Narrow Results

This paper seeks to study and investigate the wave dispersion behavior in porous functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) beams. The beams comprise four patterns of single-walled carbon nanotubes (SWCNTs) distributed in the polymer matrix. The mixture rule is used to estimate the CNTR beams’ material properties. Innovative to this study are three porosity models describing the porosity distributions within the matrix and a three-unknown integral higher-order shear deformation theory (HSDT) modeling analytically the CNTRC beams with a novel shape function expressing the distributions of shear stresses and strains. The equations of motion for CNTRC beams are derived based on Hamilton’s principle. The stiffness and mass matrices are formulated by a generalized solution of harmonic wave propagation to express the wave dispersion relations. Numerical comparisons with previously published works verify the applicability of this mathematical model. The paper studies the effects of CNTs patterns through the polymer matrix, porosity models, and volume fractions of the porosity and CNTs. Based on the analytical results, augmenting the porosity and CNTs volume fractions leads to faster phase and group velocities. Furthermore, the impact of CNTs volume fractions, porosity models, and porosity volume fractions becomes more pronounced as the wavenumber increases.

The acoustic wave equation is solved numerically for two and three-dimensional systems at the limit between near and far field propagation. Our results show that for large sound velocities, corresponding to wavelengths larger than the system, near field properties are dominant. When the near field conditions are no longer satisfied, standing waves close to the sound emitters and interference patterns between the near field and far field solutions appear. Our procedure is applied to sound sources, which broadcast coherent and continuous waves as well as to sources emitting bursts of incoherent and uncorrelated waves. Both cases can be used to simulate the spreading of low frequency seismic waves observed close to volcanoes and hydrocarbon reservoirs.

In this paper, Smoothed Particle Hydrodynamics (SPH) is used to simulate the propagation of waves in an intermediate depth water channel. The major advantage of using SPH is that no special treatment of the free surface is required, which is advantageous for simulating highly nonlinear flows with possible wave breaking. The SPH method has an option of different formulations with their own advantages and drawbacks to be implemented. Here, we apply the classical and Arbitrary Lagrange–Euler (ALE) formulation for wave propagation in a water channel. The classical SPH should come with an artificial viscosity which stabilizes the numerical algorithm and increases the accuracy. Here, we will show that the use of classical SPH with an artificial viscosity may cause the waves in the channel to decay. On the other hand, we will show that using the ALE-SPH algorithm with a Riemann solver is more stable, and in addition to producing the pressure fields with much less numerical noise, the waves propagate in the channel without dissipation.

This is a duplicate pubication and the authors submitted and published the same article in APL.

Stable wave propagation is important for heart health, however, the electromagnetic radiation could affect normal signal propagation of heart, even make a sudden cardiac arrest. In this paper, the effect of electromagnetic radiation on the propagation of stable target wave generated by linear feedback control is studied in detail. It is confirmed that there are different transitions of electrical activities in cardiac tissue, which are transitions from target wave to spiral wave, some isolated islands of pattern waves coexisted, broken pattern and even the quiescent state, are generated when the electromagnetic field is imposed on the cardiac tissue in three ways. Furthermore, it is interesting to find there are different real affected regions, in which the electrical activities of nodes are destroyed, when the radiation signal is imposed on the cardiac tissue in different ways. It is also found the kinds of dynamical behaviors in the media are dependent on the real affected region. These results state that electromagnetic radiation could change the electrical activities, even destroy and suppress the wave propagation of wave source, and the ways of electromagnetic radiation imposed on the media are also important.

We consider stochastic second-order partial differential equations. We indroduce a noisy non-linear wave equation and discuss its connections, in particular via the Lorentz transformation, with known stochastic models.

Utilization of Optical Low Coherence Reflectometry (OLCR) for measurement of coherent backscattering of light from media with randomly-distributed spherical particles shows the influence of Mie resonances over the parameter interval where particle radii are comparable to the wavelength of light. Results advance the understanding of the theoretically and practically important problem of wave propagation in multiscattering random media.

The problem of a quantum particle moving in a narrow, bent two-dimensional channel is used to illustrate features of collisions in systems with semi-constrained structures. The collision theory of such systems is developed and, under certain general restrictions on the geometry, the following properties are rigorously established: (1) The (localized) Møller wave operator exist and the S operator is unitary in the scattering channels. (2) The singular spectrum is discrete in intervals away from the continuum thresholds. The discussion is based on a time-dependent approach.

