Symmetric Wave Research Articles

The Peculiarities of Acoustic Normal Waves Propagation in Thin Porous Sheets of Thermally Expanded Graphite

Thermally expanded graphite belongs to a new class of graphite materials with unique physical, chemical and mechanical properties. Acoustic wave velocity is one of the most important characteristics for study of porous materials including thin porous sheets of thermally expanded graphite. In this paper peculiarities of symmetric mode S0 Lamb wave propagation and SH-wave with horizontal polarization in sheets of thermally expanded graphite are experimentally investigated. To determine their velocities a differential measurement scheme on the base of a low-frequency acoustic flaw detector DIO1000 LF and specialized piezoelectric transducers with dry point contact was used. Additionally the longitudinal wave velocity in direction of sheet thickness was determined using piezoelectric transducers based on polyvinylidene fluoride. Indicatrices of normal wave velocities in the rolling plane were plotted and it was shown that the maximum acoustic anisotropy is characteristic for the S0-mode. The velocity minimum corresponds to the longitudinal direction of the rolling plane in which the maximum elongation of gas pores was observed. Influence of thickness and density of thermally expanded graphite sheets on the velocities of normal waves was investigated and presence of the thickness range where the minimum velocity values were observed due to the maximum inhomogeneity of layers formed in the rolling process. Method for determination of dynamic elastic moduli of porous thermally expanded graphite sheets using experimentally measured velocities of normal waves was proposed. It was shown that in the longitudinal direction of the rolling plane the Poisson's ratio took negative values which allow to attribute the specified material to auxetics ones.

Shock wave propagation in a real gas with or without gravitational field in the presence of magnetic field and monochromatic radiation via group invariance method

PurposeThis article aims to find the similarity solutions for the one-dimensional motion of spherical symmetric shock wave in non-ideal gas influenced by the azimuthal magnetic field and monochromatic radiation in the presence or absence of gravitational field. This paper also aims to study the effects of physical parameters on the strength of shock wave, and on the flow variables in the flow-field region behind the shock front.Design/methodology/approachThe Roche model is used to describe the gravitational field effects due to a massive nucleus at the point of symmetry. To derive the similarity solutions, the Lie group symmetry method has been used. Also, the numerical solutions to the present problem are obtained by using Rung–Kutta method of the fourth order with the use of Mathematica software. The effects of variation in the parameter of non-idealness of the gas, the gravitation parameter, the strength of the ambient magnetic field and the adiabatic index of the gas on the shock wave, and on the flow variables is discussed. A comparative study between with and without gravitational field is also, made.FindingsFor different choices of the arbitrary constants that appeared in the solution of infinitesimal generators, we have obtained seven distinct cases of similarity solutions. In the absence of the gravitational field, the similarity solution exists to the power and exponential law shock paths, but in the presence of gravitational field, the similarity solution exists to the power law shock path case only. In the absence of gravitational field, the shock strength is enhanced in the exponential law shock path case in comparison to the power law shock path case. It is found that the shock wave decays with an increase in the value of the adiabatic exponent, the strength of magnetic field, non-idealness of the gas or gravitational parameter.Research limitations/implicationsThe consideration of medium under the influence of gravitational field due to a heavy nucleus at the center and presence of magnetic field decrease the shock strength. This result may be helpful in designing space vehicle and jet engine.Practical implicationsThe result of the present study may be used in the analysis of data from the measurements by space craft in the solar wind and in neighborhood of the Earth’s magnetosphere.Social implicationsThe obtained results may be used for mankind.Originality/valueThe study of spherical shock wave propagation influenced by monochromatic radiation and azimuthal magnetic field in a non-ideal gas with or without gravitational field has yet to be discussed by any authors by using the Lie group symmetry method. In this article, we have discussed all possible cases of similarity solutions using the Lie group symmetry method, which is not studied by anyone as known to us.

