Wave Envelope Research Articles

Modulation of electromagnetic waves in a relativistic degenerate plasma at finite temperature

We study the modulational instability (MI) of a linearly polarized electromagnetic (EM) wave envelope in an intermediate regime of relativistic degenerate plasmas at a finite temperature (T≠0) where the thermal energy (KBT) and the rest-mass energy (mec2) of electrons do not differ significantly, i.e., βe≡KBT/mec2≲ (or ≳) 1, but the Fermi energy (KBTF) and the chemical potential energy (μe) of electrons are still a bit higher than the thermal energy, i.e., TF>T and ξe=μe/KBT≳1. Starting from a set of relativistic fluid equations for degenerate electrons at finite temperature, coupled to the EM wave equation and using the multiple scale perturbation expansion scheme, a one-dimensional nonlinear Schödinger (NLS) equation is derived, which describes the evolution of slowly varying amplitudes of EM wave envelopes. Then, we study the MI of the latter in two different regimes, namely, βe<1 and βe>1. Like unmagnetized classical cold plasmas, the modulated EM envelope is always unstable in the region βe>4. However, for βe≲1 and 1<βe<4, the wave can be stable or unstable depending on the values of the EM wave frequency, ω, and the parameter ξe. We also obtain the instability growth rate for the modulated wave and find a significant reduction by increasing the values of either βe or ξe. Finally, we present the profiles of the traveling EM waves in the form of bright (envelope pulses) and dark (voids) solitons, as well as the profiles (other than traveling waves) of the Kuznetsov–Ma breather, the Akhmediev breather, and the Peregrine solitons as EM rogue (freak) waves, and discuss their characteristics in the regimes of βe≲1 and βe>1.

Computational modeling of wave propagation in plasma physics over the Gilson–Pickering equation

In this paper, the Gilson–Pickering equation is studied which enables a wave propagation in plasma physics and crystal lattice theory. Based on the auxiliary transformations, some sets of the nonlinear form of ODE along with some analytic solutions are derived. To study the characterizations of the new waves, the crystal lattice theory and plasma physics is studied by using the modified exponential Jacobi technique and generalized rational tan(ϕ/2)-expansion technique. Through the new approaches, some solitary solutions are proposed. Meanwhile, influence of the coefficients in that equation for the periodic and soliton is illustrated. The effect of the free variables on the solutions is investigated. The behavior of these solutions on qualitatively of different structural natures relying on physical parameters coefficients is analyzed. The reported bright explosive envelopes, explosive solitons, periodic blow up, bright periodic envelope and huge solitary waves are highly applied in plasma and nuclear physics, optical communications, electro-magnetic propagations, superfluid and plenty other applied sciences. For more details about the physical dynamical representation of the presented solutions, are illustrated with profile pictures using Mathematica and Matlab 18, to obtain complete configurations. The proposed approaches can be applied to several equations arising from all nonlinear applied sciences.

Envelope solitons in weakly dissipative dusty plasma

A hydrodynamic model is applied to characterize the linear and nonlinear characteristics of collisional dust acoustic waves of degenerate inertialess ions and electrons. The dispersion properties of dust acoustic waves are derived, inertia provided by dust particles, and restoring force is due to electrons and ions. In nonlinear analysis, we follow the reductive perturbation technique to derive the dissipative nonlinear Schrödinger equation. The modulated growth rate of instability, the envelope, and rogue waves are investigated numerically as well as analytically. This paper will provide an important contribution to understanding the linear and nonlinear properties of electrostatic excitations in degenerate dusty plasma, which are relevant to the DUSTY DAZ WDs.

Nonlinear optical rectification of GaAs/GaAlAs quantum dot under tangent square potential

We have investigated in detail the effects of the depth and range of the limiting potential, the quantum size parameter, temperature and hydrostatic pressure on the nonlinear optical rectification (NOR) coefficient in GaAs/GaAlAs parabolic quantum dots (QDs) with a tangent square potential. Firstly, we add the tangent-square potential of the system along the z-axis to the original parabolic QD, and then the corresponding Schrödinger equation of the modified system can be solved to find the analytical forms of different splitting energy levels and envelope wave functions. Finally, the analysis and conclusions of the numerical simulations indicate that the above parameters have significant effects on the nonlinear optical properties of the modified system.