In this paper, on the basis of gradient elasticity theory with one gradient parameter, wave propagation in rectangular nanoplates is studied. In the governing equation, the influences of initial stresses and elastic foundation are also considered. An analytical approach is used to solve the governing equation. The effects of different parameters such as gradient parameter on the circular and cut-off frequencies are presented. One can see that the initial stress and gradient parameter play an important role in investigating the wave propagation in nanoplates.

In this paper, the effect of magnetic field on the wave propagation in rectangular nanoplates based on two-variable refined plate theory is studied. In order to capture the size effects, the strain gradient theory with one length scale parameter is used. From our knowledge, it is the first time that two-variable refined plate theory is adopted for studying bulk waves in nanoplates. This type of refined plate theory has only two unknowns which reduces the complexity of the governing equations. To show the accuracy of this work, several comparisons are made with available results in open literature.

Based on nonlocal strain gradient theory, wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes (SWCNTs) is studied in this paper. With consideration of thermal effect and surface effect, wave equation is derived for fluid-conveying viscoelastic SWCNTs under longitudinal magnetic field utilizing Euler–Bernoulli beam theory. The closed-form expressions are derived for the frequency and phase velocity of the wave motion. The influences of fluid flow velocity, structural damping coefficient, temperature change, magnetic flux and surface effect are discussed in detail. SWCNTs’ viscoelasticity reduces the wave frequency of the system and the influence gets remarkable with the increase of wave number. The fluid in SWCNTs decreases the frequency of wave propagation to a certain extent. The frequency (phase velocity) gets larger due to the existence of surface effect, especially when the diameters of SWCNTs and the wave number decrease. The wave frequency increases with the increase of the longitudinal magnetic field, while decreases with the increase of the temperature change. The results may be helpful for better understanding the potential applications of SWCNTs in nanotechnology.

This study introduces innovative analytical solutions for the $(2+1)$-dimensional nonlinear Jaulent–Miodek ($𝕁𝕄$) equation, a governing model elucidating the propagation characteristics of nonlinear shallow water waves with finite amplitude. Employing analytical methodologies such as the Khater II and unified methods, alongside the Adomian decomposition method as a semi-analytical approach, series solutions are derived with the primary aim of elucidating the fundamental physics dictating the evolution of $𝕁𝕄$ waves. Within the realm of nonlinear fluid dynamics, the $𝕁𝕄$ equation encapsulates the behavior of irrotational, inviscid, and incompressible fluid flow, wherein nonlinear effects and dispersion intricately balance to yield stable propagating waves. This equation encompasses terms representing nonlinear convection, dispersion, and nonlinearity effects. The analytical methodologies employed in this investigation yield solutions for various instances of the $𝕁𝕄$ equation, demonstrating convergence, accuracy, and computational efficiency. The outcomes reveal that the Adomian decomposition method yields solutions congruent with those obtained through analytical techniques, thereby affirming the precision of the derived solutions. Furthermore, this study advances the comprehension of the physical implications inherent in the $𝕁𝕄$ equation, serving as a benchmark for evaluating alternative methodologies. The analytical approaches elucidated in this research furnish accessible tools for addressing a diverse array of nonlinear wave equations in mathematical physics and engineering domains. In summary, the introduction of novel exact and approximate solutions significantly contributes to the advancement of knowledge pertaining to the $(2+1)$-dimensional $𝕁𝕄$ equation. The ramifications of this research extend to the modeling of shallow water waves, offering invaluable insights for researchers and practitioners engaged in the field.

Synchronization phenomena in coupled oscillatory systems are very important models to describe various higher-dimensional nonlinear phenomena in the field of natural science. In this paper, phase synchronization in a ring of van der Pol oscillators coupled by time-varying resistors is studied. The coexistence of in-phase and anti/N-phase states and various interesting phase synchronization patterns are observed when the parameters are changed. Further, the influence of duty cycle of time-varying resistors for the observed phase synchronization patterns is investigated.

Harmonic wave propagation in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. The study extends previous results obtained for the mono-coupled oscillators to bi-coupled ones. The considered bi-coupled model refers to a chain of linearly coupled mechanical oscillators characterized by on-site cubic nonlinearities in both the longitudinal and rotational degrees of freedom. Pass, stop and complex regions are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized map arising from the relevant linear stability analysis. By varying the parameters governing both the coupling between the two d.o.f. and the nonlinearity, a variable scenario of propagation regions can be obtained, which includes the limit case of mono-coupled behavior. Theoretical predictions are validated through numerical results in terms of orbits, bifurcation diagrams and basins of attraction, obtained via nonlinear map iteration. They highlight a rich variety of regular and nonregular bounded solutions.

