jumps in the density of protons (N2/N1)p and alpha particles (N2/N1)α at the boundaries of diamagnetic structures (DS) of various types both in the quasi-stationary slow solar wind (SW) and in sporadic SW. For DS of quasi-stationary slow SW, associated with streamer belt or chains, in the statistics considered in the paper there is a single linear dependence of (N2/N1)α on (N2/N1)p. This means that these jumps have the same physical nature and are related to diamagnetism at the boundaries of DS of quasi-stationary SW streams of various types.
 At the front of interplanetary shock waves (ISW), the (N2/N1)α jump is approximately twice as large as the (N2/N1)p jump. This reflects the features of the collective collisionless plasma heating at ISW fronts and requires further studies. A maximum excess (almost 3 times) of the increase in the alpha-particle density (N2/N1)α over the increase in the proton density (N2/N1)p is observed in eruptive prominences.
 The magnetospheric response in such phenomena as auroras, proton and alpha particle fluxes, geomagnetic field, and geomagnetic pulsations is similar under the influence of DS of various types and ISW. The detected features of the magnetospheric response to the contact with DS of different types and ISW can be interpreted as impulsive passage of the DS matter (plasmoid) into the magnetosphere.
 The results of studies of the (N2/N1)α jumps can be used as an additional important argument in identifying cases of impulsive penetration of DS into the magnetosphere and in examining the physical nature of these penetrations.

Illustrations of Bessel Beams in s-Polarization, p-Polarization, Transverse Polarization, and Longitudinal Polarization

The generation of Bessel beams (BBs) and their characterization in a wide range of the electromagnetic spectrum are well established. The unique properties of BBs, including their non-diffracting and self-healing nature, make them efficient for use in material science and engineering technology. Here, I investigate the polarization components (s-polarization, p-polarization, transverse polarization, and longitudinal polarization) created in scalar BBs owing to their conical wave front. For emphasis, I provide a theoretical analysis to characterize potential experimental artifacts created in the four polarization components. Further, I provide a brief discussion on how to prevent these artifacts in scalar BBs. To my knowledge, for the first time, I can generate vector BBs in s-polarization and p-polarization via the superposition of two orthogonally polarized scalar BBs. This method of generation can provide the four well-known types of vector modes categorized in the V-point phase singularity vector modes. I suggest a suitable experimental configuration for realizing my theoretical results experimentally. The present analysis is very practical and beneficial for young researchers who seek to utilize BBs in light applications of modern science and technology.

Stability and uniqueness of generalized traveling front for non-autonomous Fisher–KPP equations with nonlocal diffusion

This paper is concerned with the stability and uniqueness of generalized traveling front of non-autonomous Fisher–KPP equations with nonlocal diffusion. In such non-autonomous nonlocal dispersal equations, both the diffusion kernel and the reaction term generally depend on time. The existence of generalized traveling wave fronts of such equations has been studied in Ducrot and Jin (2022). By using comparison principle and part metric, we show the generalized traveling front is asymptotically stable under well-fitted perturbation and it is also unique.

Numerical investigation on spall fracture in metallic materials due to laser shock peening via phase field approach to fracture

Laser shock peening (LSP) is an effective surface reinforcement technique for metallic materials. However, when LSP is applied to a thin specimen, an undesirable result, spall fracture, may occur. In this work, the spall fracture generated in multiple-shock LSP processes is investigated via the phase field approach to fracture, and is validated with the experimental result. In particular, the relations between the formation of spall fracture and the shock number, the shock wave pressure, the specimen thickness and the fracture toughness of specimen are studied. The results indicate that the formation of spall fracture in multiple-shock processes is an accumulative process, and is mainly influenced by the shock wave pressure and the specimen thickness, and multiple shocks will complicate the interaction between the tensile wave tail and the compressive wave front of the shock wave, leading to an enlargement of the spall fracture region.

Jetting and shock wave during oblique hypervelocity impact of spherical projectile

Abstract Space debris impacts on whipped shields are dominantly non-vertical. During the initial impact stage of a projectile on a target, wave propagation and evolution occur in their interior with co-dominant material fragmentation. In this study, the effects of the impact conditions (impact velocity and attack angle) on the critical conditions for jet generation were examined based on the asymmetric jetting theory. In the geometric propagation model (GPM), the effect of the attack angle was considered, and a wave front deflection angle parameter was introduced. The modified GPM could describe the geometric features and position of a wave front during an oblique impact. Combined with smoothed particle hydrodynamics numerical simulations, the interior of projectiles, fragmentation features and pressure attenuation were studied. It was found that in large attack angle cases, the projectile material is more likely to reach the critical conditions for jet generation. The modified GPM is an oblique elliptic equation that is a function of the equivalent speed, impact velocity, attack angle, time and deflection angle. It may be applicable to hypervelocity events involving any monolithic material as long as the equivalent speed and deflection angle can be provided from numerical simulations. The impact conditions exhibit a quantitative relationship with the pressure attenuation in a projectile, among which the impact velocity has a more significant effect. This study established a quantitative analysis method for the initial impact stage of the oblique hypervelocity impact of a spherical projectile on a flat plate.

Oscillating Nonlinear Acoustic Waves in a Mooney–Rivlin Rod

Harmonic wave excitation in a semi-infinite incompressible hyperelastic 1D rod with the Mooney–Rivlin equation of state reveals the formation and propagation of the shock wave fronts arising between faster and slower moving parts of the initially harmonic wave. The observed shock wave fronts result in the collapse of the slower moving parts being absorbed by the faster parts; hence, to the attenuation of the kinetic and the elastic strain energy with the corresponding heat generation. Both geometrically and physically nonlinear equations of motion are solved by the explicit Lax–Wendroff numerical tine-integration scheme combined with the finite element approach for spatial discretization.

Hyperbolic Conduction and Radiation Heat Transfer in Axisymmetric Cylinders with Variable Properties

This work investigates the combined mode of hyperbolic heat conduction and radiation transfer in a one-dimensional axisymmetric cylinder filled with absorbing, emitting, and scattering media. The volumetric radiation is investigated thanks to the semianalytic solution of the matrix formulation of the spherical harmonics equations PN. The governing hyperbolic energy equation is solved using the finite volume method (FVM) with Roe’s correction of interface fluxes in order to enhance the performances of the method, and the lattice Boltzmann method (LBM) has been designed for comparisons. The effects of the parameters such as constant and spatial-dependent scattering albedos, temperature-dependent thermal conductivity, heat-generated sources, extinction, and the conduction–radiation parameter on both the temperature and heat flux distributions for steady and transient states within the medium are examined. The results of the present work are in excellent agreement with those available in the literature. The PN−FVM results are also compared to those obtained with the PN−LBM combination, and excellent agreement is obtained. These results show that the mentioned parameters have a significant effect on both the temperature profiles and the hyperbolic sharp wave front. This study also shows that the proposed layered approach is an efficient, fast, and accurate solution method for radiative analysis in inhomogeneous media, whereas the Roe’s correction of interface fluxes in the FVM is suitable to accommodate a thermal wave front in non-Fourier analysis.