Evolyutsiya nelineynykh volnovykh impul'sov v teorii uravneniya sinus-Gordon

The solution to the Whitham modulation equations for envelopes of one-phase periodic waves evolving according to the sine-Gordon equation is obtained. Using the hodograph method, these equations are reduced to a linear partial differential equation, and the class of solutions to this equation with separation of variables is described. The theory is illustrated by an example in which a complete analytic solution is obtained for the problem of nonlinear wave packet evolution accompanied with self-contraction and a decrease in the number of oscillations in the Whitham nonlinear region.

Abnormal transmitral flow: what is the rhythm?

Echocardiography was performed on 78-year-old woman for the follow-up of moderate mitral valve regurgitation (MR). A single-lead electrocardiographic (ECG) tracing showed bradycardia with irregular heart rhythm between 46 and 53 beats per minute. The echocardiographic image of pulsed wave Doppler at mitral inflow is displayed in Panel. There was a progressive shortening of the interval between E (early) and A (late) diastolic filling waves, followed by an absent A wave. A gradual shortening of the A-A wave interval was also noted. The interval between A wave and MR envelope remains constant. This typical pattern is consistent with Wenckebach phenomenon in sinoatrial (SA) exit block. SA exit block is due to failed propagation of pacemaker impulses beyond the SA node. In Type I second-degree SA block (Wenckebach), there is a progressive delay in the conduction from the SA node to the atrium until one impulse is completely blocked, leading to intermittent failure of atrial depolarization and ensuing absence of A wave in the Doppler inflow pattern. Moreover, the A-A wave interval is gradually decreased (i.e. the atrial rate accelerates) as the increment in the conduction delay from the SA node to the atrium becomes progressively smaller.

Quasi-permanent meanders of the Kuroshio Extension: Laboratory experiments with altimetry and numerical simulations

This is a study of gyres bounded by a barrier in the west and forced by a localized upwelling. It is motivated by observations of quasi-permanent meanders of the Kuroshio Extension in the North Pacific Subtropical Gyre. Laboratory experiments are performed in a rotating tank where a parabolic shape of the surface of water is used to model the latitudinal variation of the Coriolis parameter. Optical altimetry provides accurate records of circulations and allows us to observe the evolution of β-plumes (Rossby wave envelopes), including their reflection from the barrier. Experiments are supplemented by numerical simulations which extend the range of the control parameters. We demonstrate that meanders occur in the northern branch of the gyres, within an eastward current similar to those in the Kuroshio Extension. The meanders are due to the Rossby wave reflection from the boundary. The wavelength of the meanders is selected by the condition of stationarity of the westward propagating Rossby-wave phase within an eastward current.

Investigation on nonlinear optical properties of symmetric and asymmetric double V-shaped AlxGa1-xAs/GaAs potential wells with structural parameters and external electromagnetic fields

ABSTRACT Linear, nonlinear and total optical absorption coefficients and relative refractive index changes for symmetric and asymmetric double V-shaped quantum well configurations formed within AlxGa1-xAs/GaAs heterostructure have been theoretically investigated. Responses of these coefficients to well widths, barrier widths and aluminium concentrations within the barrier as well as applied external electromagnetic fields were the subject of this study. The electronic spectra of the structures are obtained as a solution to the Schrödinger equation with relevant potential and external agents in the framework of effective mass and envelope wave function approximations. The optical properties are calculated by the analytical expressions obtained by iterative solutions within the compact density matrix approach. Although increasing barrier width and aluminium concentration act similarly significant red shifting on the referred coefficients for both symmetric and asymmetric double V-shaped wells, the varying well widths act differently for each configuration. Strengthening electric and magnetic fields shift the resonance peaks to blue for both symmetric and asymmetric wells. The results show that optical properties can be controlled by structural parameters, external probes and asymmetry of double V-shaped wells.