DISPERSION OF LAMB WAVES IN MULTILAYER STRUCTURES

Low cost, the possibility of online monitoring and high sensitivity distinguish the method of structural monitoring using Lamb waves from other available methods. Structural analysis based on Lamb waves in heterogeneous materials requires fundamental knowledge of the behavior of Lamb waves in such materials. This basic knowledge is critical for signal processing in determining possible damage that can be detected by the propagating wave. Recently, Lamb wave methods have been used to simultaneously survey large areas of composite structures. However, such methods are more complex than traditional ultrasonic testing because Lamb waves have dispersive characteristics, namely, the wave speed varies depending on the frequency, modes and thickness of the plates. Experimentally measured group velocities of Lamb waves in composite materials with anisotropic characteristics do not coincide with theoretical group velocities, which are calculated using the dispersion equation of Lamb waves. This discrepancy arises because in anisotropic materials there is an angle between the direction of the group velocity and the direction of the phase velocity. This work investigates the propagation characteristics of Lamb waves in composites, focusing on group velocity and characteristic wave curves. For symmetric laminates, a robust method is proposed by imposing boundary conditions on the mid-plane and top surface to separate symmetric and antisymmetric wave modes. The dispersive and anisotropic behavior of Lamb waves in two different types of symmetrical laminates is theoretically studied in detail. The dispersion of Lamb waves was studied for 10 symmetric and asymmetric modes. It is shown that only fundamental modes are not characterized by a cutoff frequency, which indicates the interaction of fundamental modes with composite layers in the low-frequency range. A high level of group velocity dispersion was discovered for the SH0 and S0 modes. It is concluded that in isotropic laminates, dispersion is characteristic of symmetric modes. It is shown that the frequency dependence of the group velocity of Lamb waves of laminar composites can be represented in polynomial form.

Correction to “Symmetric waves are traveling waves of some shallow water scalar equations”

Correction to “Symmetric waves are traveling waves of some shallow water scalar equations”

The Relationship between Cardiomyocyte Action Potentials and Ion Concentrations: Machine Learning Prediction Modeling and Analysis of Spontaneous Spiral Wave Generation Mechanisms

The changes in cardiomyocyte action potentials are related to variations in intra- and extracellular ion concentrations. Abnormal ion concentrations can lead to irregular action potentials, subsequently affecting wave propagation in myocardial tissue and potentially resulting in the formation of spiral waves. Therefore, timely monitoring of ion concentration changes is essential. This study presents a novel machine learning classification model that predicts ion concentration changes based on action potential variation data. We conducted simulations using a single-cell model, generating a dataset of 850 action potential variations corresponding to different ion concentration changes. The model demonstrated excellent predictive performance, achieving an accuracy of 0.988 on the test set. Additionally, the causes of spontaneous spiral wave generation in the heart are insufficiently studied. This study presents a new mechanism whereby changes in extracellular potassium ion concentration leads to the spontaneous generation of spiral waves. By constructing composite myocardial tissue containing both myocardial and fibroblast cells, we observed that variations in extracellular potassium ion concentration can either trigger or inhibit cardiomyocyte excitation. We developed three tissue structures, and by appropriately adjusting the extracellular potassium ion concentration, we observed the spontaneous generation of single spiral waves, symmetrical spiral wave pairs, and asymmetrical double spiral waves.

Equivalent tensile elastic modulus measurement of cross-ply composite plates using S1 mode of Lamb wave

Abstract This paper proposes a simple and effective Lamb wave-based measurement method for the elastic moduli of cross-ply composite plates with large thickness, considered equivalent to a single-layer orthotropic plate with nine independent elastic constants. Due to the low-frequency signals required for measuring large thickness plates and the large wavelength of the low-frequency signals, the size of composite plates is highly required. Therefore, it is considered to use the first order symmetric (S1) mode wave to increase the signal frequency and reduce the wavelength. The effects of elastic constants on the phase velocities of the S1 mode are investigated. The phase velocity of the S1 mode depends only on the equivalent tensile elastic modulus and in-plane Poisson’s ratio in the low-dispersive frequency-thickness product regime. Moreover, the in-plane Poisson’s ratio of cross-ply laminates changes sufficiently small to neglect its effect on the phase velocities of the S1 mode. Therefore, the tensile elastic moduli of the cross-ply laminated plates can be estimated using the S1 mode, and the mapping relations between the phase velocities of S1 mode and the elastic moduli are established. The proposed approach has been numerically and experimentally tested on cross-ply glass fiber reinforced laminates with large thickness, and validated by theoretical values and conventional tensile tests.

Space-time dispersive symmetric Pearcey-Pearcey wave packets in the fractional Schrödinger equation.

This study presents an investigation into the propagation characteristics of a symmetric Pearcey-Pearcey space-time (SPPST) wave packet in a dispersive medium for the first time, to the best of our knowledge, in an optical system based on the fractional Schrödinger equation. Subsequently, the influence of the dispersion (normal and abnormal dispersion) on the SPPST packet is analyzed comprehensively. By manipulating the parameters of the SPPST wave packet including the parameters of the symmetric Pearcey beam, the value of the chirp, and the dispersion in the medium, it is possible to control its shape, orientation, and propagation dynamics. Simultaneously, the study delves into the effects of the combination of the dispersion and the second-order chirp on the evolution of SPPST wave packets and the associated intensity with these wave packets. Studying self-focusing wave packets with spatiotemporal symmetry provides new theoretical support for the development of quantum optics and optical communication.