In this paper we study the problem of electromagnetic wave propagation in a 3-D optical fiber. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem, corresponding to an open waveguide, makes the problem challenging. To solve it, we construct a transform theory which is a nontrivial generalization of a method for solving a 2-D version of this problem given by Magnanini and Santosa.³

The extension to 3-D is made complicated by the fact that the resulting eigenvalue problem defining the transform kernel is singular both at the origin and at infinity. The singularities require the investigation of the behavior of the solutions of the eigenvalue problem. Moreover, the derivation of the transform formulas needed to solve the wave propagation problem involves nontrivial calculations.

The paper provides a complete description on how to construct the solution to the wave propagation problem in a 3-D optical waveguide with cylindrical symmetry. A follow-up article will study the particular cases of a step-index fiber and of a coaxial waveguide. In those cases we will obtain concrete formulas for the field and numerical examples.

Acoustic waves travelling in axisymmetric pipes with visco-thermal losses at the wall obey a Webster–Lokshin model. Their simulation may be achieved by concatenating scattering matrices of elementary transfer functions associated with nearly constant parameters (e.g. curvature). These functions are computed analytically and involve diffusive pseudo-differential operators, for which we have representation formula and input-output realizations, yielding direct numerical approximations of finite order. The method is based on some involved complex analysis.

We consider periodically heterogeneous fluid-saturated poroelastic media described by the Biot model with inertia effects. The weak and semistrong formulations for displacement, seepage and pressure fields involve three equations expressing the momentum and mass balance and the Darcy law. Using the two-scale homogenization method, we obtain the limit two-scale problem and prove the existence and uniqueness of its weak solutions. The Laplace transformation in time is used to decouple the macroscopic and microscopic scales. It is shown that the seepage velocity is eliminated from the macroscopic equations involving strain and pressure fields only. The plane harmonic wave propagation is studied using an example of layered medium. Illustrations show some influence of the orthotropy on the dispersion phenomena.

In a previous paper, we have considered the Regge–Wheeler equation for fields of spin s = 0, 1 or 2 on the Schwarzschild spacetime in coordinates that are regular at the horizon. In particular, we have constructed in Eddington–Finkelstein (EF) coordinates exact solutions in terms of series that are regular at the horizon and converge on the entire open domain from the central singularity to infinity. Here, we extend this earlier work in two different directions. First, we consider in EF coordinates a massive scalar field that can serve as a dark matter candidate. Second, we extend the treatment of the massless case to Painlevé–Gullstrand (PG) coordinates, which are associated with radially infalling observers.

In this paper, the effect of dissipative energy arising from bulk-viscosity on the collapse of a self-gravitating viscoelastic medium permeated with a nonuniform magnetic field and rotation is analyzed using the standard Jeans mechanism. A local solution of the system of nondimensional linearized perturbation equations, having variable coefficients, is obtained using the normal modes analysis method. The Jeans instability criteria are derived from the characteristic equation (valid under the kinetic and hydrodynamic limits) for parallel and perpendicular wave propagation, modified due to bulk viscosity and Alfvén wave velocity. From the calculated critical values of Jeans wavenumber, it is found that the bulk-viscosity and magnetic field have stabilizing influence on the onset of gravitational instability for each mode of wave propagation. It is observed that the nonuniform rotation does not affect the instability criterion, however, the rotation strongly suppresses the growth rate of the Jeans instability in both the hydrodynamic and kinetic limits. Also, a comparison of the impact of various rotational and magnetic field orientations on the growth rate in viscoelastic fluid is also presented. From the analysis, it is also observed that the presence of dissipative energy reduces the growth rate, in both modes of wave propagation.

The BEM has been used to compute the variations in the pressure field caused when a dilatational point load is placed inside a confined fluid channel. The channel was assumed to be filled with a homogeneous fluid and the presence of irregularities in its floor was considered. The width of the channel was fixed, and the influence of the walls was analyzed. This paper extends previous work by the authors^1,2 in which the fluid channel was considered to have infinite width. The Green's functions are defined in the frequency domain. They are obtained by superposing virtual acoustic sources, combined so as to generate the boundary conditions of both the free surface of the channel and the rigid surfaces of the floor and side walls. The responses in the time domain are obtained by means of Fourier transforms, making use of complex frequencies. The main features and spectral representation of the signals scattered by irregular floors are then described and used to elucidate some important aspects of wave acoustics, which may provide the basis for the development of non-destructive testing and imaging methods.