Investigation of optical soliton solutions for the perturbed Gerdjikov-Ivanov equation with full-nonlinearity

We have discussed the perturbed Gerdjikov-Ivanov (pGI) equation describing optical pulse propagation (PP) with perturbation effects, which has various applications in optical fibers, especially in photonic crystal fibers. According to our literature review, we have discovered new and original soliton types using the Sardar sub-equation and the modified Kudryashov methods, which have not been applied to this model before. We obtained dark, bright, periodic-singular and periodic-M-shaped soliton solutions, respectively. The analytical forms of the obtained solutions are represented by 3D, 2D and contour graphics. In addition, the physical effects of the solution parameters on the wave envelope have been described and clearly interpreted by presenting their 2D graphics.

Chaos and complexity in the dynamics of nonlinear Alfvén waves in a magnetoplasma.

The nonlinear dynamics of circularly polarized dispersive Alfvén wave (AW) envelopes coupled to the driven ion-sound waves of plasma slow response is studied in a uniform magnetoplasma. By restricting the wave dynamics to a few number of harmonic modes, a low-dimensional dynamical model is proposed to describe the nonlinear wave-wave interactions. It is found that two subintervals of the wave number of modulation k of AW envelope exist, namely, (3/4)kc<k<kc and 0<k<(3/4)kc, where kc is the critical value of k below which the modulational instability (MI) occurs. In the former, where the MI growth rate is low, the periodic and/or quasi-periodic states are shown to occur, whereas the latter, where the MI growth is high, brings about the chaotic states. The existence of these states is established by the analyses of Lyapunov exponent spectra together with the bifurcation diagram and phase-space portraits of dynamical variables. Furthermore, the complexities of chaotic phase spaces in the nonlinear motion are measured by the estimations of the correlation dimension as well as the approximate entropy and compared with those for the known Hénon map and the Lorenz system in which a good qualitative agreement is noted. The chaotic motion, thus, predicted in a low-dimensional model can be a prerequisite for the onset of Alfvénic wave turbulence to be observed in a higher dimensional model that is relevant in the Earth's ionosphere and magnetosphere.

Propagation of novel traveling wave envelopes of Zhiber–Shabat equation by using Lie analysis

In this paper, we aim to find novel forms of wave structures by employing some innovative ideas. Various solitary wave solutions of the Zhiber–Shabat equation have been extracted using the Lie symmetry analysis and the extended direct algebraic method. In the mathematical community, the considered model has several applications, notably in integral quantum field theory, fluid dynamics, and kink dynamics. First of all, the Lie symmetry has been used to determine the corresponding similarity reductions through similarity variables and wave transformation with the help of optimal systems. Afterward, the method described has been used to create new complex, hyperbolic, rational, and trigonometric forms of solutions to the problem. Depending on the strength of the propagating pulse, these solutions reflect dark, bright, kink-type, and periodic solitary wave envelopes. Further, two-dimensional (2D), three-dimensional (3D), as well as contour 2D graphics of the results have been analyzed by giving some specific values to parameters. At last, sensitivity analysis of the evolution equation has been observed.

Features of using the smoothed instantaneous wave energy history (SIWEH) to analyze the group structure of sea waves

The methodological features of determining the characteristics of wave groups of sea surface waves based on the function smoothed instantaneous waves through energy (SIWEH) are analyzed. The analysis is carried out by numerical simulation based on an analytical model of the group structure of waves. It is shown that when the grouping of sea waves is investigated using the SIWEH function, it is advisable to calculate the Groupiness Factors of Height (GFH) in two stages. At the first stage, transform the SIWEH function into a wave envelope, and at the second stage, calculate the GFH using a known envelope. The previously proposed direct calculation of GFH by the SIWEH function leads to significant errors. The effect of the change in the cutoff frequency of the Bartlett filter at a fixed frequency of dominant waves on the calculated values of GFH is investigated. It is shown that when the cutoff frequency changes ±30%, the GFH changes do not exceed 5%.