An Explicit and Symmetric Exponential Wave Integrator for the Nonlinear Schrödinger Equation with Low Regularity Potential and Nonlinearity

An Explicit and Symmetric Exponential Wave Integrator for the Nonlinear Schrödinger Equation with Low Regularity Potential and Nonlinearity

Symmetric irrotational deep-water waves are traveling waves

In this paper, we show that a periodic solution to the irrotational two-dimensional deep-water wave problem with the horizontal velocity components at the surface, and wave profiles are symmetric, and periodic in the x-variable, necessarily defines a traveling wave. The proof relies on employing the Maximum principle for harmonic functions in unbounded domains and structural properties of the governing equations for nonlinear deep-water waves.

A variable kinematic multi-field model for lamb wave propagation analysis in smart composite panels

The study explores the propagation of symmetric and antisymmetric fundamental Lamb waves in laminated composite strips, employing multi-field piezo-elastic plate models. The findings indicate the necessity of employing higher-order kinematic models to enhance the accuracy of wave propagation assessments. To further optimize computational efficiency, node-dependent kinematic models are utilized. The research delves into the tradeoff between reducing computational costs and maintaining result accuracy demonstrating a reduction of up to 60% in computational expenses in simple models while keeping the error below 1%. Two-dimensional wave propagation in laminated composite plates was further considered, expanding the scope due to material orthotropy.

Production of high-purity non-diffracting optical vortex arrays with high topological charge

In this paper, we have realized the high purity non-diffracting optical vortex arrays with a high topological charge using quasi-symmetrical plane waves for the first time. The triangular vortex arrays with l = ±2 can be generated by six quasi-symmetrical plane waves, and the square vortex arrays with l = ±3 can be generated by eight quasi-symmetrical plane waves. The adjacent vortex units have opposite topological charges. We have also obtained the relations between the periods of the field formed by the six/eight quasi-symmetrical plane waves and the periods of the field formed by the three/four symmetrical plane waves. The simulation and experimental results demonstrate the feasibility of this method.

Formation of Finite Time Singularity for Axially Symmetric Magnetohydrodynamic Waves in 3-D

Formation of Finite Time Singularity for Axially Symmetric Magnetohydrodynamic Waves in 3-D

Novel insights into the propagation of the generalized Boussinesq equation: Dynamics of bidirectional symmetric solitary waves

In this work, we explore the propagation of bidirectional solitary wave solutions in the generalized (2+1)-dimensional Boussinesq equation. The proposed model was recently introduced by Wazwaz and Kaur as an application to describe wave propagation in various multidimensional physical systems, including shallow water waves and similar phenomena. Via implementing a collection of effective approaches, we extract a diversity physical structures of the proposed model manifesting their propagation in a form of moving simultaneous symmetric bidirectional waves. The proposed methodologies will include the use of sine/cosine-function method, sinh/cosh-function method, tanh–coth expansion approach, and the rational form trial solutions including trigonometric and hyperbolic functions. By conducting graphical analyses, we illustrate the various physical structures and dynamic behaviors of this class of nonlinear partial differential equations. The results of this work are expected to facilitate the study of wave interactions, propagation dynamics, and soliton formation in multidimensional settings.

Scalar bosons with gravitational effects near Schwarzschild’s black hole: The Rindler recipe

In this study, we explore the quantum effects in the Schwarzschild spacetime for massive and massless scalar particles in the presence of an external gravitational field. The methodology involves the analytical solution of the Klein–Gordon equation for the scalar particles in the near-horizon spacetime limit, using Rindler approximation. The results show that the quantum effects differ significantly for the massive and massless cases, they possess similar characteristics near the event horizon. Bosons without mass that are distant from the event horizon undergo a reduced gravitational impact and possess a symmetric wave function that remains unchanged when they approach the event horizon. However, the symmetry is lost, indicating that the particle strives for a lower energy state and becomes erratic as it nears the event horizon. This aligns with the anticipated behavior of particles within the Schwarzschild horizon. The particles have an energy spectrum even for tremendous values of the Schwarzschild radius, which entails the validity of the Rindler approximation in the near horizon geometry. We have observed that the quantum effects of massive and massless particles differ based on the mass. Specifically, massive and massless scalars behave differently due to their geometric differences, which results in different eigenstates. Although they both tend to seek lower energy levels when they approach the event horizon, their behavior is not the same.