Embedded iron object detection using asynchronous full wave envelope detector technique in ground penetrating radar system

&lt;span lang="EN-US"&gt;The use of a ground penetrating radar (GPR) system that operates at low frequencies allows the detection of embedded objects underground from the earth’s surface deeper than high frequency. However, the output signal generated from the system using &lt;a name="_Hlk111888456"&gt;&lt;/a&gt;pulse modulation (PM) technique and high-frequency carrier, has many high ripple signals consequently resulting in a blurry image. Nevertheless, this ripple signal can be minimized by reprocessing the signal using an envelope detector method. In this study, an envelope detection technique called ArJED&lt;sup&gt;©&lt;/sup&gt; asynchronous full-wave (AFW) was used in the GPR system and was tested at a frequency range from 0.06 to 0.08 GHz. A dipole antenna has been used as an embedded object detection sensor of the GPR system. The detection system of embedded objects involves four depths starting with 2 cm depth, 5 cm, 7 cm, and 20 cm. A comparison of embedded object images before and after the application of the envelope detection technique was done and proved that the proposed envelope detection technique has produced a clearer radargram image of the GPR system.&lt;/span&gt;

High dynamic range thickness measurement using a double heterodyne interferometer

The present study theoretically demonstrates a high dynamic range optical interference measurement approach based on phase change of the amplitude modulated (AM) wave envelope obtained by on-axis heterodyne interference, which can measure thicknesses from sub-wavelength to several millimeters. First, the AM light wave generated by on-axis heterodyne interference is split into two AM light waves. The sample thickness is obtained from the position of the interference fringes, produced by interfering with the transmitted AM light wave through the sample and reference AM wave. Furthermore, the proposed measurement approach is simplified via 4-beam optical interference using circularly polarized heterodyne-modulated waves.

Optical solitons to the fractional order nonlinear complex model for wave packet envelope

This research deals with the fractional order nonlinear complex model, which is a general form of nonlinear Schrodinger equation. This model demonstrates boson gas among 2 as well as 3 body collisions, nuclear hydro-dynamics allied with Skyrme energies, in addition the optical rhythm propagations within dielectric non-Kerr media. To analyze and generate complex dynamics, optical soliton solutions of the model are derived through improved generalized Riccati equation mapping scheme. As a result, bright, dark and combo bright-dark optical wave envelopes and oscillating pulse bright optical solitons are obtained. The effects of fractionality and parameters are also illustrated with few numerical graphics of the achieved results. The achieved optical (bright and dark) solitons solutions can be used in signal transmission through optical fiber communications system.

A Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticity

This paper is a study of the water wave problem in a two-dimensional domain of infinite depth in the presence of non-zero constant vorticity. A goal is to describe the effects of uniform shear flow on the modulation of weakly nonlinear quasi-monochromatic surface gravity waves. Starting from the Hamiltonian formulation of this problem and using techniques from Hamiltonian transformation theory, we derive a Hamiltonian Dysthe equation for the time evolution of the wave envelope. Consistent with previous studies, we observe that the uniform shear flow tends to enhance or weaken the modulational instability of Stokes waves depending on its direction and strength. Our method also provides a non-perturbative procedure to reconstruct the surface elevation from the wave envelope, based on the Birkhoff normal form transformation to eliminate all non-resonant triads. This model is tested against direct numerical simulations of the full Euler equations and against a related Dysthe equation derived recently by Curtis, Carter &amp; Kalisch (J. Fluid Mech., vol. 855, 2018, pp. 322–350) in the context of constant vorticity. Very good agreement is found for a range of values of the vorticity.

Acoustic-gravity waves generated by a point source on the ground in a stratified atmosphere-Earth structure

SUMMARY An analytically based method is proposed to simulate the acoustic-gravity waves in the horizontally stratified atmosphere-Earth structure generated by a point force on the Earth's surface. The method solves the linear momentum, continuity and adiabaticity equations in the atmosphere and elastodynamic equations in the solid Earth in the frequency–wavenumber domain. The time-domain waveforms are obtained by wavenumber integration and fast Fourier transform with respect to the frequency. Numerical simulations are conducted to investigate the properties of the acoustic-gravity waves, including both the high-frequency acoustic-mode waves and low-frequency gravity-mode waves. Simulations of the high-frequency responses show that disturbances in the atmosphere with three apparent horizontal velocities can be identified. They are, namely, the direct acoustic-mode wave generated by source travelling with the sound speed, the head wave generated by the seismic P-wave travelling with apparent horizontal speed identical to the P velocity, and the head wave generated by the Rayleigh wave with a horizontal speed same to the Rayleigh wave velocity. Simulations of the low-frequency responses show that the gravity-mode wave and Lamb wave can be identified. The gravity-mode wave travels with a speed lower than the sound seed and does not reach everywhere, especially the area directly above the source. The Lamb wave travels along the Earth surface with a speed of about 310 m s–1 and its energy decays with the altitude. We also apply our method to explaining the Doppler sounding data observed in Taiwan area during the 2011 Tohoku M 9 earthquake, and find good agreement between the predicted signals and observed data in the arrival time and wave envelope associated with the Rayleigh wave.

Low-energy amplitude-modulated radiofrequency electromagnetic fields as a systemic treatment for cancer: Review and proposed mechanisms of action.

Exposure to Low-Energy Amplitude-Modulated Radiofrequency Electromagnetic Fields (LEAMRFEMF) represents a new treatment option for patients with advanced hepatocellular carcinoma (AHCC). We focus on two medical devices that modulate the amplitude of a 27.12 MHz carrier wave to generate envelope waves in the low Hz to kHz range. Each provides systemic exposure to LEAMRFEMF via an intrabuccal antenna. This technology differs from so-called Tumour Treating Fields because it uses different frequency ranges, uses electromagnetic rather than electric fields, and delivers energy systemically rather than locally. The AutemDev also deploys patient-specific frequencies. LEAMRFEMF devices use 100-fold less power than mobile phones and have no thermal effects on tissue. Tumour type-specific or patient-specific treatment frequencies can be derived by measuring haemodynamic changes induced by exposure to LEAMRFEMF. These specific frequencies inhibited growth of human cancer cell lines in vitro and in mouse xenograft models. In uncontrolled prospective clinical trials in patients with AHCC, minorities of patients experienced complete or partial tumour responses. Pooled comparisons showed enhanced overall survival in treated patients compared to historical controls. Mild transient somnolence was the only notable treatment-related adverse event. We hypothesize that intracellular oscillations of charged macromolecules and ion flows couple resonantly with LEAMRFEMF. This resonant coupling appears to disrupt cell division and subcellular trafficking of mitochondria. We provide an estimate of the contribution of the electromagnetic effects to the overall energy balance of an exposed cell by calculating the power delivered to the cell, and the energy dissipated through the cell due to EMF induction of ionic flows along microtubules. We then compare this with total cellular metabolic energy production and conclude that energy delivered by LEAMRFEMF may provide a beneficial shift in cancer cell metabolism away from aberrant glycolysis. Further clinical research may confirm that LEAMRFEMF has therapeutic value in AHCC.

Adiabatic soliton management: Controlling solitary wave motion while keeping the wave envelope unchanged

We describe how to control the motion – both speed and propagation direction – of a nonlinear traveling wave in real time via soliton management with time-varying dispersion/diffusion and loss/gain terms. When carried out subject to certain parameter constraints we derive, the approach allows for real-time manipulation of wave motion without compromising the structure or stability of the wave, maintaining strict adiabaticity in time. This makes our approach a promising tool for physical systems which admit a degree of control through adjustable dispersion and loss/gain terms, including problems arising in nonlinear optics, atomic physics, Bose-Einstein condensates, and thermally driven chemical reactions, where one is interested in modifying the position or speed of a wave while still maintaining adiabaticity. We illustrate both the utility and simplicity of the method through several canonical examples, demonstrating how the motion of KdV solitons, Fisher-KPP solitary wavefronts, BBM solitons, nonlinear Klein-Gordon equations, and interacting nonlinear waves in a vector NLS system can be controlled in real time.

Nonlinear dispersion relation in integrable turbulence

We investigate numerically and experimentally the concept of nonlinear dispersion relation (NDR) in the context of partially coherent waves propagating in a one-dimensional water tank. The nonlinear random waves have a narrow-bandwidth Fourier spectrum and are described at leading order by the one-dimensional nonlinear Schrödinger equation. The problem is considered in the framework of integrable turbulence in which solitons play a key role. By using a limited number of wave gauges, we accurately measure the NDR of the slowly varying envelope of the deep-water waves. This enables the precise characterization of the frequency shift and the broadening of the NDR while also revealing the presence of solitons. Moreover, our analysis shows that the shape and the broadening of the NDR provides signatures of the deviation from integrable turbulence that is induced by high order effects in experiments. We also compare our experimental observations with numerical simulations of Dysthe and of Euler equations.