Features of propagation and properties of axially symmetric and azimuthal solitary waves on the curved surface of a half-space cold plasma

The analysis of the behavior features, wave characteristics, and spatial-wave structure of axial-symmetric and azimuthal solitary oscillations at the boundary of a cold semi-infinite plasma is carried out using a closed system of equations describing the interdependence of the curvature of the surface and the properties of the nonlinear surface charge of the plasma. The specificity of the nature of motion, spatial distribution, and interconnection of the parameters of wave formations of each type is described. Numerical calculations have been performed, and an approximate analytical solution has been found.

Object alignment in spatially multiplexed holograms applied to polarization sensing.

The paper presents a new algorithm for object alignment in digital holography with multiple spherical reference waves. The algorithm was applied to polarization sensing with two orthogonally polarized reference waves. A novel holographic setup was built using a diffraction grating to generate two symmetric reference waves, keeping the setup simple and highly adjustable. The angles of rotation of the polarizing elements were calculated with mean absolute errors of 0.71° and 2.96° based on intensity and phase measurements, respectively. The same algorithm can be applied to any digital holographic measurement with multiple spherical reference waves.

Enhancing defect detection in solid materials using low-duty cycle square wave lock-in thermography: a time-efficient and quantitative approach

Lock-in thermography has been used to detect material defects but has faced challenges in quantitatively identifying defects. Traditional methods with a sine wave or symmetrical square wave heat source require time-consuming frequency adjustments with multiple experiments. This study introduces a novel technique using a heat source of a low-duty cycle square wave in lock-in thermography. This harmonic-rich heat source provides information on the blind frequency and the depth of defects, significantly reducing testing time. This method was validated by finite element simulations, which generated phase maps and phase difference-frequency curves at multiple frequencies that located defects. The study explored the correlation between thermal diffusion length at the blind frequency and defect depth and the impact of transverse thermal diffusion on depth measurement. The findings indicate that phase maps at the optimal frequency are most suitable for measuring defect edges. This approach offers a promising, time-efficient, and quantitative solution for defect detection.

Flexural pulse wave velocity in blood vessels.

Arteriosclerosis is a major risk factor for cardiovascular disease and results in arterial vessel stiffening. Velocity estimation of the pulse wave sent by the heart and propagating into the arteries is a widely accepted biomarker. This symmetrical pulse wave propagates at a speed which is related to the Young's modulus through the Moens Korteweg (MK) equation. Recently, an antisymmetric flexural wave has been observed in vivo. Unlike the symmetrical wave, it is highly dispersive. This property offers promising applications for monitoring arterial stiffness and early detection of atheromatous plaque. However, as far as it is known, no equivalent of the MK equation exists for flexural pulse waves. To bridge this gap, a beam based theory was developed, and approximate analytical solutions were reached. An experiment in soft polymer artery phantoms was built to observe the dispersion of flexural waves. A good agreement was found between the analytical expression derived from beam theory and experiments. Moreover, numerical simulations validated wave speed dependence on the elastic and geometric parameters at low frequencies. Clinical applications, such as arterial age estimation and arterial pressure measurement, are foreseen.

Rotationally symmetric transverse magnetic vector wave propagation for nonlinear optics

In this paper the theory and simulation results are presented for 3D cylindrical rotationally symmetric spatial soliton propagation in a nonlinear medium using a modified finite-difference time-domain general vector auxiliary differential equation method for transverse magnetic polarization. The theory of 3D rotationally symmetric spatial solitons is discussed, and compared with two (1 + 1)D, termed “2D” for this paper, hyperbolic secant spatial solitons, with a phase difference of π (antiphase). The simulated behavior of the 3D rotationally symmetric soliton was compared with the interaction of the two antiphase 2D solitons for different source hyperbolic secant separation distances. Lastly, we offer some possible explanations for the simulated soliton behavior.

Double parton distributions with flavor interference from lattice QCD

We study double parton distributions with flavor interference in the nucleon and compare them with previous results for the flavor diagonal case. We investigate both unpolarized and polarized partons. We compare our lattice results with those obtained from the simple description of the proton in terms of an SU(6) symmetric three-quark wave function and find that this description fails for both flavor and polarization dependence. We also derive and test a factorization ansatz for the unpolarized flavor interference distribution in terms of single-parton distributions and find that this ansatz fails to a large extent.